Class 8 General Knowledge - Basic Science

Why do water pipes, in hilly areas, often burst on a cold frosty night?

Water in the pipe freezes and on freezing water expands, so pipe break.

What is a 'formula' in Chemistry?

Formula is the symbolic expression for a molecule.

Why is a small space left between each set of two rails of a railway line?

As the train moves heat is produced due to friction and due to heat rails expand. If no space is left they will bend.

How are positive and negative charges produced during a thunderstorm?

Clouds are very small droplets of water in the form of vapour. When heavy, dark rain clouds called storm clouds develop high above the ground, strong winds move upwards through the light clouds and move the layer of clouds rub apart each other. As a result extremely large electric charges are produced in the cloud due to friction. The upper layers of clouds get positively charged and the lower layers of cloud get negatively charged.

Why does not moon have an atmosphere?

Moon's thinness is $${10}^{-13}$$ times of the earth, so gases emanating from the surface escape into interplanetary vacuum.

Are the lead pencils made of lead?

No. Powdered graphite is mixed with clay and pressed into sticks.

Why is Miner's Safety Lamp a safe lamp?

The flame is covered by a gauze, so explosion does not occur on contact with inflammable gas.

The process of electric _ between clouds and the earth or between different clouds causes _.

The process of electric discharge between clouds and the earth or between different clouds causes lightning.

Why is a person in a moving vehicle thrown forward when the vehicle stops suddenly?

A person in a moving vehicle is in a state of motion. Though the vehicle suddenly stops his body remains in a state of motion, so his body leans forward.

Describe the achievements of Horticulture Development Programme.

Achievements- (i) 97503 hectare additional area was found under horticultural crops.
(ii) To include 50667 hectare 16252 hectare and 20262 hectare area under fruits, vegetables and spices respectively.
(iii) 5858 hectare area has been included for high price value crops like medicinal and aromatic plants and flowers.

Why does milk turn sour?

Due to the action of bacteria.

Why is it easier to roll a barrel than to pull it along the road?

More areas of the barrel come in touch with the earth dragging, so there will be more friction. In rolling there will be less friction.

What is the temperature $$32$$ degrees Fahrenheit in degree Celsius?

$$32^oF$$ is $$0^oC$$

Formula

$$(32°F − 32) ×\dfrac{ 5}{9} = 0°C$$

Is chemistry a physical science?

Yes, because it deals with inanimate, natural objects. It could also be a life science if we consider organic chemistry/biochemistry.

Why is Organic chemistry important? What are the applications of this branch of chemistry? Who uses it? How is it used?

Organic chemistry is the study of the structure, properties, composition, reactions, and preparation of carbon-containing compounds, which include not only hydrocarbons but also compounds with any number of other elements, including hydrogen (most compounds contain at least one carbonhydrogen bond), nitrogen, oxygen, halogens, phosphorus, silicon, and sulfur.

Organic chemistry is a highly creative science in which chemists create new molecules and explore the properties of existing compounds. It is the most popular field of study for ACS chemists and Ph.D. chemists.

How is electric discharge fatal for human beings?

When a person is hit by lightning during a thunderstorm, then the electric energy passes through the body of the person due to which the person gets severe burns which may prove fatal.

Why does Earth have day and night?

Because it turns on its axis.

If it is noon at one location on Earth, what time is it at a location directly on the other side of Earth?

Midnight.

Where is the Moon in its orbit at the time of solar eclipse?

The Moon is in front of the Sun.

The footprints on the moon were made in the early 1970 s. How do the footprints, you think look today and why?

They look the same because there is no weather on the Moon to erode them.

Match column-I with column-II and select the correct answer using the codes given below:

Falling mass-changes potential energy into Kinetic energy.
Compressed spring has potential energy.
Kinetic energy of a body is due to its motion.

When the Moon is full, where is it in its orbit around Earth?

The full Moon is opposite the Sun from Earth.

Why is the path of water curved on coming out of horizontal jet?

The gravitational pull of the earth attracts the water downward and jet pushes it forward. The resultant of these horizontal and vertical motions makes water jet parabolic.

CONCEPTUAL QUESTIONS
Are there more nanoseconds in a second than the number of seconds in a year?

No, there are roughly $$10\pi$$ million seconds in a year, which is around $$30$$ times more than the number of microseconds in a second.

What is ecosystem? Write briefly about its components and their interdependence.

(i) All the plants and animals in an area are interdependent and interrelated to each other in their physical environment, thus, forming an ecosystem. Ecosystem is a system of interdependence comprising the physical environment and the organisms living within.
(ii) Plants, animals, human beings and the environment are the components of ecosystem. Plants are the main natural component on the earth which can use the sun's energy to prepare food. Plants are the backbone of the natural resources of the country.
(iii) The nature of plants in an area, to a large extent, determines the animal life of that area. When the vegetation is altered, the animal life also changes.
(iv) Human beings are also an integral part of the ecosystem. They utilise the vegetation and wildlife. All the living beings on the earth are dependent on plants directly or indirectly.

A drop of water or mercury on a clean glass plate is circular in shape. Why?

Surface tension in the case of a drop is greater which makes its surface minimum and so spherical.

When a moving train slows down quickly, will a passenger tend to fall backward or forward. Explain why?

The passenger will fall forward. The body of the passenger is in a state of motion along with the train; his legs may stop but the body win move forward.

x and y displacements of a particle are given as x(t) = a $$sin \omega t$$ and y(t) = a $$sin 2\omega t$$. Its trajectory will look like :

$$ x = a \sin \omega t $$
$$ y = a \sin 2 \omega t $$

$$ y = \left (2 \dfrac{x}{a} \sqrt{1 - \dfrac{x^2}{a^2}} \right ) a $$

$$y^{2} = 4x^{2} \left (1 - \dfrac{x^2}{a^2} \right ) $$

At $$ y = u $$ when $$ x = 0 $$
$$ x = \pm a $$

$$\sin \omega t = \dfrac{x}{a} $$

$$ y = a 2 \sin \omega t \cos \omega t $$

$$ = 2 \cdot a \sin \omega t \cos \omega t $$

$$ \sin \omega t = \dfrac{x}{a} $$

$$ \sin^{2} \omega t = \dfrac{x^2}{a^2} $$

$$ 1 - \sin^{2} \omega t = \cos^{2} \omega t $$
$$ 1 - \dfrac{x^2}{a^2} = \cos^{2} \omega t $$

$$ \cos \omega t = \sqrt{1 - \dfrac{x^2}{a^2}} $$

So, $$ y = a . 2 \sin \omega t \cos \omega t $$

$$ = 2 . a \left ( \dfrac{x}{a} \sqrt{1 - \dfrac{x^2}{a^2}} \right ) $$

An object is placed at a distance of 10 cm from a concave mirror of focal length 20 cm.
a) Draw ray diagram for the formation of image
b) Calculate the image distance
c) state 2 characteristics of the image formed.

Given:

Focal length of concave mirror, f = -20 cm

Distance of object from the mirror, u = -10 cm

use formula, 1/v + 1/u = 1/f

or, 1/v = 1/f - 1/u

or, 1/v = 1/-20 - 1/-10

or, 1/v = -1/20 + 1/10 = 1/20

or, v = +20cm

hence, image position is the 20cm right side from the pole of the concave mirror as shown in the diagram. The image is straight and bigger than the object.

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A particle is moving along a circular path of radius $$R$$ in such a way that at any instant magnitude of radial acceleration & tangential acceleration are equal. If at $$t=0$$ velocity of particle is $$v_{0}$$, then find the time period of first revolution of the particle .

At any moment let the speed be $$v$$
Therefore the normal component of acceleration is $$\dfrac {v^2}{R}$$
Tangential Acceleration:
$$a=v^2 /R$$
$$v\dfrac {dv}{ds}=\dfrac {v^2}{R}$$
$$\dfrac {dv}{v}=\dfrac {ds}{R}$$
$$\displaystyle _{v_0}^{v}\dfrac {dv}{v}=\displaystyle_0^s \dfrac {ds}{R}$$
$$\ln \left(\dfrac {v}{v_0}\right)=\dfrac {s}{R}$$
$$v=v_0 e^{s/R}$$ and $$x=R[\ln (v)-\ln (v_0)]$$
Therefore velocity at one revolution:
$$v_{1rev}=v_0 e^{2\pi R/R}=v_0e^{2\pi}$$
Now using $$ds / dt=v$$
$$\dfrac {ds}{dt}=v$$
$$ds=\dfrac {Rdv}{v}$$
$$\dfrac {Rdv}{v}=vdt$$
$$\displaystyle \int_{v_0}^{v_1{rev}}\dfrac {Rdv}{v^2}=\displaystyle_0^t dt$$
$$R\left[-\dfrac {1}{v_{1rev}}+\dfrac {1}{v_0}\right]=t$$
$$t=R\left[\dfrac {1}{v_0}-\dfrac {1}{v_0 e^{2\pi}}\right]=\dfrac {R}{v_0}(1-e^{-2\pi})$$

A uniform solid sphere of radius $$R$$, rolling without sliding on a horizontal surface with an angular velocity $$\omega_{0}$$, meets a rough inclined plane of inclination $$\theta = 60^{\circ}$$. The sphere starts pure rolling up the plane with an angular velocity $$\omega$$. Find the value of $$\omega$$.

Angular momentum conservation
$$\left (\dfrac {2}{5} mR^{2}\right ) \omega_{0} + mv_{0}R \cos 6i = \dfrac {7}{5} mR^{2}\omega$$
$$\dfrac {2}{5} mR^{2}\omega_{0} + m\omega_{0}R^{2} \times \dfrac {1}{2} = \dfrac {7}{5}mR^{2}\omega$$
$$\dfrac {9}{10} mR^{2}\omega_{0} = \dfrac {7}{5} mR^{2}\omega$$
$$\Rightarrow \omega = \dfrac {9}{14} \omega_{0}$$.

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes.A man cycling with a speed of 20 $$km\;{h^{ - 1}}$$ in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion.and every 6 min in the opposite direction .What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

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What is chemistry?

$$\text{Chemistry is the branch of science that deals with the properties, composition, and structure of elements and}$$ $$\text{compounds, how they can change, and the energy that is released or absorbed when they change.}$$
Chemistry is involved in different areas of our lives - from the medicine, we take, the food we eat to the clothes we wear. While the systematic study of chemistry might be new to us, ancient civilizations have been using similar chemistry methods for centuries, where some of their methods are still written and preserve today.

What is the difference between distance and displacement?

Distance is a scalar quantity and displacement is a vector quantity.

Distance has only magnitude. It measures the actual ground covered. Distance can only be positive.

Displacement is measured with reference to a specific point. It is a straight line from the starting point (origin) to the end point. It is therefore also the shortest distance between two points. If the displacement vector is away from the reference point (aka datum) it is often defined as positive and if toward it is defined as negative.

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What is the $$S.I$$ unit of electric potential?

In the International System of Units (SI), electric potential is expressed in units of joules per coulomb (i.e., volts), and differences in potential energy are measured with a voltmeter.

Why force is a vector quantity?

Vector is that which have magnitude, direction and follows the law of vector algebra.so, force fulfil all the requirements of a vector so it is a vector quantity.force has magnitude, direction and follows the law of vector algebra

What does it mean for a species to be in stasis?

If a species is in stasis, it is not undergoing evolutionary change over a long period of time.
Explanation:
In modern biology, stasis means that a species is not undergoing any reactive evolutionary change over a long period of time. Essentially, that species is not evolving.
Stasis is also a term used when describing fossil records of evolution, in a theory called "punctuated equilibrium". This theory proposes that once a species appears in the fossil record, the species becomes stable and displays little evolutionary change. The species has become populous and stable enough to display little to no evolutionary change over a long period of time; the species has entered a state of stasis.

Why is acceleration measured in meters / seconds squared?

Answer

Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are m/s2, meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.

Which is warmer -30C or -30 F?

Answer :
$$30^{\circ}C$$
Explanation:
Because if we convert $$-30^{\circ}F$$ to celusis by ,
$$\dfrac{C}{100} = \dfrac{F - 32}{180} $$
we get - $$30^{\circ}F $$ equal to $$-30^{\circ}C$$
$$-30^{\circ}C = - 22^{\circ} F $$
So$$ \therefore $$ we can say $$-30^{\circ}C$$ is warmer

Why are peroxisomes important in cells?

Peroxisomes are organelles in the cell that are membrane bound and contain enzymes crucial for metabolic activity.

Peroxisomes are important because they are:

1. involved in lipid production

2.involved in oxidation reactions in the cell

3.Providing metabolic energy

In plants they perform the function of :

1. ( in the seed) converting fatty acids to carbohydrates

2. Photorespiration

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Why is the number of protons and electrons equal in an atom?

Acturally the proton and electron count of an atom are equal only when the atom is natural in charge.
The three atomic particles of an atom are the protons, which carry a positive charge, the electrons which carry a negative charge and the neutrons which have no charge.
The proton number is always the same as the atomic number for the element.
The protons and neutrons are found in the nucleus of the atom and make up the major it of the mass of the atom. The electrons are found in orbitals surrounding the nucleus.
In order for the atom to remain electrically natural the protons and electrons must balance each other.
Two examples would be Sodium $$(Na)$$ and Chlorine $$(Cl)$$
Sodium has an atomic number of $$11$$ and an amu of $$23$$
Sodium has $$11$$ protons and $$12$$ neutrons and $$11$$ electrons.
$$11$$ protons - atomic number $$11$$
$$11+12=23$$ the amu
$$11^+=11^-$$
Chlorine has an atomic number of $$17$$ and an amu of $$35$$
Sodium has $$17$$ protons and $$18$$ neutrons and $$17$$ electrons.
$$17$$ protons - atomic number $$11$$
$$17+18=35$$ the amu
$$17^+=17^-$$

Why is meiosis not a part of the cell cycle?

Meiosis results in two haploid daughter cell.
The cell cycle to its division and duplication of is DNA to produce two daughter cells both diploid.
Explanation :
Cell cycle is a series of events that occur repeatedly throughout the life of an organism to produce more cells of the same kind.
Meiosis is a special kind of cell division where two haploid cells are produced. It takes place only in the gonads.

Why are standard units of measurement important to scientists?

Standardized units of measure are important to engineering because if everyone was using different measurement systems, dimensions of different objects and inventions wouldn't be converted correctly from the inventor to other inventors or manufacturers.

Or,

Replicable data (getting the same results by conducting the same experiment) are a defining element of the scientific method, and standardized unit of measurement are a cornerstone of replicable data.

Why is impulse a vector?

MOmentum is a vector and impulse is the change of momentum.
Impulse is the change of momentum. It is possible for momentum to change such that the momentum of an object increases, decreases or reverses direction. As impulse measures those possible changes it must be able to account for the possible direction by being a vector.
During this elastic collision the momentum of small mass changes to the left. But the momentum of the large mass changes to the right. So the impulse of the small mass is to the left and the impulse of the large mass is to the right. One must be negative and the other positive.
additionally impulse must be a vector to satisfy Newton's Third Law of motion. Consider the equation relating impulse, force and time $$\Delta p= F. \Delta t$$
If body $$A$$ exerts a force on body $$B$$ then body $$B$$ must exerts an equal and opposite force on body $$A$$. If the forces are equal and opposite then so must be impulses. That is not possible if impulse is a scalar
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Why do the phospholipids surrounding the cell form a bilayer?

Answer
It is the shape and amphipathic nature of the lipid molecules that cause them to form bilayers spontaneously in aqueous environments.
Explanation :
The most abundant membrane lipids are the phospholipids . These have a polar head group and two hydrophobic hydrocarbon tails. The tails are usually fatty acids and they can differ in length.
Hydrophilic molecules dissolve readily in water because they contain charged groups or uncharged polar groups, that can form either favorable electrostatic interactions or hydrogen bonds with water molecules
Hydrophobic molecules are insoluble in water because all or most of their atoms are uncharged and non polar. They cannot form energetically favorable interactions with water molecules.
If dispersed in water , they force the adjacent water molecules to reorganize into ice like cages that surround the hydrophobic molecules.
For the above reason, lipid molecules spontaneously aggregate to bury their hydrophobic tails in the interior and expose their hydrophilic heads to water.
Being cylindrical phospholipid molecules spontaneously form bilayer in aqueous environments. In this energetically most favorable arrangement, the hydrophilic heads , face the water at each surface of the bilayer and the hydrophobic tails are shielded from the water in the interior.

Why is the atomic model useful?

The model us to make prediction about chemical and physical behaviour such as reactions, bonds, molecular geometry, binding energy, isotopes.

Why are SI units helpful?

SI units provide a way for scientists around the world to record information about observations in a manner that all scientists around the world will understand.

Imagine if scientists in the US had one way of measuring mass, scientists in Europe had a different method, and scientists in Asia had a third method. Nobody would really know what anyone else was talking about.

Whats $$ 45 $$ degrees F. in celcius?

$$ 45^0 F $$ is $$ ( 45 -32 ) = 13 F^0 $$ above freezing ( water freezes at $$ 32^0 F ) $$
$$ 180 F^0 = 100 C^0 $$ (difference between freezing and boiling on each scale)
$$ \Rightarrow 1 F^0 = \frac { 18}{10} C^0 $$
$$ 13F^0 = 13 \times \frac {18}{10}C^0 = 23.4C^0 $$
$$ 23.4C^0 $$ above freezing is $$ 23.4^0 C $$

What quantum numbers refer to a 4d orbital?

Answer
The four quantum numbers of interest are n (principal quantum number), l (angular momentum) $$ m_{1} $$ (magnetic , and $$m_{s} $$ (spin )
A generic $$4d^{2}_{z} $$ orbital has $$n = 4 $$ and $$ l = 2. n = 4 $$ specifies the energy level ,and $$l$$ specifices the orbitl's shape . $$ s \rightarrow l = 0 , p \rightarrow l = 1 $$ etc, .Thus , its $$m_{1} $$ varies as $$ 0, \pm 1, \pm 2 $$ and the orbital has projection above the plane and below the plane .
Depending on how full the orbital is, $$m_{s}$$ varies. If it happens to be a $$ 4 d^{1}$$ configuration, for example, then one of five orbitals are filled ( $$(dx^{2} - y^{2} , d_{z} ^{2} , _{dx}, d_{xz}, d_{yz})$$) with one electron. In that case, the electron is, by default,
spin $$\pm \dfrac{1}{2} $$ Thus, $$m_{s} = \pm \dfrac{1}{2}$$
In this case, it would give a term symbol of $$^{2}D_{1/2} , ^{2} D_{3/2} $$ and $$^{2} D_{5/2}$$ The notation is :
$$^{2S + 1} L_{J}$$
where $$ J = L + S$$
(The most stable one would be the $$^{2}D_{1/2}$$ state, according to Hund's rules for less-than-half-filled orbitals with the same S and the same L.)
Here, the spin multiplicity is $$ 02S + 1 = 2 (1/2) + 1 = 2 $$ ,and the total angular momentum $$ J = L + S = | m _{l} | + | m _{s} | $$
$$ = 0 + 1 /2 , 1 + 1/2 , $$ and $$ 2 + 1 / 2 = 1/ 2, 3/ 2, $$ and $$ 5/ 5 $$
$$ ( 2- -1 / 2 = 1 + 1 + 1/2 $$ , and $$ 1 - 1/ 2 = 0 + 1 / 2 $$ , which are duplicates , while by the selection rules , $$\Delta L = 0 , \pm 1, \Delta S = 0 , $$ and $$\Delta J = 0, \pm 1$$

What scientists study the history of life on earth?

A paleontologist studies fossils to under stand the history of life on earth.

An archeologists studies human artifacts and remains. These two studies can be coordinated to under the history of life on earth.

When the pressure on a gas increases, will the volume increase or decrease?

According to the general equation of the ideal gases, we have:
PV = nRT ............................................. (1)
Therefore, for a given quantity of the gas (n = constant), and at a given temperature (T = constant), equation (1) will be reduced to:
PV = constant ............................ (2)
In other words, the volume "V" is inversely proportional to the pressure "P". Thus, if the pressure "P" increases, the volume "V" will decrease.

What is the strongest of the four fundamental forces?

The four fundamental forces of nature are :-
1. Strong Nuclear Force
2. Gravitational Force
3. Electromagnetic Force
4. Weak Forces
Explanation:
The Strongest of the above listed fundamental forces is the Strong Nuclear Force which exists between Nucleons.
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What $$SI$$ units are used to measure power?

The $$SI$$ unit for power is the watt.
Explanation:
The watt $$(W)$$ is the $$SI$$ derived unit for power. It comes from the $$SI$$ base units.
Work is the action of a force through a distance
$$w=f\times d$$
The units of work are $$kg.m^{2}s^{-2}$$ or $$N.m$$
Energy is the ability to do work. It has the same units as work. The $$SI$$ unit for energy is the joule $$(J).1\ J=1\ N.m$$
Power is the measure of how much energy or work is used per unit time.
Power $$=\dfrac{energy}{time}$$
The $$SI$$ unit of power is joules per second $$(J/s)$$ or Watts $$(W)$$
In summary,
$$1\ W=1\ J/s=1\ N.m/s=1\ kg.m^{2}.s^{-3}$$

Which has the larger atomic radius: $$ Cl - $$ or $$K + $$ ?

Answer
$$Cl^{-}$$
Explanation :
Atomic size is linked to two important concepts
the energy level on which the outermost electrons reside
the effective nuclear charge of the nucleus
The first concepts is useful when dealing with atoms that are located in different periods of the periodic table
In this case, the higher in energy an atom's outermost electrons are, the further away from the nucleus they will be. This in turn implies a larger  atomic radius.
In the case of a neutral  potassium atom, you know that its electrons configuration  looks like this
$$K : 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{2} 4s^{1}$$
Potassium has its outermost electron on the fourth energy level. When the potassium cation is formed, that outermost electron is lost, which means that the electrons configuration of $$K^{+}$$ is
$$K^{+} : 1s^{2} 2s^{2} 2p ^{6} 3s^{2} 3p^{6}$$
Its outermost electrons are now located on the third energy level
Now take a look at a neutral chlorine atom
$$Cl: 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}$$
Its outermost electrons are alredy on the third energy level. When the chloride anion is formed, an electron is being added to that same energy level, so that you have
$$Cl: 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}$$
The two ions have the same electron configuration , which means that they are isoelectronic.
Now turn to the second concept, effective nuclear charge.
Both ions have their outermost electrons located on the same energy level, but they do not have the same ionic radius.
That happens because the number of protons each species has in its nucleus varies
More specifically, potassium, which has an atomic number  equal to 19, has 19 protons in its nucleus. Chlorine, on the other hand, only has 17.
This is important because in the case of the potassium atom, the outermost electrons will be attracted by the nucleus more.
In other words ,$$K ^{+} $$ has bigger effective nuclear charge than $$Cl^{-}$$ , which translates to bigger net positive charge felt by the outermost electrons.
This will compress the energy levels a bit and make the ionic radius smaller  for the potassium cation.
Therefore, the chloride anion will have the larger atomic radius.

What is the study of cells called?

Cell biology or Cytology ( Greek : Kytos = vessel) is the branch of biology that studies the different structures and functions of the cell.
Explanation:
Cells are the basic units of life.
Cell biology deals with
1.Structure and organization of cell organelles and their physiological properties.
2.Metabolic processes
3.signaling pathways
4.life cycle
5.interactions with their environment
This is done both on a microscopic and molecular level.
It includes both prokaryotic and eukaryotic cells.

What property of an object determines how much inertia it has?

Answer
Inertia is the resistance of an object towards energy .
Explanation :
Hence, objects with a heavier mass would have a higher inertia in comparison to lighter objects. In other words, mass have a direct correlation to inertia

What property is unique to stem cells?

Answer
they specialize to do specific roles.
Explanation :
A unique property of stem cells is that they can divide and differentiate, meaning they can become specialized cells. Stem cells can specialize to gain a specific function, for example a stem cell can become a liver cell.

What is thermochemistry?

When a reaction takes place, bonds between atoms are broken and then reformed. Energy is required to break bonds, and energy is released when they are formed. This is usually in the form of heat. Different reactions have different ratios of used energy to released energy, which determines whether it is endothermic (takes in more energy from it's surroundings than it release) or exothermic (releases more energy than it takes in).

Some examples of exothermic reactions are: any form of combustion (think of the heat released when you burn fuel), neutralisation and most oxidation reactions.

Some examples of endothermic reactions are: decomposition and evaporation.

The study of these processes, and the factors involved, is known as thermochemistry.

What is the percentage by mass of ammonium nitrate?

The molar mass of ammonium nitrate is $$ 800.04 . g. mol^{-1} $$

% nitrogen $$ = \cfrac { mass \quad of \quad nitrogen }{ mass \quad of \quad ammonium \quad nitrate } \times 100 $$ %

Now, using a mole of ammonium nitrate:

% nitrogen = $$ \cfrac { 2 \times 14.10. g. mol^{-1} }{80.04 .g. mol^{-1 } } \times 100 $$ % = $$ 60.0 $$ %

% oxygen = $$ \cfrac {3 \times 16.00 ..g. mol^{-1}}{80.04.g. mol^{-1 } } \times 100$$ % = $$ 60.0 $$ %

What is the percentage composition of N, H and O in ammonium nitrate,$$ NH_4NO_3 $$?

$$ 2 \times 4 g+ 4 \times 1 g + 3\times 16 h = 80 g $$

The mass of 1 mol of $$ NH_4NO_3 $$ is $$ 80 $$ g.

The mass of N is $$ 28 g $$

Percent composition of N is $$ \cfrac {28g}{80 g} \times 100 $$ % = $$ 35 $$ %

The mass of H is $$ 4g $$

Percent composition of $$ H $$ is $$ \cfrac {4g}{80 g } \times 100$$ % = $$ 5 $$ %

The mass of O is $$48 g $$

Percent composition of O is $$ \cfrac {48g}{ 80 g} \times 100$$ % = $$ 60 $$ %

What is the pressure conversion factor for torr to kpa?

You can easily link these two units by using atmospheres, or atm, as a starting point.

You know that 1 atm is equivalent to 760 torr. LIkewise, 1 atm is equivalent to 101.325 kPa, so the conversion factor that takes from torr to kPa will look like this

$$ \dfrac { 760 torr }{ 1 atm } . \dfrac { 1 atm }{ 101.325 kPa} = \dfrac { 760 torr}{ 101.325 kPa} $$

An here's your conversion factor $$ \rightarrow 760 torr $$ are equivalent to $$ 101.32 kPa $$ Which means that

$$ 1 torr . \dfrac { 101.325 kPa}{760 torr} = 0.133322368 kPa $$

And

$$ 1kPa . \dfrac { 760 torr}{ 101.325 kPa} = 7.50061683 torr $$

What is the main component of the cell membrane? Why is the main component?

The main component of the cell membrane is phospholipid material.
It provides a boundary for the cell contents and allows only small uncharged molecules to pass through while keeping larger molecules at bay.
The major components of a cell membrane are phospholipids, glycolipids, proteins, and cholesterol.
Most phospholipids contain two fatty acids, glycerol, a phosphate group, and a simple organic molecule such as choline.
The phospholipids form a lipid bilayer or membrane in which the hydrophobic tails all line up inside to avoid the water and heads line towards the exterior.
The phospholipid bilayer serves two major functions.
1. As a boundary for the cell contents.
It separates the cell contents from the surrounding environment.
2. As a police officer to control the movement of molecules into and out of the cell.
The interior of the phospholipid bilayer is nonpolar, so only small uncharged molecules like oxygen $$(O_2)$$, carbon dioxide $$(CO_2)$$, and water $$(H_2O)$$ can pass freely through the membrane, either by diffusion or by osmosis.
Large molecules cannot pass through the phospholipid bilayer.
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What is the SI unit of mass ?

Answer
kilogram (kg)
Explanation :
The SI unit of mass is kilogram.
Note that it has a prefix of kilo, which carries the value of 1000.
Meaning 1 kg = 1000 g

What is the weight in lbs of a 75-kg person?

We know that $$1 kg \approx 2.2 lbs $$
Therefore a $$ 75 $$ kg person would have a mass of
$$ 75 kg . \dfrac { 2.2 lbs}{kg} = 165 lbs $$
The actual value is around $$ 165.34 $$ lbs

What is the relationship between pressure and volume ?

Answer
They both are inversely proportional at constant temperatures.
Explanation :
There exists a relationship between pressure and volume through Boyle's Law It states that when temperature is held constant in thermodynamic systems, the volume increases as the pressure decreases (and is true the other way around).

What kind of organism has pseudopods?

Amoeba is the organism that has pseudopodia. It belongs to the Phylum Protozoa.

What is time?

$$ D = R \times T $$
In this equation Distance, and Time both are variable that can change. Time changes with the velocity. The faster something travels the slower time changes. At the speed of light time stops and no longer exists. For light or anything without mass that achieves the speed of light time does not exist.

Without space it is difficult to imagine how time could exist. The fourth dimension is part of the the other three dimensions. Before the beginning of the present universe ( The Big Bang?) neither time nor space existed.

Time is a variable it can change with both mass and velocity. Time is a part of space and is considered to be the fourth dimension of the universe.

What is the number of significant figures in each of the following?
$$ 10.0005 g $$
$$ 0.003423 mm $$
$$ 2900 +100 ft $$
$$ 8.9 \times 10^5 L $$

10.0005 g has 6 significant figures. The zeros are significant because they are between two significant figures, the 1 and the 5.

0.003423 mm has four significant figures (the leading zeros are not significant)

2900+100=3000 ft When adding or subtracting, the number of decimal places in the answer has the fewest number of decimal places as the number of decimals in the problem. So, since both numbers were whole numbers, the answer must be a whole number, and in this case, there is one significant figure in 3000 . There are 2 significant figures in 2900 and 1 significant figure in 100.

$$ 8.9 \times 10^5 L $$ has two significant figures. Only the coefficient 8.9 is significant.

What is the nucleon number?

The mass number (A), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus.

The mass number is different for each different isotope of a chemical element. This is not the same as the atomic number (Z) which denotes the number of protons in a nucleus, and thus uniquely identifies an element.

Hence, the difference between the mass number and the atomic number gives the number of neutrons (N) in a given nucleus: N=A−Z

What is the number of neutrons in $$$^{10}_5 B $$ ?

The bottom number (5) is the atomic number. The atomic number tells you how many protons an atom has.

The top number is the mass number(10). The mass number tells you the mass of the atom. The mass of the atom is the combined number of protons and neutrons. Electrons don't contribute much mass at all, so we ignore them for questions like this.

To find the number of neutrons, just take the mass and subtract the number of protons.
$$ 10 -5 = 5 $$

What is the mass of $$HCl$$ in a $$500\ mL$$ sample of $$6.0\ M\ HCl$$?

$$109\ g$$ of $$HCl$$
Molarity is represented by the following equation
$$M=\dfrac{moles\ of\ solute}{litres\ of\ solution}$$
In our case, we already have the molarity and the volume of solution. However, the volume does not have the proper units since it is given in terms of milliliters instead of liters. We can convert $$500\ mL$$ into liters by using the conversion factor $$1000\ mL = 1\ L$$. When $$500\ mL$$ is divided by $$1000\ mL/L$$, we obtain a volume of $$0.50\ L$$.
Now we can rearrange the equation to solve for the number of moles, which will allow us to determine the mass. We can do this by multiplying by liters of solution on both sides of the equation. The liters of solution will cancel out on the right side, leaving the number of moles being equal to the molarity times volume like so:
Moles of solute = (liters of solution) * (Molarity)
Moles of solute $$=(0.50\ L)(6.0\ M)=3.0\ mol$$ of $$HCl$$
Now we have to convert the $$3.0\ mol$$ of $$HCl$$ into grams of $$HCl$$. This can be done by multiplying $$3.0\ mol$$ by the molecular weight of $$HCl$$, which is $$36.46\ g/mol$$
$$(3.0\ mol)(36.46\ g/mol)=109\ g\ HCl$$

What is the isotope symbol for an atom that contain $$82$$ protons and $$125$$ neutrons?

Explanation:

The isotope of an element $$X$$ is given by $$^A_Z X$$, where $$Z$$ is proton number of the element and $$A$$ is the mass number of the element.

The mass number of this isotope will be $$82+125=207$$ units, while it has $$82$$ protons.

Looking on the periodic table, element number $$82$$ is lead, and its symbol is $$Pb$$.

Therefore, the isotope in this case will be written as:

$$^{207}_{82}{Pb}$$

Alternatively, we can write it even shorter like this,

$$^{207}Pb$$

since we know that lead can only have an atomic number of $$82$$.

$$^{207}_{82}Pb$$ or just $$^{207}Pb$$.

What is the number of moles in $$ 36 g $$ of $$ H_2O $$?

The relationship between the number of moles of a given substance present in a sample and the mass of the sample is given by the molar mass of the substance.

For any chemical species, you have

molar mass= the mass of exactly 1 mole

Now, water has a molar mass of $$ 18.015 g mol^{-1} $$ which means that

1 mole of water has a mass of $$ 18.015 g $$
$$ 18.015 g mol^{-1} = \frac {18.015 g}{ 1 mole H_2O } $$
so for very $$ 18.015 g $$ of waterpresent in your sample, you have

1 mole of water.

This means that your 36-g sample will contain

$$ 36g.\begin{matrix} \begin{matrix} given\quad by\quad the\quad molar\quad mass\quad of\quad H_{ 2 }SO_{ 4 } \\ \overbrace { 1moleH_{ 2 }O } \end{matrix} \\ 18.015 \end{matrix}=\quad 2.0\quad moles\quad H_2O $$

The answer must be rounded to two sig figs, the number of sig figs you have for the mass of water.

What is instantaneous rate of change formula?

The instantaneous rate of change is the derivative which is defined as
$$\displaystyle \lim_{\Delta x \rightarrow 0} \dfrac{f(x+\Delta x)-f(x)}{\Delta x}$$

What is the number of protons in an atom of carbon-12?

And by definition, if Z=6, there are are 6 protons, 6 massive, positively charged particles, in each carbon nucleus; this is what characterizes the element as carbon.

How many neutrons, massive, neutrally charged particles are there in $$ a^{12}C $$ atom ?

What is the mass of $$Cl$$ in $$21\ g$$ of $$NaCl$$?

$$12.78\ g$$
Explanation:
$$21\ g$$ of $$NaCl$$ is equivalent to $$0.36\ mol$$.
$$Na$$ (atomic mass $$=23\ g/mol$$), $$Cl$$ (atomic mass $$=35.5\ g/mol$$)
Mole =(Atomic Mass)(Molar Mass)
Total molar mass of $$NaCl=23+35.5=58.5\ g/mol$$
Mole $$=21\ g\ NaCl\times \dfrac{1\ mol}{58.5\ g}NaCl=0.36\ mol\ NaCl$$
$$1\ mol$$ of $$NaCl$$ consists of $$1\ mol$$ of $$Na$$ ion and $$1\ mol$$ of $$Cl$$ ion
or
$$NaCl\rightarrow Na^{+}+Cl^{-}$$
Therefore, $$0.36\ mol$$ of $$NaCl$$ is equal to $$0.36\ mol$$ of $$Cl$$.
Mass of $$Cl=$$ (Mole $$Cl$$) Atomic Mass $$Cl$$)
Mass of $$Cl=0.36\ mol\ Cl\times \dfrac{35\ g}{1\ mol}Cl$$
Mass of $$Cl=12.78\ g\ Cl$$.

What is the percent by mass of oxygen in $$ Mg (NO_3)_2 $$?

$$\text{ Percentage of oxygen} = \cfrac {\text{ mass of oxygen} }{\text{molar mass of compound} } \times 100 $$ %

$$ = \cfrac { 6 \times 16}{148 } \times 100$$ % $$= 64.86$$ %

What is the difference between organism, population, community, ecosystem, biome and biosphere ?

These are different terms used to organize life on our planet.

An organism describes an individual. You are an organism. I am an organism. The mosquito that flies by your window is an organism. An organism is a single, living thing and can be an animal, a plant, or a fungus. Organisms grow and respond to their environment.

A population is the term we use to describe multiple individuals or organisms of a single species that live within a particular geographic area. For example, there may be one population of painted turtles in one state and another population of painted turtles 250 miles away in another state.

A community is the term used to describe two or more populations of different species that occupy the same space at the same time. For example you could talk about the community of Yellowstone National Park that is made up of numerous animals such as elk, bighorn sheep, coyotes, porcupines, different species of frogs, and fish and insects and so forth.

An ecosystem is the term used to describe both the biotic (living) and abiotic (nonliving) factors in a system. The ecosystem in the image below is made up of birds, frogs, fungi, plants, mammals, bacteria, the water, the run, the rocks, the soil, and so forth.

A biome is the term used to describe organisms that occupy a certain area. Biomes are determined by the primary vegetation type, the climate of the area, and the geographic location. The plants and animals in a biome share common traits that are specific to the individual biome those plants and animals inhabit.

A biosphere is the term used to describe the combination of every ecosystem on the planet. Our biosphere is Earth. The biosphere includes all living beings and their relationships.

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What is the conversions of grams to mL?

Answer
It depends on the density of the substance you are measuring.
Explanation :
For water, the density is approximately 1 gram per mL. Even for water it varies according to temperature with maximum density $$0.9999720$$ $$ 4^{\circ}C$$
and about $$0.9982$$ grams per mL at $$^{\circ} C$$ (i.e, room temperature )
A milli-litre is the same as a cubic centimetre.

What is the conversion factor between km/hr and m/s?

Answer
to convert $$\dfrac{km}{hr} $$ to $$\dfrac{m}{sec}$$ , one needs to multiply by $$\dfrac{5}{18}$$
Explanation :
1 km/hr means 1000 meters in 3600 seconds or $$\dfrac{1000}{3600} = \dfrac{5}{18} \dfrac{m}{sec}$$
Hence, if one has to convert $$\dfrac{km}{hr} $$ to $$\dfrac{m}{sec}$$ one needs to multiply by $$\dfrac{5}{18}$$
For converting $$\dfrac{m}{sec} $$ to $$\dfrac{km}{hr} $$ one needs to divide by $$\dfrac{5}{18}$$ i.e, multiply by $$\dfrac{18}{5}$$

What is the difference between a therapist, psychologist, psychiatrist, and a counselor?

A therapist is for therapy or treatment. A Psychologist is for Psychology in a Academic level. A Psychiatrist is for Psychology in a Medical Level. A Counselor is someone who gives advice.

Explanation:

A therapist is broad term, for someone who gives you a certain type of therapy( Thus there are Physical therapist and Psychotherapist)

A Psychologist is someone who practices Psychology in a Academic level. Practically, these are the people who conduct multiple studies and researches about human behavior and mental processes.

A Psychiatrist is someone who practices Psychology in a Medical Level. Practically, these are the people who conduct diagnoses and studies about How elements both external and internal affect the mental health condition of a person. By internal hormones, body processes, diseases and motivation, By external experiences(trauma, manias, fears), Drugs & substances, Peer Pressure and Social Interaction.

A Counselor is broad term, for someone who gives advice and suggestions.(Thus Business Counselors, Finance Counselors, Guidance Counselors, Marriage & Annulment Counselors, and plain Parental Counseling)

And You forgot another special Psych-related person the Psychometricians, The field workers, who conduct surveys, Create and administer written or non-written test, assist the psychologist with their life goals and stuffs like that. "Psychology plus Mathematics"

What is the difference between Astrophysics and Cosmology?

Cosmology is a sub-field of Astrophysics, while Astrophysics is the branch of astronomy that deals with the physics of the universe, Cosmology studies the universe as a whole.

Explanation:

Astronomy is a natural science that deals with the study of celestial objects, such as stars, planets, comets, nebulae, star clusters and galaxies.

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior. Among the objects studied are galaxies, stars, planets, exoplanets, the interstellar medium, and the cosmic microwave background.

Cosmology studies universe as a whole and its phenomena at largest scales. The difference between Astrophysics and Cosmology is that Cosmology studies universe as a whole and its phenomena at largest scales.

What is the basic SI unit of density?

The derived SI unit of density is $$\dfrac{kg}{m^3}$$
Explanation:
Density is an SI derived unit. It is derived from the SI fundamental unit for mass, the kilogram, and the SI fundamental unit for length, the meter. Density is the mass per unit of volume. The SI derived unit for volume is cubic meters. So the derived SI unit for density is $$\dfrac{kg}{m^3}$$

What is the angular momentum of earth?

The angular momentum due to the earth's rotation is $$\approx 7.2\times 10^{33}Kg\ m^{2}s^{-1}$$
(this value is with respect to a co-moving observer)
Explanation:
We can estimate the angular momentum due to the earth's rotation by approximating the earth by a uniform sphere of
$$\bullet$$ mass $$M=6.0\times 10^{24}Kg$$ and
$$\bullet$$ radius $$R=6.4\times 10^{6}m$$
The moment of inertia of a uniform solid sphere about any axis passing through the center is
$$I=\dfrac{2}{5}MR^{2}$$
and so, for the earth is
$$I=\dfrac{2}{5}\times 6.0\times 10^{24}\times (6.4\times 10^{6})^{2}Kg\ m^{2}$$
$$=\approx 9.8\times 10^{37}Kg\ m^{2}$$
The earth's angular velocity is
$$\omega=\dfrac{2\pi}{1\ day}=\dfrac{2\pi}{24\times 60\times 60}s^{-1}\approx 7.3\times 10^{-5}s^{-1}$$
So, the angular momentum of the earth's rotation (with respect to an observer co moving with it) is
$$L=I\omega \approx 7.2\times 10^{33}Kg\ m^{2}s^{-1}$$
Note that
$$\bullet$$ the angular momentum due to the revolution of the earth (with respect to the sub) is much larger than this.
$$\bullet$$ since the earth has a dense inner core, the actual moment of inertia is smaller than that estimated here.

What is the Fahrenheit equivalent of $$ 15 $$ degrees Celsius?

Multiply the $$ ^oC $$ temperature by $$ 1.8. $$ Add $$ 32 $$ to this number. This the answer in $$ ^oF $$.
$$ ^o F=\left( ^{ o }C.\dfrac { 9 }{ 5 } \right) +32 $$
$$ ^oF=\left( 15.\dfrac { 9 }{ 5 } \right) +32 $$
$$ ^oF=27+32 $$
$$^oF=59$$

What is the Bronsted-Lowry acid and base versus Lewis?

A Brønsted-Lowry acid is a proton donor, while a Lewis base is an electron donor.

When a proton ($$H^+$$) accepts electrons donated from a Lewis base (like $$OH^-$$), it exceeds its valency and must break its bond with a given atom on a Brønsted-Lowry acid (like the nitrogen on $${NH_4}^+$$).

If a bond between a Brønsted-Lowry acid and a proton breaks, the Brønsted-Lowry acid donates the proton.

Thus, a Lewis base can donate electrons to acquire a proton, while the Brønsted-Lowry acid had donated that proton. They can work together!

--------------

From the other perspective, a Brønsted-Lowry base is a proton acceptor, while a Lewis acid is an electron acceptor.

If a Brønsted-Lowry acid (like $${NH_4}^+$$) accepts electrons from a Lewis base (like water in this case), then it is also a Lewis acid by definition.

Furthermore, if that proton donates itself onto the Lewis base (water in this case), that base is also a Brønsted-Lowry base (water in this case), because it accepted the proton.

Thus, a Lewis acid that possesses a proton can accept electrons to donate a proton, while the Brønsted-Lowry base accepts that proton. Again, they work together!

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What is the amount of space occupied by a substance?

Clearly, it's the volume.
Explanation:
All matter, gas, liquid, and solid expresses a volume, For gases, the volume can be altered for a given quantity (i.e. mass) by compression or expansion, and a gas will always fill a vacuum evenly. Gaseous volumes have typical units of $$L$$, or $$m^{3}$$.

What is species richness?

SPecies richness is the number of species within a community or area.
Explanation:
Species richness is the number of species within a community or area. For example, if we have two plots of lands,

AA and

BB, and plot

AA has twenty four species of plants and plot

BB has eighty four species of plants, plot

BB has higher species richness.
Species richness does not take into account the distribution of species within the area or what is referred to as species evenness.
In the example above, if the majority of the individuals in plot

BB with eighty four different types of species all come from one or two different species, this plot would have low species evenness.
In the image below, both communities have identical species richness because they contain two species of trees. In terms of their evenness, community

XX is more even than community

ZZ because there is an equal number of both tree species.

What is $$75$$ degrees fahrenheit converted into celsius and kelvin ?

To convert between Celsius (C) and Fahrenheit (F) :

$$F = \dfrac{9}{5}C + 32$$

$$\therefore C = \dfrac{5}{9} (F - 32)$$

According to question F = 75

$$= \dfrac{5}{9} (75 - 32)$$

$$= 23.889^\circ C.$$

To convert between Celsius (C) and Kelvin (K) :

$$K = C + 273.15$$

$$= 23.889 + 273.15$$

$$= 297.039 \,K.$$

(Kelvin is the SI unit of temperature).

What is electronegativity?

Electronegativity is an atom's ability to attract electrons when bonded with other atoms.

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What is $$22$$ degrees in Fahrenheit in Celsius?

This is the formula for converting Fahrenheit to Celsius"

$$C=(F-32).\cfrac{5}{9}$$

$$C=(22-32).\cfrac{5}{9}=(-10)\cfrac{5}{9}$$

$$C=-5.\overline { 5 } $$

$$22$$ degrees Fahrenheit is equal to $$-5.\overline { 5 } $$ degrees Celsius

What is electronegativity a measure of ?

Electronegativity is conceived to be the ability of an atom in a chemical bond to polarize electron density itself.
Explanation:
I write "conceived" because there is nothing fundamental about electronegativity, and its measurement depends on various ad hoc scales, of which the Pauling scale is the most famous and still widely used.
It makes sense that the most electronegative atoms, $$F$$, and
$$O$$, are the ones that are right-most in the Periodic Table. For a given Period as $$Z$$, the atomic number, increases, effective nuclear charge increases and the valence electrons are held more tightly as more protons are added to the atomic nucleus; this is manifested in the marked decrease in atomic radii across a Period.

What is a particle that moves around the outside of the nucleus?

An electron.
Explanation:
Electrons are electronegatively attracted to the nucleus, and play a big part of the element's properties and bonding behavior. They are infinitesimally small relative to the nucleus.
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What is a neutral atom?

An atom that has equal number of protons and electrons is called a neutral atom.
A neutral Sodium atom has atomic number 11, which means, it has 11 protons and since it is neutral, it also has 11 electrons.

What is $${200}^{o}F$$ in celsius?

The equation is

$$(F-32).\cfrac{5}{9}=C$$

First, substitute $$F$$ for $$200$$ degrees

$$(200-32).\cfrac{5}{9}$$

Then to solve

$$(200-32).\cfrac{5}{9}=168.\cfrac{5}{9}=\cfrac{850}{9}=93.3333333333\approx 93.3$$

What is formula for converting Farenheight to Celsius?

$$(F-32).\dfrac{5}{9}$$
Explanation:
For Fahrenheit to Celsius, I would simply do $$(^oF-32).\left(\dfrac{5}{9}\right)$$, so if my temperature in Fahrenheit was $$50$$, then my degrees in Celsius would be $$(50-32).\left(\dfrac{5}{9}\right)$$ which would equal to $$10^oc$$.
If you wanted to convert Celsius to Fahrenheit, then use $$^oC.\dfrac{9}{5}+32=^oF$$.

What is $$64$$ ounces in pounds ?

There are $$16$$ ounces in one pound, so you have to divide $$64$$ ounces by the $$16$$ ounces per pound.

$$1 \,pound = 16\,ounces$$

$$64 \,ounces . \dfrac{1 \,pound}{16 \,ounces}$$

$$\dfrac{64 \,oz \,lb}{16 \,oz}$$

$$64 \,oz \,lb / 16 \,oz = 4 \,pounds$$

Notice that the "oz" label is in both in the numerator and denominator, so it cancels out there.

What instrument measures wind speed near the earth's surface?

Anemometer : The 4 hemispherical cups rotates proportional to speed of wind and the dial shows the speed.
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What is $$80$$ degrees Celsius in Fahrenheit?

$$80^{0}$$ Celsius $$=112^{0}$$ Fahrenheit
Explanation:

	degree $$C$$	degree $$F$$
freezing point of water	$$100$$	$$212$$
freezing point of water	$$0$$	$$32$$

From this it follows that $$100C^{0}=180F^{0}$$
$$80^{0}C$$ is $$80C^{0}$$ above freezing
$$=\frac{180}{100}\cdot 80F^{0}=144F^{0}$$ above freezing
$$144F^{0}$$ above freezing is
$$144−32=112^{0}F$$

What is linear mass density?

Linear mass density is the amount of mass per unit length.
Just as ordinary density is mass per unit volume, linear density is mass per unit length. Linear densities are usually used for long thin objects such as strings for musical instruments.
EXAMPLE
Suppose we have a $$0.80\ mm$$ diameter guitar string of carbon steel ( density $$=7.860\ g/cm^3$$). What is the linear mass density of the string?
Solution:
Step 1: Find the volume of a length ( say, $$1\ m=100\ cm$$) of the string.
$$V=\pi r^2l$$
The radius of the string is half the diameter.
$$r=\dfrac {0.80\ mm}{2}=0.40\ mm=0.040\ cm$$
$$V=\pi r^2l =\pi \times (0.040\ cm)^2 \times 100\ cm=0.503\ cm^3$$
Step 2: Find the mass of the wire.
Mass $$=0.503\ cm^3 \times \dfrac {7.860\ g}{1\ cm^3}=3.95\ g$$
Step 3: Find the linear mass density.
Linear mass density $$=\dfrac {mass}{length }=\dfrac {3.95\ g}{1\ m}=4.0\ g/m$$ ( 2 significant figures).

What is $$120$$ degrees Fahrenheit in celsius?

We know that the relation between celsius and Fahrenheit temperature is given by

$$C=(F-32).\cfrac{5}{9}$$

$$C=(120-32).\cfrac{5}{9}$$

$$C=88.\cfrac{5}{9}$$

$$C=\cfrac{440}{9}$$

$$C=48.9$$ (rounded)

What is $$19C$$ in Farehneit?

To convert from Celsius to Farenheit we multipy Celsius by $$1.8$$ then add $${32}^{o}$$.

$$(19\times 1.8)+32={66.2}^{o}F$$

What is $${19}^{o}F$$ in celsius?

In order to determine how many degrees $$19$$ Farenheit is in Celsius we need to understand that there is an equation that we must use. To convert a temperature in Farenheit to Celsius that equation :

$$({f}^{o}-32).\cfrac{5}{9}={C}^{o}$$

Now we can solve for $${C}^{o}$$

$$({19}^{o}F-32).\cfrac{5}{9}={C}^{o}$$

$$=-{13}^{o}F.\cfrac{5}{9}$$

Is as same as this

$$-13.\cfrac{5}{9}$$

$$\cfrac{1}{9}=0.1111$$ those $$1$$'s actually go one repeating like that forever

Now,

$$\cfrac{2}{9}=0.2222$$ with that same repeating trend

In fact this holds true for any number less than $$9$$ that is over $$9$$ (all numbers up to $$\cfrac{8}{9}=0.8888$$. This means that

$$\cfrac{5}{9}=0.5555$$

For al intents and purposes we can round this to $$0.556$$ Now we can multiply $$-13$$ by $$0.566$$, this will give us the number of degrees Celsius:

$$-13.(0.556)=-{7.228}^{o}C$$

We can round to get

$${19}^{o}F=-7{7.2}^{o}C$$

What are the branches of chemistry and their definition ?

Organic chemistry: It involves the study of the structure, properties, and preparation of chemical compounds that consist primarily of carbon and hydrogen.

Medicinal chemistry: The design, development, and synthesis of medicinal drugs. It overlaps with pharmacology (the study of drug action).

Organometallic chemistry; The study of chemical compounds containing bonds between carbon and a metal.
Polymer chemistry: The study of the chemistry of polymers.

Physical organic chemistry: The study of the interrelationships between structure and reactivity in organic molecules.

Stereochemistry: The study of the spatial arrangements of atoms in molecules and their effects on the chemical and physical properties of substances.

Inorganic chemistry is the study of the properties and behaviour of inorganic compounds.
It covers all chemical compounds except organic compounds.
Inorganic chemists study things such as crystal structures, minerals, metals, catalysts, and most elements in the Periodic table
Branches of inorganic chemistry include:
Bioinorganic chemistry: The study of the interaction of metal ions with living tissue, mainly through their direct effect on enzyme activity.

Geochemistry: The study of the chemical composition and changes in rocks, minerals, and atmosphere of the earth or a celestial body.

Nuclear chemistry: The study of radioactive substances.

Organometallic chemistry: The study of chemical compounds containing bonds between carbon and a metal.

Solid-state chemistry: The study of the synthesis, structure, and properties of solid materials.

What is $$90^{0}F$$ in celsius?

approximately $$51.56^{0}C$$
Explanation:
To convert from Fahrenheit to Celsius, use the formula:
$$T_{^{0}C}=(T_{^{0}F}-32)*\frac{5}{9}$$
Substitute $$T_{^{0}F}$$ as $$90$$ and solve for $$T_{^{0}C}$$.
$$T_{^{0}C}=(T_{^{0}C}-32)*\frac{5}{9}$$
$$T_{^{0}C}=(90-32)*\frac{5}{9}$$
$$T_{^{0}C}=58*\frac{5}{9}$$
$$T_{^{0}C}\approx 51.56^{0}C$$

What is $$20$$ degrees celsius in Fahrenheit?

According to intial data we have

$${C}_{f}=0$$; $${C}_{b}=100$$

$${F}_{f}=32$$; $${F}_{b}=212$$

$$\cfrac{C-{C}_{f}}{{C}_{b}-{C}_{f}}=\cfrac{F-{F}_{f}}{{F}_{b}-{F}_{f}}$$

Where

$${C}_{f}:$$ the freezing poiint of pure water in Celsium scale

$${C}_{b}:$$ the boiling point of pure water in Celsius scale

$${F}_{f}:$$ the freezing point of pure water in Fahrenheit scale

$${F}_{b}:$$ the boiling point of pure water in Fahrenheit sale

On subsituting the values we have

$$\cfrac{20-0}{100}=\cfrac{F-32}{180}$$

$$\cfrac{20}{100}=\cfrac{F-32}{180}$$

$$\cfrac{1}{5}=\cfrac{F-32}{180}$$$$180=5(F-32)$$

$$36=F-32$$

$$F=68$$

What is $$42$$ degrees celsius in fahrenheit ?

To convert from Celsius to Fahrenheit, multiply by $$\dfrac{9}{5}$$ and add $$32.$$

So we have

$$ F = \, \,\dfrac{9}{5} C+ 32 $$

On putting the values we have

$$F= 75.6 + 32 = 107.6^\circ F $$

Note : convert from Fahrenheit to Celsius, do the reverse : subtract $$32$$ and multiply by $$\dfrac{5}{9}$$

The maximum default speed limit on the Autobahn in Germany is 100 km/hr. What is this speed in mi/hr?

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Is density a physical or chemical property?

Chemical property are those which can only be established by carrying out a chemical reaction (heat of combustion, flash point, enthalpies of formation etc)

Density can be established simply by determining the mass and volume of substance, no reaction is involved, so its a physical property.

What does temperature measure?

The temperature measures kinetic energy or the energy of motion of system.

Degrees Kelvin known as absolute temperature assumes that at zero degrees Kelvin $$(-273^\circ C)$$ that there is no kinetic energy measurable.

So the higher the temperature the greater the kinetic energy and the more motion there is in electrons, atoms, and molecules.

There are $$8$$ ounces in a $$h$$ pound. How many ounces are in $$7\frac{3}{4}$$ lbs?

We know that

$$124$$ ounces = $$7\frac{3}{4}$$ lbs
Explanation:
$$8$$ ounces = half a pound
$$16$$ ounces = $$1$$ pound
To determine the number of ounces in $$7\frac{3}{4}$$ lbs:
$$16\cdot 7.75=124$$

Is density temperature-dependent?

Yes, it is very much dependent

Explanation:

We know the formula for density

$$ \displaystyle density = \frac{mass}{volume} $$

Volume depends on temperature. For example, with an increase in temperature, the volume increases, so density decreases as mass remain constant.

What are some examples of quantitative and qualitative measurements ?

Quantitative measurements are those that deal with a quantity, for example:
Mass of as sample
Length of a piece of wire
Molecules in a mole
Volume of a gas
Temperature of a sample
These types of measurements are called Extensive.
Qualitative measurements are those that deal with the quality, for example:
Color of a sample
Texture of a surface
Coarseness of a powder
Aroma of a reaction
Malleability of a metal
These types of measurements are called Intensive.

There are $$5$$ miles to $$8 km$$. How many $$km$$ in $$80$$ miles?

Write a direct proportion to compare miles to Km.

$$\frac{5}{8}=\frac{80}{x}\frac{miles}{km}$$

You could decide what $$5$$ was multiplied by to give $$80$$ and do the same to the $$8$$.

$$\frac{5}{8}*\frac{16}{16}=\frac{80}{128}\frac{miles}{km}$$

or cross multiply to get

$$5x=8*80$$

$$x=\frac{8*80}{5}$$

$$x=128km$$

or, find a conversion factor,

$$5$$ miles = $$8km$$

$$1$$ mile = $$\frac{8}{5}km$$

$$80$$ miles = $$80*\frac{8}{5}=128km$$

What is anything that has mass and occupies space?

Matter.
Explanation:
Matter has two main properties: has mass, and occupies space.
Objects (matter) can have properties of energy (like kinetic or heat energy), however, generally, matter is NOT energy.
E.g. Light is a form of energy that has no mass.
Hope this helps.

The temperature $$212 F$$ is the same as what in degrees $$C$$?

We know that

F = 9/5C + 32

On putting the value we get

$$212^{0} F\rightarrow 100^{0}C$$

What is density?

Density is the mass per unit of volume of a substance.
Explanation:
Density measures the compactness in molecular arrangement in any substance which determines how heavy or light any substance is.
The density formula is $$density = \frac{mass}{volume}$$. Mass units are most commonly grams or kilograms. Volume units are most commonly cubic centimeters $$(cm^3)$$, cubic meters $$(m^3)$$, or millileters $$(mL)$$.
Examples of density include the following:
The density of water at $$4^{\circ}C$$ can be written as $$1.000g/cm^3, 1.000g/mL, 1000Kg/m^3,$$ and $$1.000kg/L$$.
The density of iron at $$0^{\circ}C$$ is $$7.874g/cm^3$$ and $$7874kg/m^3$$.
The density of sodium metal at $$0^{\circ}C$$ is $$0.968g/cm^3$$ and $$968kg/m^3$$.
In order to determine the density of a substance, you need to know its mass and its volume. Then divide its mass by its volume, remembering to divide the units as well.
Example
A $$1.26cm^3$$ sample of the element mercury has a mass of $$17.05g$$. What is it's density?
Solution
$$density = \frac{mass}{volume} = \frac{17.05g}{1.26cm^3} = 13.5 g/cm^3$$

How many arcseconds are in one arcminute?

$$1$$ degree is $$60$$ minutes and $$1$$ arc minute is $$60$$ arc seconds.

Therefore $$60$$ arc seconds in one arc minute,

How many arcseconds are in degree?

We can dimensional analysis to convert from degree to arcminutes, then from arcminutes to arcseconds:

$$1^o$$

$$=1^o.\dfrac{60\ arcminutes}{1^o}$$

$$=1^o.\dfrac{60\ arcseconds}{1\ arcminute}$$

$$60\ arcminutes$$

$$=60\ arcminutes.\dfrac{60\ arcseconds}{1\ arcminute}$$

$$=60.\dfrac{60\ arcseconds}{1}$$

$$=60.60\ arcseconds$$

$$=3600\ arcseconds$$

How many gallons is $$2$$ litres?

Note that the $$US$$ gallon is a different size than used elsewhere in the world. (I suspect you want the $$US$$ gallon but since I can't tell where you are posting from I can not be certain).

By definition( to $$3$$ decimal places)

$$1$$ liter $$=0.264$$ U.S. gallons

$$=0.220$$ Imperial/ British gallons

How many feet is in $$3$$ miles?

$$3$$ miles have $$15840$$ feet

Explanation:

Each mile has $$8$$ furlongs.

Each furlong has $$220$$ yards.

Each yard has $$3$$ feet.

So each mile has $$8\times 220\times 3=5280$$ feet.

And $$3$$ miles have $$5280\times 3=15840$$ feet.

How many $$1/3$$ cups do you need to make $$1/2$$ cup?

We need to figure out how much more than $$\dfrac{1}{3}$$ sup is $$\dfrac{1}{2}$$ cup. That translates to this equation:

$$\dfrac{1}{3}+x=\dfrac{1}{2}$$

if we subtract $$\dfrac{1}{3}$$ from both sides we get:

$$x=\dfrac{1}{2}-\dfrac{1}{3}$$

In order to subtract or add fractions we need to make the denominators (the bottom parts) of both fractions equal to each other. In order to do that we find the Least Common Multiple between them. In this case between $$2$$ and $$3$$. It is $$6$$, which is $$2$$ times $$3$$. Now we multiply the bottom and top of each fraction by the number in that multiplication above that is missing to get to $$6$$, like this:

$$x=\dfrac{1.3}{2.3}-\dfrac{1.2}{3.2}$$

Notice that we multiply the $$\dfrac{1}{2}$$ by $$3$$ in the top and bottom because we need $$3$$ to make $$2$$ times something equal to $$6$$, and that we multiply the $$\dfrac{1}{3}$$ by $$2$$ in the top and bottom for the same reason.

Once we make those multiplications we get:

$$x=\dfrac{3}{6}-\dfrac{2}{6}$$

$$x=\dfrac{1}{6}$$

We can see from the previous calculation that $$\dfrac{1}{3}$$ is equal to $$\dfrac{2}{6}$$, and that $$\dfrac{1}{6}$$ is half of $$\dfrac{2}{6}$$. so, in order to make $$\dfrac{1}{2}$$ cup you need a whole $$\dfrac{1}{3}$$ cup plus half of it.

How many feet per second is $$23$$ joules a sec?

A joule is the amount of energy required to accelerate a mass of one kilogram by one meter/$$second^{2}$$ over a distance of one meter

There is no direct conversion of joules into velocity (i.e. your " feet per second")

The following conversion factors might be of use:

$$1$$ foot $$=0.3048$$ meters

$$1$$ meter $$=3.28084$$ feet

$$1$$ pound $$=0.453592$$ kilograms

$$1$$ kilogram $$=2.20462$$ pounds

How many kilometers is $$1.7\ miles?$$

If exact, then $$2.7358848$$ kilometers, so to $$42$$ significant figures that is $$2.7$$ kilometers.

Explanation;

There are exactly $$1.609344$$ kilometres in a mile by definition.

So if the figure $$1.7$$ miles is precise, tehn in kilometers it is:

$$1.7.1.609344=2.7358848$$

If the figure given is only accurate to $$2$$ significant figures, then we should only quote the answer to $$2$$ significant figures too.

So, $$1.7$$ miles is approximately $$2.7$$ kilometers.

How many fluid oz. are in a gallon?

$$128$$ ounces $$=1$$ gallon

Explanation:

$$8$$ oz. $$=1$$ cup

$$2$$ cups $$=1$$ pint

$$2$$ pints $$=1$$ quart

$$4$$ quarts $$=1$$ gallon

$$8\times 2\times 2\times 4$$ oz. $$=128$$ oz. $$=1$$ gallon

Note that British (including Canadian) measures are different from $$US$$ measures. The same $$128\ oz$$. to $$1$$ gallon holds but ounces are a different size.

$$US$$ ounces $$\approx 29.6\ ml$$

Imperial (British) ounce $$\approx =28.4\ ml$$.

How many arcseconds are in $$1^o$$?

There are $$3600$$ arcseconds in $$1^o$$.

Explanation:

Each degree has $$60$$ arcminutes and each arminute has $$60$$ arcseconds.

Hence, $$1^o$$ degree has $$60\times 60=3600$$ arcseconds.

How many feet is in $$15$$ miles?

There is $$5280$$ feet in $$1$$ mile.

This means that $$15$$ miles is:

$$15\times 5280=79,200$$ feet.

How many feet are in $$2.4$$ miles?

There are $$3$$ feet in a yard and $$1760$$ yards in a mile.

So in $$2.4$$ miles there re:

$$2.4 . 1760.3=24.176.3=12672$$ feet

How many feet are in $$4$$ miles?

We know that

$$4$$ miles $$=21,120$$ feet

$$1\ mile=5280$$ feets

Just something you need to memorize

$$4\ miles=4\times 5280=21120$$ feet

How many feet are in $$1000$$ yards?

$$1:3=1000:F$$ or you may write $$\dfrac{1}{3}=\dfrac{1000}{F}$$

Or $$\dfrac{3\ ft}{1\ yd}=\dfrac{F\ ft}{1000\ yd}$$

However you write it, you should also get:

$$1\times F=3\times 1000$$

$$F=3000$$.

How many inches is in $$1$$ yard?

$$36\ inches$$ are there in 1 yard.

How many inches is in $$5$$ yards?

Five yard are $$180$$ inches.

Explanation:

Use dimensional analysis

$$1$$ yd$$=36\ in$$

There are two conversion factors:

$$\dfrac{1\ yd}{36\ in}$$ adn $$\dfrac{36\ in}{1\ yd}$$

Multiply $$5$$ yards by the conversion factors teh cancel;s yards and keeps inches.

$$5\ yd \times \dfrac{36\ in}{1\ yd}=180\ in$$

How many inches is there in $$1/8th$$ of a yard?

In $$1$$ yard we have $$3$$ feet and in each feet we have $$12$$ inches.

So we have $$3 \times 12 =36$$ inches in each yard.

Hence in $$\dfrac{1}{8}$$ yard, we have $$36 \times \dfrac{1}{8}=9.36 \times \dfrac{1}{28}=\dfrac{9}{2}=4\dfrac{1}{2}$$ incheas.

How many feet is in a mile?

According to British units

$$1$$ mile $$=8$$ furlongs

(A furlongs is a commonly used unit)

And,

$$1$$ furlongs $$=660$$ feet

Then

$$\rightarrow 1\ mile=(8.660)$$ feet

$$\Rightarrow =5280$$ feet

How long is an eon in years?

Eon has a number of meanings. In Astronomy, an eon refers to $$1$$ billion $$(10^9)$$ years. But it also refers to a very long, unspecified period of time, or specific geologic stages of the Earth.

Since this question is posted in Astronomy, I will assume that the answer of $$eon=10^9$$ years is the most appropriate, however it is not the most common.

How many feet are in a football field that is $$100$$ yards?

Since $$1\ yard=3\ feet$$, we can multiply $$100\ yd$$ by $$\dfrac{3\ ft}{1\ yd}$$. We are essentially

multiplying by $$1$$, but doing so allows us to cancel out the $$yd$$ unit so that we are left with only $$ft$$.

$$\dfrac{100\ yd}{1}.\dfrac{3\ ft}{1\ yd}=300\ ft$$

How long is $$7/10$$ of a mile, in feet?

Each miles has $$8$$ furlongs. Each furlong has $$220$$ yards and each yard has $$3$$ feet.

Therefore each mile has $$8\times 220\times 3=5280$$ feet and $$\dfrac{7}{10}$$ mile will have

$$5280\times \dfrac{7}{10}$$

$$=528.5280\times \dfrac{7}{1.10}=3696$$ feet.

How many degrees celsius equals one degree Fahrenheit?

Temperature in celsius is $$-17.22^oC$$
Explanation:
If $$F$$ is the temperature in Fahrenheit and $$C$$ is temperature in Celsius then
$$\dfrac {F-32}{180}=\dfrac {C-0}{100}$$
or $$\dfrac {F-32}{9}=\dfrac C5$$
Hence if $$F=1$$,
$$\dfrac C5=\dfrac{1-32}{9}=-\dfrac {31}{9}$$ and
$$C=\dfrac {(-31)\times 5}{9}=-\dfrac {155}{9}=-17.22$$

How many grams are in $$2000 mg$$?

Explanation:
$$1\ mg=10^{-3} g$$
$$2000\ mg=2000 mg \times 10^{-3}g mg^{-1}$$
$$=2.000.g$$

How many feet are in $$1/2$$ of a mile?

See a solution process below:

Explanation:

We know the conversion factor of miles to feet is:

$$1$$ mile $$=5280$$ feet

To find how many feet in a $$\dfrac{1}{2}$$ mile we can multiply each side of the equation by $$\dfrac{1}{2}$$

giving:

$$\dfrac{1}{2}\times 1$$ mile $$=\dfrac{1}{2}\times 5280$$ feet

$$\dfrac{1}{2}$$ mile $$=\dfrac{5280}{2}$$ feet

$$\dfrac{1}{2}$$ mile $$=2640$$ feet

There are $$2,640$$ feet in $$\dfrac{1}{2}$$ mile.

How many feet are in $$1$$ yard?

There are $$3$$ feet $$ in 1$$ yard.

How many cups are in two gallons?

$$32$$ cups.
Explanation:
$$16$$ cups are in a gallon.
$$2\ gallons \times 16\ cups=32\ cups$$.

How many cups are there in nine ounces?

To convert any value in ounces to cups, just multiply the value in ounces by the conversion factor 0.125. So, 9 ounces times 0.125 is equal to $$1\dfrac{1}{8}$$ cups.

How many degrees Celsius is $$67\ F$$?

$$19.44$$ degrees Celsius $$=67$$ degrees Fahrenheit
Explanation:
The formula for converting degrees Celsius to degrees Fahrenheit is
$$^oC=( ^oF-32 ) \times \dfrac 59$$
In your case,
$$C=(67-32) \times \dfrac 59$$
$$C=19.44^oC$$

How long is $$33$$ inches added to $$4$$ feet $$7$$ inches?

It is $$88$$ inches or $$7$$ feet and $$4$$ inches.

Explanation:

As each feet has $$12$$ inches, $$4$$ feet have $$4\times 12=48$$ inches. Hence $$4$$ feet and $$7$$ inches are $$48+7=55$$ inches

and adding $$33$$ inches to $$4$$ feet and $$7$$ inches is $$33+55=88$$inches.

Now as $$12$$ inches equal to one foot and $$88=7\times 12+4$$, we can also write $$88$$ inches as $$7$$ feet and $$4$$ inches.

How long in meters is $$670$$ nanometers?

$$670$$ nanometers is $$670\times 10^{-9}$$ meters or $$6.7\times 10^{-7}$$ meters in scientific notation or $$0.00000067$$ meters in standard form.

Explanation:

In metric system everything is standardized. In metric system as nano is one-billionth or $$10^{-9}$$

One nanometer is $$10^{-9}$$ meter, hence

$$670$$ nanometers is $$670\times 10^{-7}$$ meters in scientific notation or $$0.000000670$$ meters.

How many cups are in a quart?

Since there are two cups in a pint and two pints in a quart, $$2*2=4$$ cups in a quart

The official length for a marathon race is $$26.2$$ miles. How many yards long is a marathon? How many feet?

$$138,336$$ feet
$$46,112$$ yards
Explanation:
So, first of all, we are told that a marathon race is $$26.2$$ miles. We are asked to give the equal length in yards and feet.
It is really helpful to remember a few conversion factors:
1) $$1$$ mile = $$5,280$$ feet
2) $$1$$ miles = $$1,760$$ yards
So let's start with converting miles to feet.
Since each mile equals $$5,280$$ feet, let's multiply $$26.2$$ by $$5,280$$, which equals to $$138,336$$ feet.
Now let's convert from miles to yards.
Since each mile equals $$1,760$$ yards, let's multiply $$26.2$$ by $$1,760$$, which equals to $$46,112$$ yards.

How many cups are in a gallon?

$$1$$ Gallon [ Fluid, US] $$=16$$ Cups [ US]

What is an equilibrant?

It is the single force vector needed to establish equilibrium, ie to bring about the fact that the resultant of all the forces is zero.
It hence has the same magnitude as the original resultant but acts in the opposite direction.
So if $$\sum \vec{F} = F_0\angle \theta $$ then the equilibriant will be $$ F_0\angle (\theta + \pi)$$

The outside air temperature is $$30^{0}F$$, what is the temperature in Kelvin?

$$271.9K$$
Explanation:
The formula for converting a temperature from $$^{0}F$$ to $$^{0}C$$ is given by
$$^{0}C=\dfrac{5}{9}(^{0}F-32)$$

Plugging in our known temperature value, the temperature in $$^{0}C$$ is
$$^{0}C=\frac{5}{9}(30^{0}F-32)=-1.1^{0}C$$
And to convert from this Celsius temperature to Kelvin, we use the formula
$$K= ^{0}C+273$$
So,
$$K=−1.1^{0}C+273=271.9K$$

How many cups are equivalent to one pint?

$$2$$ cups $$=1$$ pint
Explanation:
This is just something that needs to be memorized:
$$8$$ ounces $$=1$$ cup
$$2$$ cups $$=1$$ pint
$$2$$ pints $$=1$$ quart
$$4$$ quart $$=1$$ gallon

How does mass affect density ? How does volume affect density ?

Density increases as mass increases, vice versa
Density increases as volume decreases, vice versa
This is because mass, the numerator of the equation, would cause the final answer (density) to increase when it increases, assuming the volume remains constant
And when the denominator of a fraction is large, in this case volume, it would cause the final answer to become smaller!

The ratio of two people's weight remains the same, whether measured in pounds or kilograms? $$( 1kg = 2.2lb )$$

Yes
Explanation:
If I am twice as heavy as you the ratio of our weights is $$2:1$$ whether you weigh me in pounds, kilograms or anything else.
If I am $$100 kg$$ and you are $$50 kg$$, the ratio is $$100:50=2:1$$
If I am $$220 lb$$ and you are $$110 lb$$, the ratio is $$220:110=2:1$$
$$(100 kg = 220 lb, 50 kg = 110 lb)$$

How many cups are in $$20$$ quarts?

$$80$$ cups $$=20$$ quarts
Explanation:
Handy relation to memorize:
$$8$$ ounces $$=1$$ cup
$$2$$ cups $$=1$$ pint
$$2$$ pint $$=1$$ quart
$$4$$ quarts $$=1$$ gallon
If you remember the above then
$$1$$ quart $$=2$$ pints $$=2\times 2$$ cups $$=4$$ cups
and if $$1$$ quart $$=4$$ cups
then
$$20$$ quarts $$=20\times 4$$ cups $$=80$$ cups

How many cups are in $$1/2$$ a gallon?

We know the conversion factor of gallons to cups is:
$$1$$ gallon $$=16$$ cups
To find the number of cups in $$\dfrac 12$$ gallon we can multiply each side of the equation by $$\dfrac 12$$ giving:
$$\dfrac 12 \times 1$$ gallon $$=\dfrac 12 \times 16$$ cups
$$\dfrac 12$$ gallon $$=\dfrac {16}{2}$$ cups
$$\dfrac 12$$ gallon $$=8$$ cups
Therefore, there are $$8$$ cups in $$\dfrac 12$$ gallon

Is it possible to add a scalar to a vector? Why or why not?

We cannot add a vector and a scalar quantities together because they have different dimensions.

Explanation:

A vector quantity is defined as a physical quantity which has both magnitude and direction. For example, velocity, displacement etc. A scalar quantity is a quantity which has magnitude only but no direction. For example, distance, speed etc.
It is impossible to add the two together because of their different dimensions . This basically means that being a vector quantity a particular physical quantity will have both magnitude and direction. Summing the two quantities together we have to describe the direction of the resultant quantity. As a scalar quantity does not have a direction it would be next to impossible to describe the direction of the resultant.

How does chemistry relate to biology ?

All living things are made of elements, molecules, and compounds. Metabolism is the sum total of all the chemical reactions that occur within the cells of living things.

The freezing point of an aqueous sodium chloride solution is -0.20C. What is the molality of the solution?

$$ 0.055 \dfrac{\mathrm{mol}}{\mathrm{Kg}} $$
Explanation:
$$ \Delta T=K_{f} \times m \times i $$
where:$$ m \rightarrow $$ is the molality of the solute expressed in $$ \dfrac{m o l}{K g} $$
$$ \Delta T \rightarrow $$ is the difference between the freezing point of the solution $$ \left(T_{f}\right) $$ and that of the pure solvent $$ \left(T_{i}\right) $$. $$ \Delta T=T_{f}-T_{i} $$
$$ i \rightarrow $$ is the Van'to Hoff factor. It is related to the number of particles ( or ions) of the solute dissolved in the solution. in the case of $$ N a C l \quad i=2 $$ since $$ N a C l $$ fully ionizes into 2 ions
$$ K_{f} \rightarrow $$ is the freezing point depression constant of the solvent. in aqueous solutions the solvent is water and $$ K_{f}=1.86^{\circ} \mathrm{C} \cdot \mathrm{Kg} \cdot \mathrm{mol}^{-1} $$
$$ \Delta T=-K_{f} \times \underbrace{m \times i}_{\text {molality of particles }} $$
$$ \Delta T=-K_{f} \times \underbrace{m \times i}_{m^{\prime}} $$
$$ \Delta T=-K_{f} \times m^{\prime} $$
$$ m^{\prime}=-\dfrac{\Delta T}{K_{f}} $$
$$ m^{\prime}=-\dfrac{\left(T_{f}-T_{i}\right)}{K_{f}} $$
$$ m^{\prime}=-\dfrac{\left(-0.20^{\circ} \mathrm{C}-0^{\circ} \mathrm{C}\right)}{1.86^{\circ} \mathrm{C} . \mathrm{Kg} . \mathrm{mol}^{-1}} $$
$$ m^{\prime}=\dfrac{0.20 ^oC}{1.86^{\circ} \mathrm{C} . \mathrm{Kg} \cdot \mathrm{mol}^{-1}} $$
$$ m^{\prime}=0.11 \dfrac{m o l}{K g} $$
Note that $$ m^{\prime} $$ is the molality of the dissolved particles in the solution i.e $$ N a^{+}+C l^{-1} $$ while $$ m $$ is the molality of the solute $$ (N a C l) $$
$$ m \times i=m^{\prime} $$
$$ m=\dfrac{0.11}{2} \dfrac{m o l}{K g} $$
$$ m=0.055 \dfrac{\mathrm{mol}}{\mathrm{Kg}} $$

How would you convert $$\dfrac {g}{cm^{3}}$$ to $$mL$$?

If you meant g/mL, then it requires little effort. 1 $${ cm }^{ 3 }$$ is known to be equivalent to 1 mL, so you're done.

If you meant mL, it's not the same units back, so it's not a proper conversion; you're inputting a density and getting back a volume. Regardless, you would do this:

$$\frac { g }{ { cm }^{ 3 } } $$
$$\underrightarrow { reciprocate } $$ $$\frac { { cm }^{ 3 } }{ g } $$
$$\frac { { cm }^{ 3 } }{ g } X\quad g={ cm }^{ 3 }=mL$$
So, you would take a mass m in g and divide it by a density ρ in g/cm3 or g/mL, giving you the volume V in mL:

$$\rho =\frac { m }{ V } $$

⇒$$V=\frac { m }{ \rho } $$

How do you solve for $$f$$ in $$C=\dfrac{5}{9}(f-32)$$?

See solution below:'

Explanation:

$$C=\dfrac{5}{9}(f-32)$$

$$\dfrac{C}{f-32}=\dfrac{5}{9}$$

Use the property $$\dfrac{a}{b}=\dfrac{m}{n}\rightarrow a\times n=b\times m$$

$$9C=5f-160$$

$$9C+160=5f$$

$$=\dfrac{9C+160}{5}=f$$

$$\dfrac{9}{5}C+32=f$$

How does a conversion factor differ from a measurement ?

A measurement will be a number plus the unit used. For example:
Imagine you are measuring the length of a metal rod. You measure using a ruler with meters marked on it and you get a measurement of $$0.85\,m$$. Someone else uses a different ruler and gets a measurement of $$85\,cm$$
Who was wrong? Neither measurement was wrong. If you multiply the the second reading by the conversion factor $$\dfrac{1\,m}{100\,cm},$$ the result will agree exactly with the first reading.
$$85 \,cm \,.\, \dfrac{1\,m}{100\,cm} = 0.85\,m$$

How much is $$90$$ C in Fahrenheit?

Explanation:
The conversion for Celsius to Fahrenheit is:

$$\displaystyle{F}=\frac{9}{{5}}{C}+{32}$$

Plug in the C value, resulting in:

$$\displaystyle{F}={\left(\frac{9}{{5}}\cdot{90}\right)}+{32}$$

$$\displaystyle{F}=\frac{810}{{5}}+{32}$$

$$\displaystyle{F}={162}+{32}$$

$$F=194$$

How does a hypothesis becomes a theory ?

An example Avogardo's Hypothesis ( famous) that equal volumes of gases would contain equal numbers of particles ( molecules or atoms) was based on the kinetic theory of gases.
Avogardo's Hypothesis remained a hypothesis for over 100 years before definitive empirical experiments proved his hypothesis correct. By then the kinetic theory of gases had been widely accepted.
A hypothesis predicts what is expected to happen. For example if I lower the temperature the volume of the ballon should shrink. This is a hypothesis.
This hypothesis is based on Charles Law one of the gas laws in the kinetic theory of gases. The kinetic theory explains that the movement of gases is do to the velocity of the particles. The greater the temperature the greater the velocity.
So if the temperature is lowered the velocity should be less according to theory.
This leads to the hypothesis that the the volume will shrink or decrease. The experimental evidence proves the hypothesis is correct. The correct prediction of the hypothesis gives support to the theory.
Good Theories make good predictions ( Hypothesis)
Bad Theories make bad predictions ( Hypothesis )

How to convert L to dm3 and ml to cm3 Questions: 1) $$10cm3$$ to Gm? 2) $$10L$$ to Gm? 3) $$10mL$$ to Gm? 4) $$10dm3$$ to Gm?

There is no conversion necessary. Litres and $$dm^3$$ are numerically identical, as are $$ml$$ and $$cm^3$$.

Explanation:

$$dm^3$$ is "cubic decimetres". A decimetre is $$10$$ cm - if you cube $$10$$ cm you get $$10 \times 10 \times 10 = 1000\,cm^3$$ which is $$1$$ litre.

$$ml$$ are milliliters or "thousandths of a litre". Therefore $$1\,ml$$ is the same as $$1\,cm^3$$

How to convert $$2.5$$ radian to degree/minute/second?

1) converting to degree : (Multiply by $$\displaystyle\frac{180}{\pi}$$)

$$= 2.5 \times \displaystyle\frac{180}{\pi}=\displaystyle{143.31}^{o}$$

2) converting to minutes :$$(0.31 \times 60)$$

$$= 0.31 \times 60= 18.6^{`}$$

3) converting into seconds :$$(0.6 \times 60)$$

$$= 0.6 \times 60= 36^{``}$$

So , $$2.5$$ radians$$=\displaystyle{143}^{o}\,18^{`}36{``}$$

How to convert rev/s into rad/sec?

Explanation:

$$\displaystyle{1}\ \text{ revolution}={2}\cdot\pi\ \text{ rad}$$

Therefore, multiply the rotation rate, in units of rev/s, by the conversion factor

$$\displaystyle\frac{{{2}\cdot\pi\ \text{ rad}}}{{{1}\ \text{ rev}}}$$

The rev's will cancel leaving you with rad/s.

How much is $$23$$-kg in pounds?

Explanation:

$$\displaystyle\text{1 kg=2.205 lb}$$

$$\displaystyle{23}\,{\text{kg}}\times\frac{{{2.205}\text{lb}}}{{{1}\,{\text{kg}}}}=\text{51 lb}$$

The atomic weight of aluminum is 26.982 u, how many aluminum atoms are there in a 4.55g sample of aluminum?

$$ 1.02 \cdot 10^{23} $$ atoms of $$ \mathrm{Al} $$
Explanation:
The key to this problem is the correct interpretation of what atomic weight means.
Notice that aluminum is said to have an atomic mass of $$ 26.982 \mathrm{u} $$. The unit usedhere is the unified atomic mass unit, $$ u $$.
The unified atomic mass unit is defined as $$ \dfrac{1}{12} $$ th of the mass of a neutral carbon-12 atom and is approximately equal to the mass of one nucleon, as in the mass of one proton or one neutron. Also, you should know that you have
$$ 1 \mathrm{u}=1 \mathrm{g} / \mathrm{mol} $$
This means that the mass of one mole of aluminium atoms will be $$ 26.982 \mathrm{g} $$.
As you know, one mole of any element contains exactly $$ 6.022 \cdot 10^{23} $$ atoms of that element.
This means that if you know how many moles of aluminium you have in 4.55 g. you can use Avogadro's number to find the number of atoms.$$ 4.55 \not g \cdot \dfrac{1 \mathrm{mole} \ \mathrm{Al}}{26.982 \mathrm{\not g}}=0.168631 \mathrm{moles} \ \mathrm{Al} $$
Therefore, you will have
1845351_1885307_ans_cf8afe5702b049c9a6f4e5f11be2c0eb.png

1845351_1885307_ans_cf8afe5702b049c9a6f4e5f11be2c0eb.png

How much is $$70$$ degrees Fahrenheit in Celsius?

Explanation:

To convert Fahrenheit to Celsius, the normal method is to subtract $$32$$ then divide by $$1.8$$ (i.e. $$\displaystyle\frac{9}{{5}}$$).

So in our example:

$$\displaystyle\frac{5}{{9}}{\left({70}-{32}\right)}=\frac{5}{{9}}{\left({38}\right)}=\frac{190}{{9}}={21}.\overline{{{1}}}$$

How much is $$10$$ kg in pounds?

Explanation:

Here is a conversion that I set up (using $$1\,lb = 453.6\,g$$):
$$\displaystyle{10}\ \text{ kg}{\left(\frac{{{1000}\ \text{ g}}}{{{1}\ \text{ kg}}}\right)}{\left(\frac{{{1}\ \text{ lb}}}{{{453.6}\ \text{ g}}}\right)}$$
$$\displaystyle{10}\,{{\ \text{ kg}}}{\left(\frac{{{1000}\,{{\ \text{ g}}}}}{{{1}\,{{\ \text{ kg}}}}}\right)}{\left(\frac{{{1}\ \text{ lb}}}{{{453.6}\,{{\ \text{ g}}}}}\right)}\displaystyle={\color{blue}{{22.0462}\ \text{ lbs}}}$$

Reaction:
$$\mathrm{Mg}+2 \mathrm{HCl} \rightarrow \mathrm{MgCl}_{2}+\mathrm{H}_{2}$$

What volume of hydrogen is produced from the reaction of 50.0 g of Mg and the equivalent of 75.0 g of HCl?

We address the reaction...
$$ M g(s)+2 H C l(a q) \rightarrow M g C l_{2}(g)+H_{2}(g) \uparrow $$
And this is a redox reaction. What is oxidized, and what is reduced?
Moles of metal $$ =\dfrac{50.0 \cdot g}{24.3 \cdot g \cdot m o l-1}=2.06 \cdot $$ mol...
Moles of acid $$ =\dfrac{75.0 \cdot g}{36.5 \cdot g \cdot m o l^{-1}}=2.06 \cdot $$ mol...
Given the stoichiometry, CLEARLY, there is insufficient acid to effect complete oxidation....and the METAL is the reagent in excess, and the acid is the reagent in deficiency...
At most, we could make HALF an equiv with respect to dihydrogen gas... and since the molar volume under these conditions is $$ 24.8 \cdot L \cdot \mathrm{mol}^{-1} $$

So, the volume of dihydrogen is....
$$ 24.8 \cdot L \cdot m o l^{-1} \times 1.03 \cdot m o l= 25.544 \ L $$

What is an activated complex?

An Activated Complex is a high energy state that a reaction goes through in order to change reactants to products.

You can see here in the picture just how high energy the complex is.

Activation Energy is what is required to overcome this complex.

With the complex overcome, reactants become products.

1852814_1886344_ans_08d6543d7c944c8e8264b850f25fc3df.jpg

How can you calculate mass if density and volume are known ?

Density is mass per unit volume. The equation is
$$density = \dfrac{mass}{volume}.$$
If density and volume are already known, you can calculate mass by multiplying density by volume.
mass = density $$\times$$ volume

1848207_1886832_ans_dca25c7cebf34781bf953f7db35995d4.jpg

1848207_1886832_ans_dca25c7cebf34781bf953f7db35995d4.jpg

How much is $$63$$ kg in pounds?

Explanation:

We know:

$$\displaystyle{1}{k}{g}={2.20}{P}{o}{u}{n}{d}{s}$$

$$\displaystyle{63}{k}{g}={2.20}\cdot{63}{P}{o}{u}{n}{d}{s}$$

$$\displaystyle{63}{K}{g}={138.6}{P}{o}{u}{n}{d}{s}$$

This is how you can convert Kg to pound or vice-versa.

Specific gravity of HCl is 1.What is its Molarity of such solution containg 17 gm of HCl?

How do you find volume when given mass?

We know that,

Density, $$ \rho = \frac{Mass}{Volume} $$

If the mass is known, volume is inaccessible without density.

In what units is wind speed measured?

Answer
There are a few traditionals, an American and two metrics
Explanation :
Beaufort - scale : runs from 0 (no wind at all ) to 10 (storm) and up.
Knots: nautical miles per hour (former British)
mph: 'normal' miles per hour (US)
km/h: kilometers per hour
SI: m/s meters per second
These may all be converted into each other, except the Beaufort scale. Here every number represents a wind speed range

How do you convert seconds to days ?

There are:
$$24$$ hours in a day
$$60$$ minutes in an hour
$$60$$ seconds in a minute
So there are:
$$24 \,.\, 60 \,.\, 60 = 86400$$ seconds in a day

Why is a $$1\,dm^{3}$$ volume equivalent to $$1\,L$$ ?

$$d$$ is the abbreviation for deci $$= 10^{-1}.$$
Thus $$1\,dm^{3} = (1 \times 10^{-} \,m)^3 = 1 \times 10^{-3} \,m^{3}$$
$$c$$ is the abbreviation for centi $$= 10^{-2}.$$
And $$1\,cm^{3} = (1 \times 10^{-2} \,m)^{3} = 1 \times 10^{-6} \,m^{3}$$
And thus there are $$1000 \,cm^3 \,dm^{-3}$$ or $$1000 \,cm^{3} \,L^{-1}$$
And there are also $$1000\,L \,m^{-3}.$$ A cubic metre is a very large volume.
And thus $$1\,mol \,dm^{-3} = 1\,mol \,L^{-1},$$ which is the familiar unit of concentration.

$$32$$ gallons is how many pints?

Explanation:
The conversion factor of gallons to pints is:
$$1$$ gallon = $$8$$ pints
To find how many pints in $$32$$ gallons we can multiply each side of the equation by $$32$$
$$32*1$$ gallon = $$32*8$$ pints
$$32$$ gallon = $$256$$ pints

$$3 km/h= m/s$$?

$$0.833$$ m/s
Explanation:
First you need to understand what $$3 km$$ per hour means.
In $$1$$ hour the distance covered is $$3km$$
However, we want to change to metres.
Knowing that $$1 km = 1000 m$$ gives us:
In $$1$$ hour the distance covered is $$3km$$
In $$1$$ hour the distance covered is $$3000*1000$$
In $$1$$ minute you will cover $$\frac{1}{60}$$ of the distance in an hour
In $$1$$ second you will cover $$\frac{1}{60}$$ of the distance in a minute.
$$3km/hour=\frac{3*1000}{60*60}m/s$$ = $$\dfrac{ 3*1000}{ 3600}$$
$$=0.833m/s$$

Which one is greater 5000cm. or 5 meters?

5000 cm is a lot greater than 5 meters.

Explanation:

Each meter has 100 centimeters and therefore 5 meters are equal to 5×100=500 cm.

Hence 5000 cm is a lot greater than 5 meters.

How are protons, neutrons, and electrons similar?

These are all the fundamental particles of matter.
Explanation:
Protons are massive, positively charged nuclear particles. Neutrons are massive, neutrally charged nuclear particles. You are no doubt aware that together, the protons and
neutrons form the nucleus, the massive elemental core, which is held together by the strong nuclear force, a short range force that is greater than the electrostatic force of
repulsion. So much for nucular physics.
Orbiting the nucleus, are various numbers of electrons, fundamental particles of negligible mass, but of opposite electronic charge to the proton. The sharing and transfer of
electrons between atoms, results in chemical bonding, and the formation of ions, and molecules.
Knowledge of the fundamental particles, neutrons, protons, and electrons, thus underpins current understanding of chemistry and physics.

When calculating percent error, what does it mean if I get a negative number for mass?

It means that the experimental mass is greater than the accepted mass. However, mass cannot be negative.
Explanation:
It means that the experimental mass is greater than the accepted mass. However, mass is always positive. If you are calculating percent error, the difference between the experimental value and the accepted value is an absolute value. So even if you get a negative number in your calculation, because it is an absolute value, it is positive.

How many $$1cm^3$$ in a $$10m^2$$ volume?

$$1 cm^3 = 1\times (10^2 . m)^3$$

Explanation:

The centi prefix means $$10^2$$

So, $$1 cm^3 = 1\times (10^2 . m)^3 = (1\times 10^{-2}.m\times 1\times 10^{-2}.m\times 1\times 10^{-2}.m) = 1\times 10^{-6} m^3$$

The conversion factor is $$10^6 cm^3m^{−3}$$

What is the scientific name for Gold?

Gold has symbol $$Au$$ on the periodic table, which states for aurum in Latin. It is a transition element and is element $$79$$ on the periodic table.

It is a solid at room temperature and is one of the least receive elements you can find. Its appearance is a shiny, yellow metal.

$$3/4$$ lbs is equal to how many ounces?

$$12$$ ounces.
Explanation:
As one pound is equal to $$16$$ ounces, $$\frac{3}{4}$$ pound is equal to
$$16*\frac{3}{4}=12$$ ounces.

As sample size increases, what happens to the standard error of M?

Stand error is defined as standard deviation devided by square root of sample size.
$$se = \dfrac{\sigma}{\sqrt n}$$
Therefore, as sample size increases, the standard error decreases

$$10$$ yards is how many inches?

$$360$$ inches.
Explanation:
As $$1$$ yard is equal to $$36$$ inches,
$$10$$ yards are equal to $$10*36=360$$ inches.

What functional groups are found in proteins?

The one functional group that is found in all proteins is the amide group or peptide bond.

In addition, proteins may contain a wide range of functional groups in the sidechains of the amino acid residues:

$$\bullet $$ alcoholic OH groups in serine and threonine

$$\bullet $$ phenolic OH groups in tyrosine

$$\bullet $$ SH groups in cysteine

$$\bullet $$ COO groups in aspartic and glutamic acids

$$\bullet $$ $$ \mathbf{N H}_{2} $$ groups in lysine

$$\bullet $$ CONH2 groups in asparagine and glutamine

$$100$$ yards is equal to how may feet?

$$300$$ feet
Explanation:
Since one yard equals three feet, $$100$$ yards * $$3$$ feet = $$300$$ feet.

$$2$$ pounds equals how many ounces?

$$2lbs*16=32ozs$$
Explanation:
$$1$$ Pound has $$16$$ ounces. $$(1lb=16ozs)$$
Therefore for $$2$$ pounds:
$$2lbs*16=32ozs$$
Conversions between the units in the imperial system
Ounces are used in both weight and capacity.
$$16$$ ounces make $$1$$ pound, but $$16$$ fluid ounces make $$1$$ pint.

$$25 mm$$ is equal to how many $$cm$$?

$$25mm = 2.5cm$$
Explanation:
Using the related conversion
That is $$1cm=10cm$$
$$25mm=(2*10mm)+(\dfrac{1}{2}*10mm)$$
So, we have $$2+\dfrac{1}{2}cm=2\dfrac{1}{2}=2.5cm$$
or using ratio method
$$\dfrac{1cm}{10mm}=\dfrac{x\cdot cm}{25mm}$$ required to calculate value of $$x$$
using cross multiplication:
$$10x=25$$
$$x=\dfrac{25mm}{10mm}=2.5cm$$

Introduction to vectors
Why are vectors important in physics?

Knowledge of vectors is important because many quantities used in physics are vectors. If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect.
Some of the key vector quantities in physics: force, displacement, velocity, and acceleration.An example of the importance of vector addition could be the following:
Two cars are involved in a collision. At the time of the collision car A was travelling at $$ 40 \mathrm{mph}, $$ car $$ \mathrm{B} $$ was travelling at $$ 60 \mathrm{mph} $$. Until I tell you in which directions the cars were travelling you don't know how serious the collision was.
The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of 100 mph!

$$100$$ kilometers is equal to how many miles?

Using the Fibonacci sequence as a rough approximation:
$$100=89+8+3$$ so sum $$55+5+2=62$$
Explanation:
The ratio between miles and kilometres is close to the limiting ratio between successive terms of the Fibonacci sequence.
$$1,1,2,3,5,8,13,21,34,55,89,...$$
So $$5$$ miles is about $$8$$ kilometres, $$21$$ kilometres is about $$13$$ miles, etc.

Is density an intensive or extensive property ?

Density, $$\rho = \dfrac{Mass}{Volume}.$$
For chemists, the most useful units are possibly $$g \,mL^{-1},$$ or $$g\,cm^{-3}.$$ Gases (lower density materials) are reported in $$g \,L^{-1}.$$

Curium has a half life of $$1.5$$ horse, how much of a $$1000g$$ sample remains after : $$1.5$$ hrs? $$3$$ hrs? $$4.5$$ hrs? $$6$$ hrs?

Let's assume the radioactive decay of curium follows first-order kinetics.
Given,
$$t_{\dfrac{1}{2}}=1.5\ hr$$
$$[A]_0=1000 g$$
Recall
$$t_{\dfrac{1}{2}}=\dfrac{\ln (2)}{k} (1)$$
$$\ln \left( \dfrac{|A|_t}{|A|_0}\right)=-kt (2)$$
Let's derive the rate constant,
$$\Rightarrow =\dfrac{\ln (1)}{t_{\dfrac{1}{2}}} \approx 0.46 hr^{-1}$$
and arrange $$(2)$$
$$[A]_t=[A]_0 e^{-kt}$$
Hence,
is how your data would work out
Note: I need a relatively advanced to solve this, lost beginning chemistry students use simple arithmetic,
$$\left( \dfrac{1}{2}\right)^2$$, where $$n=\dfrac{t}{t_{\dfrac{1}{2}}}$$

Derive the formula for Celsius to Fahrenheit?

The Fahrenheit freezing point of water is $$32^{o}F$$ and its boiling point is $$212^{o}F.$$
$$212^{o}F-32^{o}F=180^{o}F$$ between the freezing point and boiling point of water.
The Celsius freezing point of water is $$0^{o}C$$ and its boiling point is $$100^{o}C.$$
$$100^{o}C-0^{o}C=100^{o}C$$ between water's freezing and boiling points.
This results in a ratio for $$C$$ to $$F$$ of $$\dfrac {100}{180}$$ or $$\dfrac {5}{9}$$, and
this results in a ratio for $$F$$ to $$C$$ of $$\dfrac {180}{100}$$ or $$\dfrac {9}{5}.$$
Then $$32^{o}F$$ equal $$0^{o}C,$$ so
The formula for $$^{o}C$$ to $$^{o}F$$ is
$$\left(^{o}C \times \dfrac {9}{5}\right)+32=^{o}F$$

Can displacement be negative?

Displacement can be negative because it defines a change in the position of an object while carefully monitoring its direction.

For our example the object we will consider is you. If you leave your present position and walk down a hallway to get a drink and you walk $$6m$$ to where the drink is located, your displacement is $$6m$$ in the h (hallway) direction. We will take this first trip as the positive direction

Then you walk back towards your original location in the −h the opposite direction. But Surien calls you to her office which is 15m further past your office. It is still in the direction −h opposite the drink location.

Your displacement is now $$6m-6m-15m=-15m$$ in the h direction. Notice both displacements had to be subtracted from the +h of your first trip because both were in the $$-h$$ direction from it.

Then you return to your original location.
Now your total displacement is:

$$6m-6m-15m+15m=0m$$ in the h direction.

Because of positive and negative displacement vectors, you have essentially gone nowhere. You can verify this by looking around. You are back at your original location.

While accomplishing this feat, you have managed to cover a distance of $$6m+6m+15m+15m=42m$$

How do you convert $$36$$ cm/sec to mph ?

$$1\ cm/s = 0,022369362920544023\ mph $$
it's $$0,8052970651395848 $$

Explanation :
But the math is done this way

How to convert cm/ sec to mile/ hour ?

1) Length $$ \rightarrow $$ numerator

$$100.000\ cm $$ which is a km is approximately $$0.62$$ mile

If we divide a mile by $$100.000$$ we find $$1\ cm $$ is approximately $$0,00000621 $$ mile

2) time $$ \rightarrow $$ denominator

$$1$$ hour is $$60$$ min which is $$60 \times 60 = 3600\ sec $$

$$1$$ second is $$\dfrac{1}{3600} $$ hours

$$0,00000621$$ mile divided by $$1/3600 $$ hours gives the magic number of $$0,0223$$

then multiply by $$36$$ to find your answer

$$1/4 lb$$ is how many ounces?

$$\frac{1}{4}lb =4 oz$$.
Explanation:
$$1 lb. =16 oz$$. (consider this a definition)
$$\frac{1lb}{4}=\frac{16oz}{4}=4 oz$$.

Can matter be destroyed?

Matter can neither be created nor destroyed. This is the law of conservation of matter (mass).
One can prove this by performing a simple experiment at home. Fill a plastic bottle with water until it is halfway full. Now weigh it.
For example, it might be $$100\ g.$$
Now put this bottle into a freezer and let the water freeze. You may notice that after the water freezes, the bottle has expanded.
Weigh the bottle again. It will be exactly $$100\ g.$$
The amount of water (matter) stayed the same, but the volume just changed a bit.
We are really using the Law of Conservation of Mass-Energy. It states that the sum of mass and energy must always remain constant in any physical process.
In nuclear reactions, the mass of the products is less than that of the reactants. The lost mass is converted into its equivalent amount of energy according to Einstein's equation, $$E=mc^{2}.$$
The total of mass-energy is the same before and after the reaction. Even though mass is not conserved, mass-energy is conserved.
The Law of Conservation of Mass works in everyday life because the energy changes are so small that we can ignore them.
For further information (incase you need/want to know it), the Law of Conservation of Mass is applied to chemical equation balancing.
For example:
$$H_{2} + O_{2} \longrightarrow H_{2}O$$
Would this equation be balanced? No, because when you start out with a "something", you must end with the same amount of "something". In this case the something is $$O.$$
In this equation written above, you start out with $$2$$ Oxygens and you end with only $$1$$ Oxygen. So it is clear that this equation is unbalanced since it goes against the Law of Conservation of Mass (matter cannot be destroyed nor created).
So what do you do?
You balance it by adding coefficients so there would be the same amount of element on both sides.
$$H_{2} + O_{2} \longrightarrow H_{2}O$$
Now if you look at the amount of each element:
$$H:\ 4$$ on both sides
$$O:\ 2$$ on both sides.
Matter was neither created nor destroyed.

Angular speed of hour hand of a clock in degree per second ?

The hour hand goes $$360^\circ$$ in $$12$$ hours. So we can say that its angular speed is
$$\dfrac{360^\circ}{12\,hours} = \dfrac{30^\circ}{1\,hours}$$
Now I just need to convert units.
$$\dfrac{30^\circ}{1\,hour} \,.\, \dfrac{1\,hour}{3600\,s} = \dfrac{0.00833^\circ}{s}$$

$$1\frac{3}{4}$$ hours equals how many minutes?

$$105$$ minutes
Explanation:
$$1$$ hour is $$60$$ mins
$$\frac{1}{2}$$ hour is $$30$$ mins
$$\frac{1}{4}$$ hour is $$15$$ mins
$$1+\frac{1}{2}+\frac{1}{4}=1\frac{3}{4}$$
$$60+30+15=105$$ minutes.

$$1 cm$$ equals how many meters?

There are $$100 cm$$ in a meter and hence $$1 cm$$ equals $$\frac{1}{100}$$ or $$0.01$$ meters.

$$1 kg$$ is equal to how many pounds?

Approximately $$2.2lb$$
Explanation:
$$1$$ (international) pound is exactly $$453.59237$$ grams, which is $$0.45359237kg$$.
So, $$1kg=\frac{1}{0.45359237}\approx 2.2046lb$$

How force is a vector quantity ?

Force, $$F = mg $$ is a vector quantity because acceleration due to gravity , $$g$$, is a vector quantity.

Explanation :

$$F = mg $$

Where $$m$$ is the mass (in kilograms) of the object in question and $$g$$ is acceleration due to gravity. Mass is a scalar quantity; mass has no dependence on direction whatsoever.

$$g$$ is a vector, as acceleration due to gravity (in $$ \dfrac{m}{s^2} $$) is directed downwards.

Since $$g$$ is a vector $$F$$ is also a vector, because $$mg$$ is affected by the downward direction of $$g$$

If Earth has a mass of $$5.972 * 10^{24} kg$$ and Mars has a mass of $$6.39 * 10^{23} kg$$, and the distance between them is $$225 * 10^6 m$$, with what force does Earth pull on Mars?

$$5.03*10^{21}$$ Newtons
Explanation:
Newton's law of gravitation states that force of gravity $$F$$ between two objects of mass $$m_1$$ and $$m_2$$ at a distance of $$r$$ from each other is given by
$$F=G\dfrac{m_{1}+m_{2}}{r^{2}}$$, where $$G$$ is gravitational constant whose value is $$6.67×10^{−11}$$ $$N\dfrac{m^{2}}{kg^{2}}$$
Here the objects are Mars, whose mass is $$6.39*10^{23} kg$$. and Earth with mass $$5.972*10^{24} kg$$. As the distance between two is $$225*10^6m$$.
Then Earth pulls Mars with a force $$F$$, where
$$F=6.67*10^{-11}\dfrac{6.39*10^{23}*5.972*10^{24}}{(225*10^{6})^{2}}$$
$$=\dfrac{6.67*6.39*5.927}{225^{2}}*10^(-11+23+24-12)$$
$$=0.00503*10^{24}$$
$$=5.03*10^{21}$$ Newtons

If the speed of light is $$3×10^8$$, determine the distance it takes in $$1$$ light year. Report your results in $$km$$ and in $$m$$.

We know that

$$c$$ = the speed of light = $$3.0×10^8m s^{−1}$$

Explanation:

And so we multiply this by one year to get the distance travelled:

$$3.0×10^8ms^{−1}×1 year×365 days\, year^{-1}$$$$×24hours\, day^{−1}×60minutes\,hour^{−1}$$

$$×60seconds\,minute^{−1}$$

$$\equiv 9.5×10^{15} m$$

Convert $$18\ km/h$$ to $$m/s$$? Answers with steps

$$18\ km/h=5\ m/s$$
Explanation:
To convert $$km/h$$ to $$m/s$$ we need to first convert the units.
So $$1\ km/h=\dfrac{1000}{60.60}$$
upon solving this we get $$1\ km/h=\dfrac{5}{18}m/s$$
now multiply the $$km/h$$ into $$\dfrac{5}{18}$$
you will get the answer as $$5\ m/s$$

What is the $$SI$$ unit of acceleration?

the SI unit of acceleration is $$m/s^2 $$ (meter per sec square)

$$acc=$$ change in velocity / time

Why is angular momentum perpendicular ?

Answer
In simple terms angular momentum is just the rotation of any object.
The formula of angular momentum is:-
L= mrv
This formula possess cross product of "r" with "v" i.e. "r x v" (x denotes cross product)
This particular relation denotes that angular momentum is perpendicular to the radial vector.

Can average rate of change be negative?

Yes.
Remember that the rate of change could be things like acceleration, not just speed.
Even through speed itself is a scalar and cannot be negative, you can have a negative velocity by adding direction (which makes it a vector)
Also, if your speed is decreasing,you decelerate, which is another word for negative acceleration.
For example,let's say you had the function $$\sin (x)$$ to show the speed in respect to time.
grapgh $$\left\{\sin x [-10,10,-5,5]\right\}$$
We can see that your speed increases until it reaches a certain point. There , we see that it decreases to a certain point. The decrease represents negative rate of change.

What is $$0.25$$ kilometers expressed in centimeters?

$$0.25$$ Kilometers have $$25,000$$ centemeters.
Each kilometer has $$1000$$ meters and each meter has $$100$$ centimeters.
Hence each kilometer has $$1000\times 100 =100,000$$ centemeter, and
$$0.25$$ kilometer have $$100,000\times 0.25=25,000$$ centimeters.

Can a rate of change be negative?

Yes, it can, if a quantity is decreasing, then its rates of change will be negative

Convert $$22\ m/s^{2}$$ to $$km/m^{2}$$?

$$79.2\ km/\min^{2}$$
Explanation:
$$\Rightarrow 22\dfrac{m}{s^{2}}$$
Convert $$m$$ to $$km$$ as we know that $$1\ km=1000\ m$$
$$\Rightarrow 22\dfrac{m}{s^{2}}\times \dfrac{1\ km}{1000\ m}$$
$$\Rightarrow \dfrac{22}{1000}\dfrac{km}{s^{2}}$$
Convert $$s^{2}$$ to $$\min^{2}$$ as we know that $$(1\ \min)^{2}=(60\ s)^{2}$$
$$\Rightarrow \dfrac{22}{1000}\dfrac{km}{s^{2}}\times \dfrac{3600\ s^{2}}{1\ \min^{2}}$$
$$\Rightarrow \dfrac{22}{1000}\times 3600\dfrac{km}{\min^{2}}$$
$$\Rightarrow \dfrac{22}{10\times 100}\times 36\times 100\dfrac{km}{\min^{2}}$$
$$\Rightarrow \dfrac{22\times 36}{10}\dfrac{km}{\min^{2}}$$
$$\Rightarrow \dfrac{797}{10}\dfrac{km}{\min^{2}}$$
$$\Rightarrow 79.2\dfrac{km}{\min^{2}}$$

How many significant figures are in the measurement $$0.020\ km $$ ?

Two significant figures.

Explanation :

$$0.020 $$ has two significant figures.

The $$2$$ is significant because all non-zero numbers are significant.

The second $$0$$ is significant because all zeros at the end of a decimal are significant.

The other zeros are not significant, because they are just place holders.

How many microliters are in $$41.0\ mL $$ ?

$$41000$$ microliter

Explanation :

$$1\ ml = 1000$$ microliter

Using this equality, we will make two conversion factors.

$$1\ ml /1000 $$ microliter or $$1000$$ microliter / $$1\ ml $$

$$41\ ml \times $$ ($$1000$$ microliter / $$1\ ml$$)

$$41000$$ microliter

What is the difference uniform and constant velocity ?Is acceleration zero in case of both constant and uniform velocity?

UNIFORM VELOCITY: when an object is moving in a straight line, without any acceleration. No change in speed or direction is experienced.

CONSTANT VELOCITY: when the speed of an object has not changed even though the object may have experienced a change in direction (zero acceleration).

To answer the second half of your question: Yes, acceleration is zero for both uniform and constant velocity based upon these two definitions.

The density of a sample of aluminum is $$2.70 g/cm^3$$. You submerse a sample of aluminum in water, and the volume of the water rises $$1.3 L$$ ($$1.3 L$$ is displaced by the aluminum). Using the correct number of significant figures, what is the mass of the sample?

The mass of aluminum is $$3500 g$$, rounded to two significant figures.

Explanation:

Density is mass per unit of volume.

$$density=\frac{mass}{volume}$$

The displaced volume of water is the volume of the aluminum sample.

Since the given density is in $$g/cm^3$$, the unit for the volume of water needs to be converted to $$cm^3$$.

$$1 L=1000 mL$$

$$1 mL=1 cm^3$$

$$1.3L*\frac{1000mL}{1L}*\frac{1cm^3}{1mL}=1300cm^3$$

In order to determine the mass of an object when its density and volume are known, the equation needs to be rearranged to isolate mass

mass = density * volume

Substitute the given density and volume into the equation and solve.

$$mass=2.70\frac{g}{cm^3}*1300cm^3=3510g=3500g$$ rounded to two significant figures.

What values of $$m_l$$ are permitted for an electron with $$l=3$$ ?

Answer
Seven

Explanation :

The values that the magnetic quantum number can take depend on the value of the angular momentum quantum number as described by the relation
$$m_{l} = +l\ to -l$$

In your case, you have
$$ l = 3 $$
In your case, you have
$$m_{l} = \left \{ -3, -2, -1, 0,1, 2,3 \right \}$$

The fact that the magnetic quantum number can take 7 possible values for an f subshell tells you that this subshell holds a total of 7 orbitals, each described by a value of the magnetic quantum number.

1842419_1888459_ans_07fec2f9bd0c4f91a1c4d5aae3c49fdb.PNG

Which Lewis electron-dot diagram is correct for a $$ S^{2 -}$$ ion ?

Explanation :
Sulphur belongs to group 16. It has 6 valence electrons.

A 2 charge indicates that the atom has gained 2 electrons. This makes the total number of valence electrons equal to 8.

1842355_1888416_ans_5e2c389c68584c7385bedf3a68328281.jpeg

Explain why displacement is a vector quantity?

Displacement is defined as the final distance-vector minus the initial distance vector.

Let's say you're driving to work in the morning. You first drive north for $$5$$ miles, and then drive east for another $$5$$ miles.

Now let's say that when you get there, you take out a street map. If you were to draw a straight line starting at your house and ending at your workplace, that line would be your displacement vector. That straight line would be $$\sqrt{50}$$ miles long, (use the Pythagorean theorem) and it would be pointing northeast. Since the line has a direction, it needs to be a vector quantity. If it weren't a vector quantity, you wouldn't be able to draw it on a map at all, because it would just be a number.

Another reason why displacement needs to be a vector is that it's defined as the subtraction of two vectors, and a vector minus another vector is always a vector.

State the CGS and SI unit of surface tension.

Surface Tension $$=\dfrac{force}{length}$$
SI unit = $$N/m=Kg/s^2$$
CGS unit = $$g/s^2$$

A heavy of mass m hangs between two fixed points A and B at an angle 0 with the horizontal as shown in the figure . What is the tension at the lowest point in the string .

Answer
$$ 2 T \sin \theta = M g $$
$$ T \cos \theta = T_{1} = T_{2} = \left ( \dfrac{M g}{2 \sin \theta} \right ) \cos \theta $$
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A bob of mass $$m$$ is suspended by a light string of length $$L$$. It it imparted a horizontal velocity $${v}_{0}$$ at the lowest point $$A$$ such that it completes a semi-circular trajectory in the vertical pane with the string becoming slack only on reaching the topmost point $$C$$. Obtain an expression for (i) $${v}_{a}$$; (ii) the speeds at points $$B$$ and $$C$$ (iii) the ratio of the kinetic energies $$({K}_{B}/{K}_{C})$$ at $$B$$ and $$C$$. Comment on the nature of the trajectory of the bob after it reaches the point $$C$$.

(i) Let the particle at the top most point be $$u$$ m/s
As the partice is in vertical circular motion
so the centripetal acceleration is being provided by $$mg$$ alone as string has slacked os
$$mg=\cfrac{m{u}^{2}}{L}$$
So $$u=\sqrt {gL}$$ at the top most point (when string slacks) speed of $$C$$
Now applying the energy conservation between $$A$$ and $$C$$
we have
$$\cfrac { m{ v }_{ 0 }^{ 2 } }{ 2 } +0=\cfrac { m{ u }_{ }^{ 2 } }{ 2 } +mg(2)$$
$$\cfrac { m{ v }_{ 0 }^{ 2 } }{ 2 } =\cfrac { m{ u }_{ }^{ 2 } }{ 2 } +mg(2L)$$
so $${v}_{0}=\sqrt {5gL}$$...speed of A
(ii) for point $$C$$
applying conservation of energy
$$\cfrac { m{ v }_{ 0 }^{ 2 } }{ 2 } +0=\cfrac { m{ u }_{ B }^{ 2 } }{ 2 } +mg(L)$$
$$\cfrac { m{ v }_{ 0 }^{ 2 } }{ 2 } =\cfrac { m{ u }_{ B }^{ 2 } }{ 2 } +mg(L)$$
$${u}_{B}=\sqrt{3gL}$$....speed of $$B$$
(iii) Ratio of kinetic energy will be
$$\cfrac{K{E}_{B}}{K{E}_{C}}=\cfrac{\cfrac { m{ u }_{ B }^{ 2 } }{ 2 } }{\cfrac { m{ u }_{ }^{ 2 } }{ 2 } }$$
$$=\cfrac{2gL}{gL}=\cfrac{2}{1}$$
The object will complete the circular path and its trajectory will be circular as string has slacked at the highest point

A sample of sulfur hexafluoride gas occupies $$8.62 \,L$$ at 221 degrees Celsius. Assuming that the pressure remains constant, what temperature (in Celsius) is needed to reduce the volume to $$2.61\, L$$?

Your variables, L and $$^\circ C$$ represent volume and temperature. The gas law that involves the relationship between the volume of a gas and its temperature is

Charles' law states that the volume of a given amount of gas held at constant pressure is directly proportional to its Kelvin temperature. This means that as the temperature increases, the volume also increases, and vice-versa. The equation used to solve gas problems involving Charles' law is:

$$\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$$

where the temperatures must be in Kelvins. Add $$273.15$$ to the Celsius temperature to get the Kelvin temperature.

Organize your data:

Known

$$V_{1} = 8.62\,L$$

$$T_{1} = 221^\circ C + 273.15 = 494\,K$$

$$V_{2} = 2.61\,L$$

Unknown

$$T_{2} = ?$$

Solution

Rearrange the equation given above to isolate $$T_{2}.$$ Insert your data into the new equation and solve.

$$T_{2} = \dfrac{V_2T_1}{V_1}$$

$$T_{2} = \dfrac{2.61\,L \times 494\,K}{8.62\,L} = 150\,K$$

To convert from Kelvins to degrees Celsius, subtract $$273.15$$ from the Kelvin temperature.

$$150\,K - 273.15 = -123^\circ C$$

A body of mass gm is attached to a spring constant k = 100 N/m and it is performing damped oscilliations . If damping constant is 0 .2 and driving force is F = F (ot) , where F = 20 N . Find the amplitude of oscillation at resonance

Answer
$$ B = \dfrac{200}{2} $$
$$ \omega = \sqrt{\dfrac{1000}{6}} $$
$$ \dfrac{1}{\omega} = \dfrac{\sqrt{6}}{100} $$
$$ = 10\sqrt{\dfrac{6}{10}} $$ = 7.7 m
$$ m \dfrac{d^{2}x}{dy^{2}} = F_{R} - F_{R} + F $$
So$$ M \dfrac{d^{2}x}{dt^{2}} + b \dfrac{dy}{dt} + ky = F_{o}\cos \omega t $$
$$ \beta = \dfrac{Fo}{b \omega_{o}} = \dfrac{20}{0.2 \times \omega o}$$

$$\beta = \dfrac{200}{\omega_o}$$

What is the temperature $$-34^oC$$ expressed in Kelvin?

$$239.15\ K$$

Explanation:

$$273.15\ K=0^oC$$

So to convert from $$^oC$$ to $$K$$ add $$+273.15$$ to $$^oC$$ to convert to $$K$$

$$+273.15+(-34)=+239.15 K$$

The Mohs scale is a measure of what of a mineral?

Hardness.

Explanation:

Mohs scale is a scale of $$1$$ to $$10$$ base on the hardness of a mineral. Talc would be a $$1$$ and diamond is a $$10$$.

The scale is not linear however, as the differences between numbers is not uniform. For example, Calcite (3) is 3 times harder than Gypsum (2) but Fluorite (4) is only about twice as hard as Calcite.

State Kepler's law of motion :

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A particle is thrown from the top of a building of height $$50\ m$$ with a velocity $$30\ m/s$$ at an angle of $$30^{th}$$ above the horizontal then the distance from the base building to the point where the particle hits the ground is

We know that

$$t_1 =\dfrac {24\sin \theta}{y}$$

$$=\dfrac {2\times 30\times \sin 30^o}{y}$$

$$=\dfrac {60}{10}\times \dfrac {1}{2}=3$$

$$t_2 =5==ut+\dfrac {1}{2}at^2$$

$$t_2 =2\sec $$

$$t=t_1 +t_2 =5\ \sec$$

$$x=4\cos 30^o \times t$$

$$=30\times \dfrac {\sqrt 3}{2}\times 5$$

$$=75\sqrt 3\ m$$

Express for time period of a simple pendulum by dimensional analysis.

The time period of simple pendulum depends onm length of spring (s) and acceleration due to gravity (g)
$$[l]$$ = length = $$[L]$$
$$[g]$$ = acceleration = $$[LT^{-3}]$$
$$[T]$$ = Time period = $$[T]$$
Let $$[T]\propto [L]^a[LT^{-2}]^6$$
comparing LHS and RHS
$$a+b=0,a=-b$$
$$-2b=1,b=-1/2$$
So, $$a=-1/2$$
$$T\propto (8)^{1/2}(g)^{-1/2}$$
$$T\propto \sqrt{\frac{l}{g}}$$
$$T=211\sqrt{\frac{l}{g}}$$
$$2:11$$

Define angular velocity. Show that the centripetal force on a particle undergoing uniform circular motion is $$- m\omega^2 \overrightarrow{r}$$.

The rate of change of angular position of the rotating body.

$$\text{Explanation}:$$

Angular velocity applies to those objects that move along a circular path. Angular velocity is measured in radian/second or angle/seconds. Similarly, the rate of change of angular velocity is angular acceleration.

Now we know that if an object is moving in a circular path with constant speed still its velocity will be changing as its direction is changing at every point. It means that it is accelerating and it is inward acceleration. This inward acceleration is called centripetal acceleration.

$$a(c)=\dfrac{ V^2}{r}$$ where $$V$$ is the magnitude of the velocity and $$r$$ is the radius of the circular path of motion.

$$\omega$$ represents angular velocity and is linked with the linear speed with the formula;

$$V=r\omega.$$

centripetal acceleration will now be$$ \dfrac{(\omega r)^2}{r}$$

$$a(c)=r\omega $$

we know the$$ F =ma$$

centripetal force, therefore is equal to m into $$a(c) =-mr\omega^2$$.

$$10$$ divisions of vernier scale.

Actual diameter:
$$=MSD +(0.1)*(0.2)$$
$$=1.30+0.02$$
$$=1.32$$

Obtain the dimension of power and force.

$$F = ma$$
$$F = M . L T^{-2}$$
$$P = F. V = MLT^{-2} . LT^{-2}$$
$$= ML^2 T^{-3}$$

In a boat race on still water the speed of one boat is to that of another is $$4 : 7$$. When the number of rowers in each boat is increased by $$5$$. Their speeds are found to be as $$13:19$$. Assuming that the speed of each boat is proportional to numbers of rowers in it. Find the original number of rowers in each boat.

Let number of rowers in $$B_1 = x$$
$$B_2 = y$$
given $$\frac{x}{y} = \frac{4}{7}$$
$$x = \frac{4}{7}y$$$$\frac{x + 5}{y + 5} = \frac{13}{19}$$
$$\frac{\frac{4}{7}y + 5}{y + 5} = \frac{13}{19}$$
$$\frac{76}{7}y + 95 = 13 y + 65$$
$$13y - \frac{76y}{7} = 30$$
$$\frac{91y - 76y}{7} = 30$$
$$15 y = 30 \times 7$$
$$y = 14$$ $$x = 8$$

What are derived units ?

Derived units are the combination of base unit to express a physical quantity. The combination will contain base unit in multiplied or divided form.

For ex:

Derived unit of velocity is $$m/s $$

It is an SI unit of measurement.

SI unit of Force = newton (derived units)

$$1\ N = 1\ kg m/s^{2} $$

A particle is moving eastwards with a speed of 6m/s. After 6 s, the particle is found to be moving with same speed in a direction $$60^{\circ}$$ north of east. The magnitude of average acceleration in this interval of time is

$$v_i = 6\hat{i}$$
$$v_f = 3\hat{i} + 3\sqrt{3}\hat{j}$$
$$\Delta\vec{v} = \vec{v_f} - \vec{v_i}$$
$$\Delta\vec{v} = -3\hat{i} + 3\sqrt{3}\hat{j}$$
$$|\Delta\vec{v}| = \sqrt{9 + 27} = 6 m/s$$
$$|\vec{a}| = \dfrac{|\Delta\vec{v}|}{t} = \dfrac{6}{6}$$
$$|<\vec{a}>| = 1 m/s^2$$

Block $$A$$ in the diagram below has a mass of $$1.81\ kg$$ and block $$B$$ has a mass of $$3.36\ kg$$. The coefficient static friction between all the surface is $$0.25$$ Blocks $$A$$ and $$B$$ are connected by a light flexible cord passing around a small frictionless pulley that is fastened to a wall. The cord will not stretch when it is pulled as its ends.

$$p-f-T=m_Ba$$
$$T-f=m_A a$$
$$p-2f=(m_A+m_B)a$$
$$\therefore P=(m_A+m_B)a+2f$$
$$=5.44a+2 \times 7.24$$
$$P=5.44a+14.48$$
$$T=m_A a+f=1.81 a+7.24$$
$$\therefore p-f-T=m_Ba$$
$$5.44 a-7.24-1.81 a-7.24=3.63 \times a$$
$$N_{12}+m_B g=N_g$$
$$m_A g+m_B g=N_g$$
$$f_g= \mu N_g= \mu (m_A+m_B)g$$
$$=0.25(1.81+3.63)\times 10$$
$$4 \times (1.81+3.63)$$
$$=21.76 \ N$$
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Figure (9-E11) shows a small block of mass m which is started with a speed v on the horizontal part of the bigger block of mass M placed on a horizontal floor. The curved part of the surface shown in semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

As there is no external force on system so momentum is conserved.
$$mv + M(o) = (m + M)V$$
$$V = \dfrac{mv}{m + M}$$ (V = common velocity)

The distance travelled by an object in time $$ (100 \pm 1) s $$ is $$(5.2\pm 0.1)m.$$ What is the speed and its error?

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A beaker of radius $$15\ cm$$ is filled with a liquid of surface tension $$0.075\ N/m$$. Force across an imaginary diameter on the surface of the liquid is $$\dfrac 9x \times 10^{-2}N$$. Find $$x$$.

$$F=S \times l$$
$$=0.075 \times 2\times 15 \times 10^{-2}$$
$$=2.25\times 10^{-2}$$
Now $$2.25 \times 10^{-2}=\dfrac {9}{x}\times 10^{-2}$$
$$\therefore x=\dfrac {9}{2.25}=4$$

A . bullet fired from a gun with a velocity of $$ 140ms^{-1} $$ strikes the ground at the same level as the gun at a distance of 1 km . Find the angle of inclination with the horizontal at which the bullet is fired .Take $$ g = 9.8ms^{-2} $$.

Answer
$$ 1000 = \dfrac{U^{2} \sin ( 2 \theta)}{g} $$
$$ 1000 = \dfrac{140\times 140}{98} \sin (2 \theta) $$
$$ \dfrac{9800}{140 \times 140} = sin (2 \theta) $$
$$ \sin ( 2 \theta) \approx .5 $$
$$ 2 \theta = 30^{o} $$
$$ \theta = 15^{o} $$

What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106m.)

From Newton’s law of gravitation, we know that the force of attraction between the bodies is given by

NCERT Solutions for Class 9 Science - Chapter 10 Image 5

Two concentric shells of different masses $$m_1$$ and $$m_2$$ are having a sliding particle of mass $$m$$. The forces on the particle at positions $$I,II$$ and $$III$$ are respectively.

$$E_{III}=\frac{Gm_2}{r_3}+\frac{Gm_1}{r_2}$$

$$E_{II}-\frac{Gm_2}{r_2}+\frac{Gm_1}{r_2}$$

$$E_I=\frac{Gm_1}{r_1}+\frac{Gm_2}{r_1}=\frac{G(m_1+m_2)}{r_1}$$

$$E_{III}:E_{II}:E_I=E_{III}:E_{II}:E_{I}$$

$$E_{III}=0$$

$$\because$$ inside a shell

$$E_{II}=\frac{Gm_2}{r_2^2}$$

$$E_I=\frac{G(m_1+m_2)}{r_1^2}$$

$$F_1:F_2:F_3-E_1:E_2:E_3$$

$$=\frac{G(m_1+m_2)}{r_1^2}:\frac{Gm_2m}{r_2^2}:0$$

In the arrangement shown in figure, the mass of the body $$A$$ is $$n=4$$ times that of the body $$B$$. The height $$h=20cm$$. At a certain instant, the body $$B$$ is released and the system is set in motion. What is the maximum height (in cm) the body $$B$$ will go up? Assume enough space above $$B$$ and $$A$$ sticks to ground. ($$A$$ and $$B$$ are of small size) $$(g=10m/s^2)$$.

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(a) A $$2Kg$$ block situated on a smooth fixed inclined is connected to a string of negligible mass, with spring constant $$k=100Nm^{-1}$$, via a friction-less pulley. The block is released from rest when the spring is unstretched. How far does the block move down the incline before coming (momentarily) to rest? What is its acceleration at its lowest point?
(b) The experiment is repeated on a rough incline. If the block is observed to move $$0.20m$$ down along the incline before it comes to instantaneous rest,calculate the coefficient of kinetic friction.

By work energy theorem

$$W$$ by all forces = $$\Delta KE$$

$$=1-\frac{1}{2}k\Delta x^2+mg\sin37$$

$$\Delta x=0-0$$

$$\Delta x=\frac{2mg\sin37^0}{k}$$

$$\Delta x=\frac{2*2*10*5}{100}$$

$$\Delta x=0.24m$$

At this point $$T-mg\sin37^0=ma$$

also $$T=k\Delta x$$

$$k\Delta x-mg\sin37^0=ma$$

$$100*0.24-2*10*\frac{3}{5}=2*a$$

$$24-12=2*a$$

$$a=6m/s^2$$

A wheel is rotating with angular velocity $$2rad/s$$. It is subjected to a uniform angular acceleration $$2.0rad/s^2$$
(a) What angular velocity does the wheel acquire after $$10s$$?
(b) How many revolutions will it make in this time interval?

$$w=w_0+\alpha t=2+2*10=22rad/s$$

$$\theta=w_0t+\frac{1}{2}\alpha t^2=2*10+\frac{1}{2}*2*10*10=120rad$$

$$2\pi\rightarrow 1rad$$

$$120\rightarrow \frac{120}{2\pi}\cong 19rad$$

A stone weighting $$0.5kg$$ tied to a rope of length $$0.5m$$ revolves along a circular path in a vertical plane. The tension of the rope at the bottom point of the circle is $$45$$ newton. To what height will the stone rise if the rope breaks at the moment when the velocity is directed upwards? $$(g=10m/s^)$$

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A bomb explodes into three fragments of equal masses. The two fragments have linear momentum as $$-3p\hat{i}$$ and $$2p\hat{j}$$. What will be the magnitude of momentum of third fragment?

Initial momentum = $$0$$

By law of conservation of momentum

Final momentum shall be zero.

$$-3p\hat{i}+2p\hat{j}+x=0$$

$$x=3p\hat{i}-2p\hat{j}$$

Magnitude of third fragnment is P√13

A flywheel of radius $$ 0.4m $$, mass $$ 10kg $$ Initially at rest after one minute Increase its speed from $$ 0 $$ to $$ 300 rpm $$ then the torque on the flywheel is :-

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Calculate the mass of $$ 2.5 $$ g atom oxygen.

2.5 g atom oxygen means 2.5 mole oxygen

Mass of 2.5 g atoms of oxygen = 16 x 2.5 = 40 g

A particle of mass 1 kg is moving on a circular path of radius 1 m. Its kinetic energy is $$ K = bt^{4}, $$ where $$ b = 1 J/s. $$ The force acting on the particle at $$ t = 1s $$ is $$ (2x)^{1/2} m/s^{2}.$$ Find the value of $$ x $$.

$$ Mass, \;m = 1 \;kg $$

$$ Radius, \;r = 1 \;m $$

$$ KE = bt^{4} $$

$$ = t^{4} $$

$$ \frac{1}{2} mv^{2} = t^{4} $$

$$ \frac{1}{2} \times 1 v^{2} = 1^{4} $$

$$ v^{2} = 2 $$

$$ v = \sqrt{2} m/s $$

$$ a = \frac{v^{2}}{r} = {(\sqrt{2})^{2}}{1} = 2 $$

$$ F = 2 \Rightarrow (2x)^{\frac{1}{2}} = 2 $$

$$ \Rightarrow 2x = 4 $$

$$ x = 2 $$

The masses of two bodies are measured to be $$ 15 . 7 \pm 0.2 kg $$ and $$ 27.3 \pm 0.3 $$ kg What is the total mass of the two and the error in it ?

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A painter is raising himself and the crate on which he stands with an acceleration of $$5m/s^2$$ by a mass-less rope and pulley arrangement. Mass of the painter is $$100kg$$ and that of the crate is $$50kg$$. If $$g=10m/s^2$$, then the tension

Tension = $$T$$

for whole system as

$$T=(100+50)g=(150)a$$

$$T=150g+150a$$

$$T=150*10+150+5$$

$$=1500+750$$

$$=2250$$

Now, for max

$$T-N=mg+ma$$

$$2250=100*15$$

$$T-1500$$

$$=2250-750=750$$

Therefore tension = 750 N

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State and explain Bohr's model with limitations.

Electrons revolve around the nucleus in a fixed circular path termed "orbits" or "shell" or "energy level", Every circular orbit have a certain amount of fixed energy and these circular orbits were termed orbits shells.

A body of mass $$2\ kg$$ is lying on a rough inclined plane od inclination $$30^o$$. Find the magnitude of the force parallel to the incline needed to make the block move
Up the incline

$$F=mg \sin \theta +\mu mg \cos \theta$$
$$=mg (\sin 30+0.2 \times \cos 30^o)$$
$$=30(1/2 +0.2\times \sqrt 3 /2)=30(0.5+0.1732)$$
$$=20\times 01.6732$$
$$=13.464$$
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A body of mass $$2\ kg$$ is lying on a rough inclined plane od inclination $$30^o$$. Find the magnitude of the force parallel to the incline needed to make the block move
Down incline.
Coefficient of static friction $$=0.2$$

$$F=\mu g \cos \theta -mg \sin \theta$$
$$=mg \left(0.2\times \dfrac {\sqrt 3}{2}-\dfrac 12 \right)$$
$$=20(0.1732-0.5)\to$$ Negative
$$\therefore $$ We dont need $$fx$$ apply force.
$$t$$ will shell slide down $$\Rightarrow F=0$$
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Three forces of magnitude $$5N,12N$$ and $$13N$$ acting simultaneously on a particle to keep it in equilibrium. The angle between the force $$5N$$ and $$13N$$ is

From figure we have

$$\tan \theta =\dfrac{12}{5}$$

$$\sin \phi =\dfrac{5}{13}=\sin 23^o$$

$$\phi =23^o$$

$$\theta =90-23=67^o$$

so $$\alpha =23+90$$

$$=113^o$$

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Three bodies of equal masses are placed at $$(0 , 0) , (a , 0) $$ and at $$ \left (\dfrac{a}{2} , \dfrac{a \sqrt{3}}{2} \right ) $$.
Find out the coordinates of center of mass.

We know that

Center of mass is given by

$$X_{cm} = \dfrac{m_{1} x_{1} + m_2x_{2} + m_3x_{3}}{m_1+m_2+m_3} $$

$$ = \dfrac{m \times 0 + m \times a + m \times a/2}{3m} $$

$$ = \dfrac{3m}{2 \times 3m} = \dfrac{a}{2} $$

Similarly of y coordinates

$$y_{cm} = \dfrac{m y_{1} + m y_{2} + m y_{3}}{3m} $$

$$ = \dfrac{m \times 0 + m \times 0 + m \times a \sqrt{3} /2}{3m} $$

$$ = \dfrac{a \sqrt{3}}{3 \times 2} $$

$$ = \dfrac{a \sqrt{3}}{6} $$

COM $$ = \dfrac{a}{2} , \dfrac{a \sqrt{3}}{6} $$

$$Wb/\Omega$$ unit is representing which physical quantity?

$$V = IR$$

$$\dfrac {V}{I}$$

$$\dfrac {Weber}{\Omega} = \dfrac {kg\ m^{2}s^{-2} \triangle^{-1}}{kg\ m^{2}s^{-3} \triangle^{-2}}$$

$$= A \times S$$

$$=$$ Its charge

Because charge = current ×time

A small body of mass $$m$$ is located on a horizontal plane at the point $$O$$. The body acquires a horizontal velocity $$v_{0}$$. Find the mean power developed by the friction force during the whole time of motion, if the friction coefficient $$k = 0.27, m = 1.0\ kg$$, and $$v_{0} = 1.5\ m/s$$.

According to question

We know that

$$N = mg$$

$$f = kN

$$f = kmg$$

$$\because ma = f$$

$$a = kg$$

So, $$a = 0.27\times 10$$

$$[a = 2.7\ m/s^{2}]$$

$$\because v_{f} = 1.5 m/s^{2}$$

$$v_{i} = 0\ m/s$$

$$v_{f} = v_{i} + at$$

$$1.s = 0 + 2.7 t$$

$$t = 0.565$$

$$w = ∆K.E = \dfrac {1}{2} mv_{f}^{2} - \dfrac {1}{2} mv_{i}^{2}$$

$$w = \dfrac {1}{2}×1\times (1.5)^{2} - 0$$

$$w = 1.125g$$

So, $$power = \dfrac {w}{t} = \dfrac {1.125}{0.56}$$

$$= 2watt$$.

What is meant by unit of physical quantity.

The quantities that can be measured are called as physical quantity . By measuring the quantity we can define the properties associated with it.

Unit is a basic standard used for measured of these physical quantity and is a accepted internationally.

A 50 kg boy runs at a speed of 10 m/s and jumps onto a cart as shown in the fig . The cart is initially at rest . If the speed of the cart with the boy on it is 2.50 m /s , what is the mass of the cart ?

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If a point is moving under uniform acceleration covers successive equal distance in time $$t_1, t_2$$ and $$t_3$$, then the correct relation between $$t_1, t_2$$ and $$t_3$$ is

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What is unit vector? Explain it.

Unit vector:
It is the vector having magnitude "one"
$$\dfrac {\vec a}{|a|}$$

Two block of mass 4 kg and 6 kg an attach in a vertical with the help of ideal strings . Find tension of point A and B

Answer
$$T_A = 4 g + T_B$$ .......(1)
$$T _B = 6g$$
$$ T _{B} = 6 \times 10 = 60 N $$

From equation 1st

$$ T_{A} = 4 \times 10 + 60 $$
$$ T_{A} = 100 N $$

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In the following fig $$ r_{1}$$ and $$r_{2} $$ are 10 cm and 20 cm.respectively . If the moment of inertia of the wheel a $$ 1500\ kg-m^{2} $$v , then determine its angular acceleration :-

Given:

$$ r_{1}=10\ cm\\r_2=20\ cm\\I=1500\ kg-m^{2} $$

Torques $$\tau_r=I\alpha$$

$$ 5 \times r_{2} + 10 r_{2} - 15 \times r_{1} = I\alpha $$

$$ 5 \times 0 .2 + 10 \times 0 .2 - 15 \times 0 .1 = 1500\alpha $$

$$ 1500 \alpha = 1 + 2 - 1.5 = 1.5 $$

$$ \alpha = \dfrac{1.5}{1500} = 0.001 $$

A bullet is fired with speed 50 m /s at $$45^{o} $$ angle. Find the height of the bullet above the point of projection when its direction of motion makes angle $$ 30^{o} $$ with the horizontal

Answer
Speed = 50 m/s
$$ 50 \cos 45^{o} = v \cos 30^{o} $$

$$ v = \dfrac{50 \times 1.414}{1 .732} $$

$$ v = 40 .82 m/s $$

$$ v^{2} = u^{2} - 2 gh $$

$$ v^{2} \sin^{2} 30 = (50)^{2} \sin^{2} 45 - 2 \times 10 \times h $$

$$ h = 41 . 66 m $$

$$ h = \dfrac{125}{3} m $$

Determine the minimum coefficient of friction between a thin rod and a floor at which a person can slowly lift the rod from the floor , without slipping to the vertical position applying at its end a force always perpendicular to its length

Consider a general position
In n direction $$ f -F sin \theta = 0 $$
$$ f = F sin \theta $$
In y direction $$ F cos \theta + n = mg $$
$$ T-A = 0 \Rightarrow F l - n y \frac {1}{2} cos \theta = 0 $$
$$ F = \frac { mg cos \theta }{ 2 } $$

For ro supplying
$$ f < MN \Rightarrow M \Rightarrow \frac {f}{N} $$
$$ M = \frac { F sin \theta }{mg - f cos \theta } M \ge \frac { sin \theta - cos \theta }{ 2 - cos^2 \theta } $$
$$ M min = \frac { sin^2 \theta cos \theta }{ 2 - cos^2 \theta } = \frac {1}{ 2 \sqrt {2} } $$
1874054_1901249_ans_90d0d956b26a4b318bf9bb5b46d52a97.png

1874054_1901249_ans_90d0d956b26a4b318bf9bb5b46d52a97.png

Establish the relationship between related physical quantities using the dimensional analysis ?

Principle of Homogeneity

$$ [M]^{a} [L]^{b} [T]^{c} = [M]^{x} [L]^{y} [T]^{2} $$

$$a = x $$

$$b = y $$

$$c = z $$

$$ \theta = n_{1} u_{1} = n_{1} [M_{1}^{a} L_{1}^{b} T_{1}^{c}] $$

$$ \theta = n_{2} u_{2} = n_{2} [M_{2}^{a} L_{2}^{b} T_{2}^{c}] $$

$$n_{1} u_{1} = n_{2} u_{2} $$

$$n_{1} [M_{1}^{a} L_{1}^{b} T_{1}^{c} ] = n_{2} [M_{2}^{a} L_{2}^{b} T_{2}^{c}] $$

$$F = m \times a $$

$$F = kg m/s^{2} $$

$$m = kg $$

$$a = m/s^{2} $$

A boy of mass 40 kg is hanging from the horizontal branch of a tree. The tension in his arms is minimum when the angle between the arms is:

Let T be the tension in the arms

Let $$2 \theta$$ be the angle b/w arms

$$2 T \cos \theta = mg$$

$$T = \frac{mg} {2 \cos \theta}$$

T is minimum when $$\cos \theta$$ is maximum.

$$\theta = \theta^{'}$$ W

$$T = \frac{mg} {2} = \frac{40 \times 10} {2} = 200 $$

On Celsius scale , the temperature of the body is increased by $$45^{\circ} C $$. The increase in temperature on Fahrenheit scale is

We know that

$$F = \dfrac{9}{5} T + C $$

$$F_{1} - F_{2} = \dfrac{9}{5} \times ∆T $$

$$ = \dfrac{9}{5} \times 45 $$

$$ = 81 $$ Fahrenheit

Using dimension show that $$ 1 \;Jaule = 10^{2} erg $$

Work $$ = [mL^{2}T^{-2}] $$

$$ 1 \;Jaule = (\frac{m_{1}}{m_{2}})^{1} (\frac{L_{1}}{L_{2}})^{2} (\frac{T_{1}}{T_{2}})^{-2} \times erg $$

$$ = (\frac{kg}{g}) (\frac{m}{cm})^{2} (\frac{sec}{sec} )^{-2} erg $$

$$ = ( \frac{l \omega o}{l}g) (\frac{l \omega}{l}cm)^{2} erg $$

$$ L = 10^{3} \times 10^{4} erg $$

$$ 1 \;Joule's = 10^{2} erg $$.

A block of mass $$100g$$ slides on a rough horizontal surface. If the speed of the block decreases from $$10ms^{-1}$$ to $$5ms^{-1}$$, find the thermal energy developed in the process.

Work done by all forces = $$\Delta KE$$

$$W_{friction}+W_{gravity}=\frac{1}{2}m(v_f^2-v_l^2)$$

$$v_f=5m/s$$

$$v_l=10m/s$$

$$\therefore W_{friction}=\frac{1}{2}m(25-100)$$

$$=-\frac{1}{2}*\frac{100}{1000}*75$$

$$=-3.75J$$

In the figure shown, the acceleration of A is $$2\,m/s^2$$ to left and acceleration of B is $$1\,m/s^2$$ to left.
Find the magnitude of acceleration of C in $$,m/s^2$$

$$l_2 = l_1 + l_3$$
$$l_1 + l_2 + l_3 + 2l_4 = constant \Rightarrow 2l_1 + 2l_3 + 2l_4 = constant$$ ............(i)
differentiate (i)
$$\dfrac{2dl_1}{dt} + \dfrac{2dl_3}{dt} + \dfrac{2dl_4}{dt} = 0$$
$$\dfrac{d^2l}{dt^2} + \dfrac{d^2l_3}{dt} + \dfrac{d^2l_4}{dt} = 0$$
$$a_{A} + a_{B} + a_{C} = 0$$
$$\Rightarrow 2 + (-1) + a_{C} = 0$$
$$a_{C} = -1 \,m/s^2$$
$$a_{C} = 1\,m/s^2$$ - in upward direction
1874077_1901439_ans_24ad5c9923234db6a3b1180769656b39.png

1874077_1901439_ans_24ad5c9923234db6a3b1180769656b39.png

Find the value of T = ?

$$T_{net} = -mgd \sin \theta $$
$$I \alpha = -mgd \sin \theta $$
For small angles $$ \sin \theta = \theta $$

$$I \alpha = -mg d \theta $$
$$ \alpha = -\dfrac{mgd}{I} \theta $$

Consequently,
$$ \omega^{2} = \dfrac{mgd}{I} $$, thus

$$ \omega = \sqrt{\dfrac{mgd}{I}} $$

Since $$T = \dfrac{2 \pi}{\omega} $$, then

$$T = \dfrac{2 \pi}{\sqrt{\dfrac{mgd}{I}}} = 2 \pi \sqrt{\dfrac{I}{mgd}} $$
1874257_1901628_ans_741cfe51b49e4062ab6a3d556b707bab.png

1874257_1901628_ans_741cfe51b49e4062ab6a3d556b707bab.png

What is the work done?

$$A\to B$$ & $$D\to C$$

$$\Delta v=0, w_{AB}= w_{BC}=0$$

$$w_{DC}=-P\Delta v=-3x(2-1)=-6\ atm \ l$$

$$w_{AD}^2 =-P\Delta v=-1\times (2-1)=-1\ atm\ l$$

So, total work $$=|-6-1|l\ atm$$

$$=7\ l\ atm$$

What are scalar and vector quantities

Scalar quantity name only magnitude

Example :mass, energy

Vector quantity have both magnitude as Direction

Example :force, velocity

What would be the position of the car B with respect to the car A at t = 0 ? ( assume that car B starts uniform motion from t = 0 )

$$ tan \theta = \frac {15}{3} = 5 $$

$$ tan \theta = \frac {y}{3} = 5 $$

$$ y = 15 $$

At t = 0 position of B is $$ -15 m $$ from position of car A

1880843_1902224_ans_556c4660403a43ad914808709f4ad6bf.png

If the rod of the previous problem horizontal ( no banking ) what should be the minimum friction coefficient so that a scooter going at 18 km / hr does not skid ?

Answer
$$ r = 10 m $$
$$ v = 10 km 1 lim $$
$$ = 18 \times\dfrac{ 5}{18} = 5m /s $$
for not sliding
$$ \dfrac{mv^{2}}{r} = \mu $$
$$ \mu = \dfrac{v^{2}}{gr} $$
$$ \mu = \dfrac{25}{10 \times 10} = 0.25$$

Find moment of inertia of a solid hemisphere of mass M shown in figure, about an axis AA' passing through its centre of mass.

We know that

$$I_G = \dfrac{2}{5}MR^2 - \dfrac{9}{64}MR^2$$

$$= MR^2\left[\dfrac{2}{5} - \dfrac{9}{64}\right]$$

$$= \dfrac{83}{320}MR^2$$

Distance between the place $$A$$ and $$B$$ is $$225\ km$$. In a map this this distance is denoted by a segment of length $$2.5\ cm$$. In the same map if the distance of place $$C$$ from $$A$$ is $$4.2\ cm$$, then what is the actual distance between $$A$$ and $$C$$.

$$\because 2.5 \ cm =225 \ km$$

$$\therefore 1 \ cm = \dfrac{225}{2.5} \ km$$

$$\therefore 4.2 \ cm = \dfrac{225}{2.5} \times 4.2$$

$$= 378 \ km$$

Actual distance between $$AC$$

With what average velocity must the blood flow through an artery of radius $$2\times 10^{3} m$$ take place for the flow to be laminar? Find the flow rate. Viscosity of blood $$= 2.084\times 10^{-3} Pa\ s$$ and density of blood $$= 1.06\times 10^{3} kg/m^{3}. (0.98\ ms^{-1}; 1.23 \times 10^{-5} m^{3}s^{-1})$$.

(a) Radius of the artery $$r = 2\times 10^{-3} m$$
Diameter, $$D = 2\times 2\times 10^{-3}m = 4 \times 10^{-3} m$$
Viscosity of the blood $$\eta = 2.084 \times 10^{3} Pa$$
Density of the blood $$\rho = 1.06\times 10^{3} kg\ m^{-3}$$
Maximum value of Reynold number of flow to be laminar, $$N_{R} = 20N$$
Average velocity $$V_{c} = \dfrac {N_{R}\eta}{\rho D}$$

$$= \dfrac {2000\times 2.084\times 10^{3}}{1.06\times 10^{3} \times 4\times 10^{3}}$$

$$= \dfrac {4.168}{4.24} = 0.98\ m/s$$

(b) Flow rate is given by the relation:
$$R = \pi r^{2} V(avg)$$
$$= 3.14 \times (2\times 10^{-3})^{2} \times 0.983$$
$$= 1.235\times 10^{-5} m^{3}/s$$

Therefore, the corresponding flow rate is $$1.235\times 10^{-5} m^{3}/s$$.

On the normal chess board as shown $$I_{1}$$ & $$I_{2}$$ are two insects which starts moving towards each other. Each insect moving with the same constant speed.

Places where they can meet.

No. of ways

$$\left(\ ^{8}C_{0}\right)^{2}+\left(\ ^{8}C_{1}\right)^{2}+.....+ \left(\ ^{8}C_{3}\right)^{2}$$

$$=\ ^{16}C_{8}$$

1889610_1902632_ans_9848d8b6208c4061911d6567b03cc055.png

The force between two electrons when placed in air is equal to $$0.5$$ times the weight of an electron. Find the distance between two electrons.

Electrostatic force $$F_{e} = \dfrac {ke^{2}}{r^{2}}$$
Weight of electron $$W = mg$$
So, $$F_{e} = 0.5\ W$$
Or $$\dfrac {ke^{2}}{r^{2}} = 0.5\ mg$$
Or $$\dfrac {9\times 10^{9} (1.6\times 10^{-19})^{2}}{r^{2}} = 0.5 \times 9.1 \times 10^{-31}\times 10$$
$$\Rightarrow r = 7.2\ m$$.

Find velocity if mass of particle is 0.1 kg.

work done = $$\Delta kE$$

work done = area under F-S Graph

$$= \dfrac{1}{2} \times \Delta \times 10 + (4 \times 10) + \left ( \dfrac{1}{2} \times 4 \times 10 \right )$$

$$= 2 \times 4 \times 10 = 80$$

$$= \dfrac{1}{2}mv^2 - 0$$

$$v = \sqrt{ \dfrac{160}{m}} = \sqrt{\dfrac{160}{0.1}} = 40\,m/s$$

What is the max vertical height to which a baseball player can through a ball is he can throw it to a max horizontal distance of $$100\ m$$?

maximum Range given $$=100$$

$$\theta=45^{o}$$

We know that

$$\dfrac{u^{2}\sin 2\theta}{2y}=100$$

On putting the value of angle we get

$$\dfrac{u^{2}}{2g}=100$$

take $$y=10$$

$$u^{2}=2\times 10\times 100$$

$$u=10\sqrt{20}$$

$$u=20\sqrt{5}$$

$$H=\dfrac{u^{2}\sin^{2}\theta}{g}$$ & $$H\max \theta=90^{o}$$

We also know that

$$H\max =\dfrac{u^{2}}{g}$$

$$H\max =\dfrac{2000}{10}=20$$ meter $$AP$$

I complex $$g$$ as $$10$$

When the wedge moves through a distance x, the speed of the rod is:

The wedge moves x towards right. the rod will come down by say y

$$\dfrac{y}{x} = tan45^\circ$$

$$y = x$$

Now, K.E. of rod = loss in P.E. of rod

$$\dfrac{1}{2}mv^2 = mg \,y$$

$$v^2 = 2gy$$

$$v = \sqrt{2gx}$$

as the rod remains in contact with the wedge the speed of wedge and rod one equal let it be v.

change in P.E. = change in K.E.

$$\Rightarrow mgx = 2 \times \dfrac{1}{2} mv^2$$

$$\Rightarrow v = \sqrt{gx}$$

$$W_{net} = \Delta K.E.$$ by work energy theorem for rod

$$\Rightarrow W_{gr} + W_{NR} = \dfrac{1}{2}mv^2$$

$$\Rightarrow W_{NR} = \dfrac{1}{2}mgx - mgx$$

$$= \dfrac{-mgx}{2}$$

1889625_1902643_ans_040c00bc4b41499aaf161eb86e973714.png

Prove $$x = x_0 + v_0t + \dfrac{1}{2}at^2$$

$$x_0$$ = initial distance

$$v_0$$ = initial velocity

$$\therefore x' = v_0t + \dfrac{1}{2}at^2$$

$$\therefore x = x_0 + x'$$

$$= x_0 + v_0t + \dfrac{1}{2}at^2$$

Where does the package strike the ground relative to the point directly below where it was released?

According to question

$$u=41\ m/s$$

$$y=0$$

$$y=at+\dfrac{1}{2}at2$$

$$165=0+\dfrac{1}{2}\times 10\times t^{2}$$

$$t^{2}=33$$

$$t=\sqrt{33}$$

$$t=5.8$$

$$x= u\times t$$

$$x=41\times 5.8=237.8$$

A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of $$400\ m$$ in $$20\ s$$. Calculate the acceleration and the force acting on it if its mass $$7$$ metric tonnes.

U=0 because body starts from rest

Therefore we have

$$S=\dfrac{1}{2}at^{2}$$

$$400=\dfrac{1}{2}a\times (20)^{2}$$

$$400=\dfrac{a}{2}\times 400$$

$$a=2$$

$$F=ma$$

$$=7\times 1000\times 2$$

$$=14000$$

Derive the kinematic equation for uniformly accelerated motion by using of the analytical method of $$v-t$$ graph.

$$\therefore$$ Acceleration = slope of graph

$$=\dfrac {BC}{AC}=\dfrac {BD -CD}{OD}$$

$$=\dfrac {v-v}{t}$$

$$\Rightarrow a=\dfrac {v-v_0}{t}$$

$$\therefore v=v_0 +at$$

2008533_1903150_ans_347967d0b90f454ea3e82324c39cbcbc.png

Define Mole fraction and Molarity.

Mole fraction

It is the ratio of the number of moles of a particular component to the total number of moles of all the components in the mixture.

Molarity

It is the number of moles of solute per litre of the solution. It is the ratio of the number of moles of solute to the volume of solution in liter.

The magnitude and direction and section of velocities of two identical frictional as before they strike each them are as shown . Assuming e = 0.9 determine the magnitude of each after the impact .

Answer
$$ M_{nu} = V_{A} \cos 30^{o} = 30 \times \dfrac{\sqrt{3}}{2} = 15\sqrt{3} $$
$$ N_{Ay} = V_{A} \sin 30^{o} = 30 \times \dfrac{1}{2} = 15 $$
$$ M_{Byc} = - V_{B} \cos 60^{o} = -40 \times \dfrac{1}{2} = -20 $$
$$ N_{By} = B_{\beta u} \sin 60^{o} = 40 \times \dfrac{\sqrt{3}}{2} = 20\sqrt{3} $$
$$ V_{A u} - V_{\beta u} - 0.9(-20 - 15\sqrt{3}) $$
$$ V_{Au} - V_{B u} = 18 - 13 -5\sqrt{3} $$
$$ 2 V_{Au} = - 38 + 1.5 \sqrt{3} $$
$$ V_{A} = -17 .70096 ms^{-1} $$

1874833_1903670_ans_d33dad066dc440debd63ae7bc97e3d10.PNG

1874833_1903670_ans_d33dad066dc440debd63ae7bc97e3d10.PNG

A particle A of mass 2 m is held on a smooth horizontal table and is attached to one end of an inefastic string which runs over a smooth light pulley at the edge of the table. At the end of the string there hangs another particle B of mass m ,The distance from A to pulley is 1 . The particle A is then projected towards the pulley with velocity u .
The common velocity when A reaches the pulley (assume that B has not yet reached the ground )

Answer
mg - T = ma
T = 2 ma
mg = 3 ma
= g/3
$$ t = \dfrac{2 u}{g} $$
$$ l = l' + u $$
$$ t = \dfrac{2 u}{g} $$
$$ l' = l - ut $$
$$ l u \times \dfrac{2u}{g} $$
$$ l' = l - \dfrac{2 u^{2}}{g} $$
$$ v^{2} = vo^{2} + 2 as $$
$$ vo = \dfrac{4 u}{3} $$
$$ s = l' $$
$$ v^{2} = \dfrac{160^{2}}{9} + 2 \times \dfrac{g}{3} \times \left ( l - \dfrac{2 v^{2}}{g} \right ) $$
$$ V = \sqrt{\dfrac{16u^{2}}{g} + \dfrac{2}{3} g \left ( \dfrac{- 20^{2}}{g} \right )} $$
$$ V = \sqrt{\dfrac{ u u ^{2}}{g} + 6 g u} $$

1874919_1903701_ans_844e7885c1c04c438900857702b7ba95.PNG

1874919_1903701_ans_844e7885c1c04c438900857702b7ba95.PNG

What is absolute error, mean absolute error and relative error?

Absolute error - The difference between true value (usually mean value) and measured value is called an absolute error.
Mean absolute error - (only magnitude of $$\Delta a$$
$$a= a_{mean} \pm \Delta a_{mean} \implies $$ a lies between $$a_m - \Delta a_{mean}$$ to $$a_m + \Delta a_{mean}$$
$$\Delta a_{mean} = \dfrac{|\Delta a_1| + | \Delta a_2| + ........|\Delta a_n|}{n}$$

Relative error $$= \dfrac{\Delta a_{mean}}{a_{mean}}$$
Relative $$\% = \pm \dfrac{\Delta a_{mean}}{a_{mean}} \times 100 = fractional \ error \times 100$$

How do you convert grams to moles and moles to grams?

Convert 25.0 g of water to moles of water.

We know that $$ 1 mole H_2 O = 180.2 g H_2 O $$

we can use this to create the conversion factors $$ \frac {1 mol H_2 O}{ 18 .02 H_2O} $$ and $$ \frac { 18.02 g H_2 O}{ 1 mol H_2O } $$

We choose the one that gives us the correct units for the answer. So we choose the first one and write

$$ 25.0 g H_2 O \times \frac { 1 mol H_2 O}{ 18.02 h H_2 O } = 1.39 mol H_2 O $$

815 gal/h is equivalent to how many qt/sec?

There are 4 quarts in a gallon, and there are 60 minutes in a hour. Since there are 60 seconds in a minute, there are $$ 60 \times 60 = 3600 $$ seconds in an hour

here we have

$$ \frac { 815 ( galllons )}{1 h} = \frac { ( 815 \times 4)( quarts)}{3600 (s) } $$

$$ 815 \times 4 = 3260 $$ quarts per hour

then

$$ \frac {3260}{3600} = \frac {326}{360} = 0.905 $$ quarts per second

A body travelling along a straight line traversed one third of the total distance with a velocity $$ 4 ms ^{-1} $$ . The remaining part of the distance was covered with a velocity $$ 2ms^{-1} $$ for the other half of time . What is the mean velocity average over the whole time of motion ?

Let total distance d
Let time covered for first one third distance $$bet _{1} $$
Then
$$ t_{1} = \dfrac{d / 3}{4} = \dfrac{d}{12} $$
$$t_{2} $$
be time for next two journeys
$$ d- \dfrac{d}{3} = \dfrac{2d}{3} = 2t _{2} + 6t_{2} = 8t_{2} $$
$$ t _{2} = \dfrac{d}{12} $$
average velocity
$$ = \dfrac{Total distance }{Total time } = \dfrac{d}{t_{1} + 2t_{2}} = \dfrac{d}{\dfrac{d}{12} + \dfrac{2d}{12}} = 4m /s $$

A test charge q is moved without acceleration from A to C along the path from A to B and then d=from B to C in electric field E as shown in the fig
Calculate the potential difference between A and C .
At which point (of the two ) , the electric potential is more and why ?

Answer
VA > VB = VC
$$ \therefore $$ potential decrease in the direction of electric of electric field .
Electric field is given by
$$ \vec{B} = E = \dfrac{- d v}{dn} $$
$$ Ve - Vx = - \int^{4}_{0} E dx $$
$$ Ve - Ve = - 4 E $$

How many quarts are in 10 gallons?

The conversion factor for gallons to quarts is:

$$ 1 gal = 4qt $$

To find how many quarts in 10 gallons multiply each side of the equation by 10:

$$ 10 \times 1 gal = 10 \times 4 qt $$

$$ 10 gal = 40 qt $$

There are 40 quarts in 10 gallons.

What is scalar quantity

Scalar quantity those quantity require only magnitude not direction
1875115_1903740_ans_74c1a0d1a75346e794b01d31999b0e1f.PNG

Why does 1 amu = 1 g/mol?

The mole is defined as the number of particles in 12 g of carbon-12, known as $$ ^{12}C $$So, we say that in one mole of carbon-12, the sample has a mass of 12 g.
In other words,
mass of carbon-12=12 g/mol.
Still with me? Good.
Now, we also know that the mass of a single carbon-12 atom is exactly 12 amu, as it is an isotope.
and so mass of carbon-12

=12 amu/atom

Combining, we have:

12 amu/atom=12 g/mol

$$ \Rightarrow $$1 amu/atom=1 g/mol

How can i convert centimeters to meters?

To do any conversion, you find the relationship between the two units. In this case, 100 cm = 1 m.

This gives you two conversion factors:

$$ \frac { 100cm}{1 mm} $$ and $$ \frac { 1 m}{ 100 cm } $$

Convert 789 cm into metres.

You multiply by a conversion factor: $$ \frac { 100 cm}{ 1 mm} $$ or $$ \frac {1 m}{100 cm} $$

Choose the one that gives you the correct units for the answer.

$$ 789 cm \times \frac {1m}{100cm} = 7.89 m $$

Note that the "cm" cancels out and leaves you with the answer in “m”. If you had chosen the other conversion factor, you would have gotten

$$ 789 cm \times \frac { 100 cm}{1 m} = 78900 cm^2 / m $$

The strange units for the answer tell you that you have made a mistake.

Second Method

If you can’t remember that 100 cm = 1 m, you can always use the definition of centi.

centi $$ = 10^{-2} $$ so $$ 1cm = 10^{-2} m $$

Then you can convert “cm” to “m”.

$$ 789 cm \times \frac {10^{-2} m}{1 cm} = 7.89 cm $$

Third Method

Here is an easy acronym for you to memorize.

khan’s hot dogs use dead cow meat $$ \rightarrow k\quad h\quad d\quad u\quad d\quad c\quad m $$

The letters stand for kilo hecto deka (unit) deci centi milli.

'u' always stands for whatever base unit you are in, in this case, “metres”.

You want to go from “c” to the base unit “u” (metres). “u” is two places to the left of “c”, so you move the decimal point two places to the left.

789 cm= 7.89 m

How many pints are in a cup?

$$2$$ cups $$= 1$$ pint

Divide both sides of the equation by 2:

$$ \dfrac {2}{2} cups = \dfrac {1}{2} pints = 0.5 pints $$

How many $$ cm^3 $$ in $$m^3 $$ volume ?

The centi prefix means $$ 10^{-2} $$

so $$ 1 cm^3 = (1 \times 10^{-2} . m)^3 = $$

$$ ( 1 \times 10^{-2} . m \times 1 \times 10^{-2} . m \times 1 \times 10^{-2} . m) = 1 \times 10^{-6} . m^3 $$

Thus there are 1 million $$ cm^3 $$ in a cubic metre. Do you agree? All I have done is expanded the prefix centi using the cubic exponent. Since, there are 1 million $$ cm^3 $$ in a cubic metre, there are $$ 10 \times 10^7 cm^3 $$ in a $$ 10 m^3 $$ volume

The conversion factor is $$ 10^6 cm^3 m^{-3} $$

How many cups are in 20 quarts?

Handy relations to memorize:

8 ounces=1 cup

2 cups=1 pint

2 pints=1 quart

4 quarts=1 gallon

If you remember the above then

$$ 1quart = 2pints = $$ 2 \times 2 $$ cups = 4 cups

and if 1 quart=4 cups

then

$$20 quarts = 20 \times 4 cups = 80 cups $$

How many cups are in a quart

Since there are two cups in a pint and two pints in a quart, 2*2 = 4 cups in a quart

How many cups are in 1/2 a gallon?

We know the conversion factor of gallons to cups is:

$$ 1 gallon = 16 cups $$

To fins the number of cups in $$ \frac {1}{2} $$ gallon we can multiply each side of the equation by $$ \frac {1}{2} $$ giving :

$$ \frac {1}{2} \times 1 $$ gallon $$ = \frac {1}{2} \times 16 cups $$

$$ \frac {1}{2} gallon =\frac {16}{2} cups $$

$$ \frac {1}{2} gallon = 8 cups $$

Therefore there are 8 cups in $$ \frac {1}{2} $$ gallon

A recipe for making creamy pasta sauce calls for 0.75 of cream. Your measuring cup measures cups. How many cups of cream should you use?

One cup measures 250ml = 0.25 litres

If the unit for 0.75 of cream is litres, then

$$ \frac {0.75 litres}{ 0.25 lires} = 3 cups $$

How many cups are in a quart?

Since there are two cups in a pint and two pints in a quart, 2*2 = 4 cups in a quart

What is the size of the universe in centimeters?

Actually, the edge of the universe is nearly 46 billion light years away.

The diameter of universe is 91 Billion light years.

Converting these two factors into centimeters, we get

edge of universe $$ 4.3520 10^{27} cm $$

Diameter of Universe $$ 8.6093 .10^{27} cm $$

A recipe calls for 1/2 gallon of punch, 3 pints of club soda, and 2 cups of ice cream. How many quarts does the recipe make?

The answer to this question requires dimensional analysis

$$ 1 gal = 4 qt $$

$$ 2pt = 1 qt $$

Convert all measures to cups. Add the number of cups and then convert cups to quarts.

Cups of punch

$$ 0.5 hal \times \frac [ 4qt]{ 1gal} \times \frac { 2 pt}{1 qt} \times \frac {2c}{ 1 pt} = 8c $$

Cups of club soda

$$ 3pt \times \frac { 2c}{ 1 pt} = 6 c $$

Cups of ice cream

2 c

Add the number of cups of each ingredient.

$$ 8c + 6c + 2 c = 16 c $$

Convert cups to quarts.

$$ 16 c \times \frac { 1pt}{2c} \times \frac { 1pt}{2 pt} = 4 pt $$

$$ 2 c = 1 ptc $$

How do you find out how many feet are in a mile?

I usually start from the number of yards in a mile and multiply by 3.

There are 1760 yards in a mile and 3 feet in a yard.

So there are 1760⋅3=5280 feet in a mile.

You can break it down into the traditional units making up a mile as follows:

One mile is 8 furlongs

One furlong is 10 chains

One chain is 22 yards

One yard is 3 feet

So one mile $$ 8 \times 10 \times 22 \times 3 = 5280 $$

How many feet in a mile?

According to British units

1 mile=8 furlongs

(A furlong is a commonly used unit)

and

1 furlong=660 feet

Then

$$ \rightarrow 1 mile = (8 .660) feet $$

$$ \Rightarrow = 528 0 feet $$

How many feet are in 1/2 of a mile?

12”make1’

3’make1yard

220yards make 1furlong

8furlongs make 1 # mile

Or 5280’ make 1 mile

Hence 2640’ make $$ ( \frac {1}{2}) $$ a mile

How many cups are equivalent to one pint?

1 Gallon [Fluid, US] = 16 Cups [US]

How many cups are there in nine ounces?

Since there are nine ounces, and each cup holds 8 ounces. So your answer is little more than 1 cup.

How many quarts are in a gallon?

There are 8 fluid ounces in a cup

There are 2 cups in a pint

There are 2 pints in a quart

There are 4 quarts in a gallon

How many feet are in 1000 yards?

$$ 1 :3 = 1000 : F $$ or you may write $$ \frac {1}{3} = \frac {1000}{F} $$

or $$ \frac {3ft}{ 1yd} = \frac {Fft}{1000yd} $$

However you write it you should also get:

$$ 1 \times F = 3 \times 1000 $$

$$ F= 3000 $$

How many feet are in 2.4 miles?

There are 3 feet in a yard and 1760 yards in a mile.

So in 2.4 miles there are:

$$ 2.4. 1760 .3 = 24.176.3 = 12672 $$ feet

How many yards are in a tenth of a mile?

If 1 mile is 1760 yards, then 1 tenth of a mile is 1 divided by 10 which equals 0.1, if you multiply 0.1 by 1760 you get 176 which is the number of yards that are in 1 tenth of a mile. 10 divided by 1760 is 176.

How many inches is in 5 yards?

Use dimensional analysis.

$$ 1yd = 36 in $$

There are two conversion factors:

$$ \frac { 1yd}{36 in } $$ and $$ \frac { 36 in}{1 yd} $$

Multiply 5 yards by the conversion factor the cancels yards and keeps inches.

$$ 5 yd \times \frac {36 in}{1 yd } = 180 in $$

How many feet are in 1 yard?

$$ 3 feet = 1 yard $$

How many feet is in 3 miles?

Each mile has 8 furlongs.

Each furlong has 220 yards.

Each yard has 3 feet.

So each mile has $$ 8 \times 220 \times 3 = 5280 feet $$

And 3 mile have $$ 528 0 \times 3 = 15840 feet $$

.4 miles is how many feet?

To get your answer, you first have to know how many feet are in a mile. There are 5,280 feet in a mile.

I divided 5,280 by 2.5 to get my answer, because if you divided 5,280 by 2, you will get half of a mile (2,640 feet) and dividing by 3 give us too small an answer.

Sorry for the poor explanation, if anyone wants to edit this for me and give a better explanation, it'd be greatly appreciated.

What is the force of gravity from jupiter on you at birth compared to the force of gravity from a nearby cobe machine?

Mass of Jupiter $$= 316$$ times of earth
radius $$= 11$$ times earth
$$g= \dfrac{Gm}{R^2}$$
$$= \left(\dfrac{316}{121} \right) g'$$
$$=2.34 \ g'$$

How many feet are in a football field that is 100 yards?

Since 1 yard = 3 feet we can multiplying 100 yd by $$ \frac { 3 ft}{ 1yd} $$ we are essentially multiplying by 1 but doing so allows us to cancel out the yd unit so that we are left with only ft

$$ \frac {100 yd}{1} . \frac { 1 ft}{ 1 yd} = 300 ft $$

How many seconds are in a 24 hour day?

Answer:
Well there are 60 seconds in a minute and 60 minutes in an hour and 24 hours in a day. Thus:
606024=86,400 seconds in a day

Your walk to school is a half a mile. Approximately how many feet is this?

Another way to ask this question:

How many feet are in half a mile?

Given,

0.5mi

Now, let's relate the two units and convert:

$$ 0.5 mi . \frac {5280 ft}{mi} \approx 2.64 . 10^3 ft $$

How do you use dimensional analysis to figure out how many seconds are in 4 years?

Answer :
All there is behind the solution is the constant stream of multiplying. This is what dimensional analysis is all about. A conversion from one unit to another requires some sort of multiplier to change one unit to another.
Here is a list of these multipliers.
1in=2.54cm
1lb=0.453592kg
$$1 second = \dfrac{1}{60} minute$$
If you want to switch these, all you need to do is to divide the non-one value with itself and the 1 to find the other, vice versa solution.
1 cm = 0.393701 in
1 kg = 2.20462 lb
1 minute = 60 seconds
From there, we are ready to move on.
1 minute = 60 seconds
1 hour = 60 minutes
$$60 seconds \times 60 minutes = 3600 seconds = 1 hour$$
24 hours = 1 day
365.25 days = 1 year (to account for leap years, the likelihood of the extra day out of 4 years is added.)
$$3600 seconds \times 24 hours = 86,400 seconds$$
and finally:
$$86,400 seconds \times 365.25 days \times 4$$
$$126,230,400 seconds$$

How to convert 2.5 radian to degree / minute / second?

Answer :
converting to degree : (Multiply by $$\dfrac{180}{\pi})$$
Converting to mintes : $$(0.31 \times 60)$$
$$= 0.31 \times 60 = 18.6$$
Converting into seconds : ($$0.6 \times 60$$)
So, 2.5 radius = $$143^{\circ} 18'36"$$

How many seconds are there in a year?

Answer :
There are 31,536,000 seconds in a year.
Explanation :
1 year $$= \dfrac{365 days}{1 year} \times \dfrac{24 hrs}{1 day}\times \dfrac{60 min}{1 hr}\times \dfrac{6o sec}{1 min}$$

You can see the all terms cancel except seconds (numerator) and year (denominator).
Plugging into a calculator, $$365 \times 24 \times 60 \times 60 = 31,536,000$$
So the answer is that there are 31,536,000 seconds in a year.

A bag of chips is 24 ounces. A serving size is $$\dfrac{3}{4}$$ of an ounce. How many servings are in the bag of chips?

Answer : 32
Explanation :
You have to divide the total ounces by the serving size to get how many serving that are in the bag of ships
$$\dfrac{24}{1}/\dfrac{3}{4}$$
To divide fraction you need to flip the denominator and the numerator this is called the reciprocal
So.
$$\dfrac{24}{1} : \dfrac{3}{4}$$
Now just multiply across which equals
$$\dfrac{96}{3}$$ or 32 Servings

How many seconds are in 7 hours?

Answer :
See the entire solution process below:
Explanation :
Multiplying these will give you the number of seconds per hour:
$$\dfrac{60 sec}{min}\times \dfrac{60 min}{hr} \Rightarrow \dfrac{60 sec}{min}\times \dfrac{60 min}{hr} \Rightarrow \dfrac{60 sec \times 60}{hr} = \dfrac{3600 sec}{hr}$$
We can now multiply this by 7 hours to find the number of seconds in 7 hours:
$$\dfrac{3600 sec}{hr} \times 7hr \Rightarrow \dfrac{3600 sec}{hr} \times 7hr \Rightarrow 3600 sec \times 7 \Rightarrow 25200 sec$$
There are 25,200 seconds in 7 hours.

How many square feet are in $$100 m^{2}$$ ?

Answer:
$$1076ft^{2}$$
Explanation :
First we obtain the conversion of feet to meters. Then we can square that to get the factor for $$\dfrac{ft^{2}}{m^{2}}$$

$$1 ft = 0.3048m$$

$$1 ft^{2} = 0.3048^{2} m^{2} = 0.0929m^{2}$$

Now we can use this factor for the desired conversion:
$$\dfrac{1 ft^{2}}{0.0929 m^{2}} \times 100m^{2} = 1076 ft^{2}$$

What is the pressure conversion factor for torr to kpa?

Answer :
You can easily link these two units by using atmospheres, or atm, as a starting point.
You know that 1 atm is equivalent to 760 torr. LIkewise, 1 atm is equivalent to 101.325 kPa, so the conversion factor that takes from torr to kPa will look like this
$$\dfrac{760 torr}{1 atm}. \dfrac{1 atm}{101.325 kPa} = \dfrac{760 torr}{101.325 kPa}$$
An here's your conversion factor $$\rightarrow 760 torr$$ are equivalent to 101.325 kPa, which means that
$$1 torr . \dfrac{101.325 kPa}{760 torr} = 0.133322368 kPa$$
and
$$1 kPa . \dfrac{760 torr}{101.325 kPa} = 7. 50061683 torr$$

How do you calculate formula mass ?

Answer
o calculate formula mass, multiply the subscript of each element in the formula by the element's atomic weight (relative atomic mass) found on the periodic table
Explanation :
To calculate formula mass, multiply the subscript of each element in the formula by the element's atomic weight (relative atomic mass) found on the periodic table.
The unit for formula mass is either u or Da (Daltons). The amu has been replaced with u, even though it is still commonly used.

How long does it take for the earth to rotate on its axis?

Answer :
It takes a day for the Earth to rotate about its axis, but there are several definitions of a day.
Explanation :
The period it takes the Earth to rotate about its axis is called a day. There are however several definitions of a day which are all slightly different. It all depend on what you measure the time relative to. Also, due to orbital effects successive days are not the same length.
A Mean Sidereal Day is one complete rotation of the Earth relative to the fixed stars - 23h 56m 4.1s
The reason why the Solar Day changes from day to day is due to the Earth's orbit being elliptical and the axial tilt.
The orbital eccentricity component is the orange line on the diagram. It have zeros at the apses.
The obliquity component, due to the axial tilt, is the green line which has zeros at the equinoxes and solstices.
The difference between the Mean Solar Day and the Actual Solar Day is described by the Equation of Time which is the blue line in the diagram and is the sum of the two components. The vertical axis is minutes difference between clock noon and solar noon.

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How many types of quarks are there and what are their names?

Answer:
There are 12 different quarks in total. The number rises to 36 if you take the color charge into account.
Explanation :
Like leptons, quarks are divided into three generations.
Each generation contains four quarks- two quarks and two antiquarks.
Each quark is assigned a flavor:
up, down, charm, strange, top, and bottom.
Antiquarks are named respectively- for example, the antiparticle of an up quark is named anti-up.
So there are
3 generations4 quarksgeneration1=12 quarks
Taking the Quantum Chromodynamics (QCD) into account will triple the number. By the QCD model, quarks have three different "colors"
Red, Green and Blue for quarks, and
Anti-Red (Cyan), Anti-Green (Magenta), and Anti-blue (Yellow) for the respective antiquarks..
So that gives 12 quarks3 color=36 quarkcolor
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1876993_1904236_ans_6c73eb9f38754c8183809a7281f13786.PNG

How many yards are in 7 miles?

Answer:
12320 yards
Explanation :
There are 1760 yards in one mile, therefore you need to multiply 1760 by 7 to find the number of yards in 7 miles.

Why does $$1\ amu=1\ g/mol$$?

Due to the definitions....

Explanation:

The mole is defined as the number of particles in $$12\ g$$ of carbon $$-12$$, known as $$\ ^{12}C$$.

So we say that in one mole of carbon $$-12$$, the sample has a mass of $$12\ g$$.

In other words,

mass of carbon $$-12=12\ g/mol$$.

Still with me ? Good.

Now, we also know that the mass of single carbon $$-12$$ atom is exactly $$12\ amu$$, as it is an isotope.

And so,

mass of carbon $$-12=12\ amu/atom$$

Combing, we have:

$$12\ amu/atom, we have:$$

$$12\ amu/atom=12\ g/mol$$

$$\Rightarrow 1\ amu/atom=1\ g/mol$$

Therefore we just proved that an atomic mass unit is the same thing as grams per mole. Hope this helps!

For a further explanation, visit:

The official length for a marathon race is 26.2 miles. How many yards long is a marathon? How many feet?

Answer:
138,336 feet
46,112 yards
See Explanation
Explanation :
So, first of all, we are told that a marathon race is 26.2 miles. We are asked to give the equal length in yards and feet.
It is really helpful to remember a few conversion factors:
1) 1 mile=5,280 feet
2) 1 miles=1,760 yards
So let's start with converting miles to feet...
Since each mile equals 5,280 feet, let's multiply 26.2 by 5,280, which equals to 138,336 feet.
Great! Now let's convert from miles to yards.
Since each mile equals 1,760 yards, let's multiply 26.2 by 1,760, which equals to 46,112 yards.

How many yards in a mile?

Answer:
A yard is equal to 0.000568182 miles.
Explanation :
There are 1,760 yards in a mile. In fractional form it looks like this:
$$\left ( \dfrac{1mi.}{1,760 yd} \right )$$

How many yards are in 5 miles?

Answer:
See a solution process below:
Explanation :
The conversion factor for miles to yards is:
1mi=1760yds
To find the number of yards in 5 miles, multiply each side of the equation by 5 giving:
$$5 \times 1mi = 5 \times 1760 yds$$
$$5 mi = 8800 yds$$
There are 8,800 yards in 5 miles.

How many yards are in a square mile?

Answer:
1 sq mile = 3,097,600 sq yd
Explanation :
You cannot convert between units of length (yard) and units of area (square mile). You can only convert:
units of length:
1 mi = 1760 yd
or
units of area:
$$1 mi^{2} = 1 mi . 1 mi = 1760 yd. 1769 yd = 3097600 yd^{2}$$

How can you calculate mass if density and volume are known ?

Answer
$$ density = \dfrac{mass}{volume} $$
$$ mass = density \times volume $$
Explanation :
Density is mass per unit volume .
The equation is
$$ Density = \dfrac{mass}{ volume} $$
If density and volume are already known, you can calculate mass by multiplying density by volume.
$$ mass = density \times volume $$

A golf ball weighs about 45.9 grams. About how many ounces would a dozen golf balls weigh?

Answer:
I've set up a conversion equation:
You can just say it out loud what you're trying to do and that will help you write out your ratios.
45.9 grams per 1 ball
1 ounce per 28.35 grams
We have 12 balls
$$\dfrac{45.9g}{ball}. \dfrac{1oz}{28.35 g}. 12(ball)$$

$$\dfrac{45.9g}{ball}. \dfrac{1oz}{28.35 g}. 12(ball)$$

$$= \dfrac{45.9.12}{28.35} \approx 19.04 oz$$

How many yards are in a 1/4 of a mile?

Answer:
440 yards
Explanation :
1 mile=1760 yards
$$\dfrac{1}{4} mile = \dfrac{1}{4}. 1760 yards$$
$$\rightarrow \dfrac{1}{4} . 1760 = \dfrac{1760}{4}$$
$$\Rightarrow = 440$$

How much is 168 cm in feet and inches?

Answer:
168 cm are equal to approximately 5 feet and 6 inches.
Explanation:
Each inch is equal to 2.54 cm.
Therefor, each cm is equal to $$\dfrac{1}{2.54} = 0.3937$$ inches.
Hence, 168 cm are equal to $$168 \times 0.3937 = 66.1416$$ inches.
As each feet has 12 inches, 5 feet are equal to $$12 \times 5 = 60$$
and hence 168 cm are equal to 5 feet and 6.1416 inches or rounding it say 5 feet and 6 inches.

What is percent error/percent deviation ?

Answer
relative error between experimental and true results
Explanation:Percent error and percent deviation are the same thing. They both measure the relative error when you compare the results you got (the experimental/measured results) and compare them to the true or accepted results.
They determine the accuracy of your results. The smaller your percent error, the better your results are. Usually 5% is acceptable in class. If it is higher, you might need to go back through your experiment to see what systematic or random errors were present.
Depending on your teacher/professor, the equation for percent error could be one of two equations. I will list both. Just use the one that your professor wants you to use. Some may want you to use the absolute value to express % error as a positive number only.
% error $$ = \dfrac{x_{measured }- x_{true}}{x_{true}} $$ 100 %
% error $$ = \left | \dfrac{x_{measured} - x_{true}}{x_{true}} \right | $$ 100 %

How much is 10 kg is pounds?

Explanation:
Here is a conversion that I set up (using 1 lb = 453.6 g):
$$10 kg \left ( \dfrac{1000 g}{1 kg} \right )\left ( \dfrac{1 lb}{453. 6 g} \right )$$

$$10 kg \left ( \dfrac{1000 g}{1 kg} \right )\left ( \dfrac{1 lb}{453. 6 g} \right )$$

$$10 kg \left ( \dfrac{1000 g}{1 kg} \right )\left ( \dfrac{1 lb}{453. 6 g} \right ) = 22.0462 lbs$$

How many pints are in a cup?

Answer:
0.5 pints
Explanation:
2 cups = 1 pint
Divide both sides of the equation by 2:
$$\dfrac{2}{2}$$ cups $$= \dfrac{1}{2}$$ oints = 0.5 pints$$

How many pints is 1 pound?

Answer:
There is no answer.
Explanation:
Pints is a measure of volume.
Pounds is a measure of weight.
They measure different physical properties, so there is no general conversion between them.
Unfortunately, in the old imperial (current US) system, there are two kind of ounces. The ounce of volume and the ounce of weight.
A glass that holds 16 fluid ounces (volume) may be filled with more or less than 16 ounces (weight) of stuff.
Because of the similarity, some people jokingly call a one pint glass (16 ounces volume) a one pound glass. It's a joke that not everyone is in on.

How do you find volume when given mass ?

Answer
These properties are not related.
Explanation :
Density , $$ p = \dfrac{Mass}{Volume} $$
If the mass is known, volume is inaccesible without density.

8 cups equals how many quarts?

Answer:
8 cups = 2 quarts
Explanation:
When I was fairly young I was taught to mindlessly recite:
2 cups, 1 pint;
2 pints, 1 quart;
4 quarts, 1 gallon.
From which it follows that there are 4 cups in 1 quart
and
therefore 8 cups in 2 quarts.

How do you convert 3.82 meters per second to kilometers per hour ?

Answer
See a solution process below:
Explanation:
First, we can write this expression as:
$$\dfrac{3.82 m}{sec} $$
Next, let's convert the seconds to hours. We know 1 minute is equal to 60 seconds and 1 hour is equation to 60 minutes so we can write multiply this expression by 1 twice without changing the value of the expression:
$$ \dfrac{3.82m}{sec} \times\dfrac{60 \sec}{1 min} \times\dfrac{60 min}{1 hr} \Rightarrow $$
$$ \dfrac{3.82}{\sec} \times\dfrac{60 \sec}{1 min} \times\dfrac{60 min}{1 hr} \Rightarrow $$
$$ 3.82 \times 60 \times \dfrac{60}{1 hr}\Rightarrow $$
$$ \dfrac{13752m}{1 hr} $$
Now, let's convert meters to kilometers.
We know 1 kilometer is equal to 1000 meters. So again, we can multiply the expression by 1 without changing the value of the expression:
$$\dfrac{13752m}{1hr} \times\dfrac{1 km}{1000 m}\Rightarrow $$
$$\frac{13752 m}{1000 hr} \Rightarrow $$

How do you convert ml to l ?

Answer
There are 1000 mL (milliliters) in 1 L (liter).So, to convert from mL to L, divide by 1000.
I hope this helps a lot! :)

How do you convert between moles and liters ?

Answer
You don't do this conversion....
Explanation:The mole is simply the number of particles. And litres is a UNIT of volume.
$$ Density = \dfrac{Mass of particles}{Volume occupied by the particles}$$CAN be related to the molar quantity, but this was not what you asked...

How do you convert grams to moles and moles to grams ?

Answer
You create a conversion factor from the molar mass and use it in your calculations.
Example 1.
Convert 25.0 g of water to moles of water.
We know that 1 mol HO = 180.2 g HO.
We can use this to create the conversion factors
$$ \dfrac{1 mol H_{2}O}{18.02 g H_{2}O} and\dfrac{18.02 g H_{2}O}{1 mol H_{2}O} $$
We choose the one that gives us the correct units for the answer. So we choose the first one and write
$$ 25.0 H_{2}O \times \dfrac{1 mol H_{2}O}{18.02 g H_{2}O} = 1.39 mol H_{2}O $$
Example 2.
Convert 1.39 mol of water to grams of water.
Here we use the other conversion factor.
$$ 1.39 mol H_{2}O \times \dfrac{18 .02 g H_{2}O}{1 mol H_{2}O} = 256 .0 g H_{2}O $$
Mass to moles
Moles
$$ \dfrac{grams}{1 mole} = grams $$
Moles of mass
Moles
$$ \dfrac{1 mole}{grams} = moles $$

How do you convert km/h to m/s?

Answer
Use dimensional analysis (a.k.a. factor-label method).
Explanation:
Given:
$$ \dfrac{x km}{h} $$
Multiply by the conversion factor
$$ \dfrac{1000 m}{1 km} $$
$$ \dfrac{x km}{h} \times \dfrac{1000 m}{1 km} $$
Please observe how the km units cancel.
Multiply by the conversion factor
$$\dfrac{1 h}{3600 s} $$
$$\dfrac{x km}{h} \times \dfrac{1000 m}{1 km} \times \dfrac{1 h}{3600 s} $$
Please observe that the hour units are canceled and we are left with the units of m/s.
Follow the rules of the multiplication of fractions to obtain the value of x:
$$ \dfrac{x km}{h} \times\dfrac{1000 m}{1 km} \times \dfrac{1 h}{3600 s} = \dfrac{5x}{18} m/s $$

How do you convert 100 g to kg ?

Answer
100 g is equal to 0.1 kg.
Explanation:
There are 1000 grams in one kilogram, so to convert grams to kilograms, you simply divide the number of grams by 1000. Technically, this is "unit conversion" and looks like this in fully expanded form:
$$ 100 g . \dfrac{1 kg}{100 g} = \dfrac{100 g .kg}{1000 g} = 0.1 kg $$

How do you convert 255 mm Hg to atm? What about 620 torr to PSI ?

Answer
THE CONVERSION RATIOS
There is a conversion factor for going from mm Hg (or torr) to atm:
1 atm=760 mm Hg=760 torr
There also exists a conversion factor for PSI. I actually don't know it, so I looked it up Turns out it's 51.7149 torr = 1 PSI.
(Google is a great resource. You should practice with it!)
PERFORMING THE CONVERSIONS
(1)
Let's start from the equality we just wrote out.
1 atm = 760 mm Hg
What happens if we divide by 1 atm? We get the actual ratio for the conversion.
$$\dfrac{1 atm}{1 atm} = 1 = \dfrac{760 mm Hg}{1 atm} = \dfrac{1 atm}{760 mm Hg} $$
This implies that multiplying by this ratio does NOT change the validity of your answer... only the units. (It preserves your numerical information.)
Thus, we get:
$$ P_{atm} = 255 mm Gh \times \dfrac{1 atm}{760 mm Hg} $$
So now you have the same pressure in different units.
(2)
Like before, we have a ratio that is equal to 1:
$$ 1 = \frac{51 ,7149 torr}{1 PSI} = \frac{1 PSI}{51.7149 torr} $$
This ratio is used as follows:
$$ P_{torr} = 620 torr \times \dfrac{1 PSI}{51.7149 torr} $$
$$ 12.0 PSI $$
Again, the same pressure as 620 torr, but in different units.

How do you convert cm to mm ?

Answer
1cm=10mm
$$\therefore $$You can multiply the number of centimeters by 10 to obtain the number of millimeters, for instance:
$$ 3.2 cm .\dfrac{10mm}{1cm} = 32 mm $$

How do you convert -70 degrees into radian measure ?

Answer
$$ - 90 degrees \equiv a \leq nt \rightarrow : - \dfrac{\pi}{2} $$
$$ -70 degrees \equiv a \leq nt\rightarrow : xradian $$
$$ x = \left ( - \dfrac{II}{2} \right ) . \left ( \dfrac{7}{9} \right ) = -\dfrac{7 \pi}{18} $$

How do you convert miles per hour to meters per minute?

Answer
You use a series of conversion factors.
Convert miles to metres
$$ 1 mi \times \dfrac{5280 ft}{1 mi} \times \dfrac{12 in}{1 ft} \times \dfrac{2.54 cm}{1 in} \times \dfrac{1 m}{100 cm} = 1609 m $$
Convert hours to minutes
1 h = 60 min
Divide the distance by the time
$$ \therefore 1 mph = \dfrac{1 mi}{1 h} = \dfrac{1609 m}{60 min} = 26.82 m/min $$
To convert miles per hour to metres per second, you multiply by 26.82.

How many nanometers are there in 1 cm ?

Answer
1 centimeter has 10,000,000 i.e. 10 million nanometers.
Explanation:
Standard unit in this system is 1 meter.
There are a billion i.e. 1,000,000,000 nano units in a standard unit and hence 1,000,000,000 nanometers in one meter.
As there are 100 centimeters in each meter,
1 centimeter has
$$\dfrac{1, 000 ,000}{100} = 10,000,000 $$ i.e 10 million nanometers.

How do you convert between moles and liters ?

Answer
You don't do this conversion....
Explanation:The mole is simply the number of particles. And litres is a UNIT of volume.
Density$$ = \dfrac{Mass of particle}{Volume occupied by the particle} $$
CAN be related to the molar quantity, but this was not what you asked...

How do I convert m/s to km or km/h ?

Answer
Look at this previous answer to a question on unit conversions:
Explanation:
There would be no way to convert m/s to km. You would need to end up with units of distance/time. However conversion from m/s to km/h can be done and you already have 2 answers to help you do that. I decided to add my thoughts on unit conversion.
The Khan
Academy video one of your previous answers included is good. I decided to add my thoughts on unit conversion. You might get some additional help from the above link to an answer I wrote about 6 months ago to a Socratic question on this topic.
I hope these answers help you,Steve
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What are some examples of Newton's third law?

Answer
-Hitting A Wall (I know, it's dumb)-Rowing a boat-Walking (Yes, As Simple As That..)
Explanation:
If you hit a Wall with your hands or legs, you get hurt. Why?
Because of Newton's Third Law. You hit the wall with a force,
and that exact same amount of force is returned by the wall.
While Rowing a boat, when you want to move forward on a boat, you paddle by pushing the water backwards, causing you to move forward.
While Walking, You push the floor or the surface you are walking on with your toes, And the surface pushes your legs up, helping you to lift your legs up.

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1878718_1904913_ans_c4d3f47c0aee4cf8a14530057c156425.PNG

What is Newton's third law?

Answer
For every action, there is an equal and opposite reaction.
Explanation:
Newton's 3rd Law states : For every action, there is an equal and opposite reaction.
Remember:
According to this law, forces always act in equal by opposite pairs.
Action and reaction force pairs don't cancel each other out because they act on different objects.
The downward force is the action force. The reaction force is the the force that is exerted.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Looking at the picture below, we see that when the force of the finger is against the wall, the force exerted by the wall is pressing back towards the finger.

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When calculating percent error, what does it mean if I get a negative number for mass?

Answer
It means that the experimental mass is greater than the accepted mass. However, mass cannot be negative. Refer to the explanation.
Explanation:It means that the experimental mass is greater than the accepted mass. However, mass is always positive. If you are calculating percent error, the difference between the experimental value and the accepted value is an absolute value. So even if you get a negative number in your calculation, because it is an absolute value, it is positive.
Note: Sometimes the experimental value is called the actual value, and the accepted value is called the theoretical value.
% $$ eror = \left | \dfrac{(accepted value) - (experimental value)}{accepted value} \right | \times 100 $$ %

% $$ error = \left | \dfrac{(theoretical value) - (actual value)}{theoretical value} \right | \times 100 $$ %
Notice that in the above formulas, absolute value bars are used to indicate that the difference between the two values is positive. Also notice that it doesn't matter which order the two values are in, because the difference is an absolute value.

How many ounces in $$1/4$$ of a pound?

$$4$$ ounces

Explanation:

Although we don't use this system in Australia any more, I

still remember that in the "imperial system" of weights: 1 pound $$=16$$

ounces.

Hence, $$\dfrac{1}{4}$$ pounds $$=\dfrac{16}{4}$$ ounces

$$=4$$ ounces

How do you convert SI units ?

Answer
Multiply or divide by powers of 10.
SI units are easy to convert because you multiply or divide by 10 - sometimes more than once. Think of a staircase - every time you step up a stair, you divide by 10; every time you step down a stair, you multiply by 10.Another way to think of it is: as you move down the staircase, the decimal moves to the right; as you climb up the staircase, the decimal moves to the left.
If you need to memorize the order of the prefixes, there are a number of mnemonics that can help you. My personal favorite is "King Henry Dropped over Dead Converting Metrics."
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How many seconds are in a 24 hour day ?

Answer
Well there are 60 seconds in a minute and 60 minutes in an hour and 24 hours in a day. Thus:
60 60 24 = 86 , 400 seconds in a day

How many pints are in a quart?

Answer
1 Quart = 2 Pints

How do you convert 4.5 gal to L? How about to mL ?

What is the SI unit of mass?

Answer
kilogram (kg)
Explanation:
The SI unit of mass is kilogram.
Note that it has a prefix of kilo, which carries the value of 1000.
Meaning 1 kg = 1000 g

How many minutes are in 1 full week?

Answer
There's no easy way to do it :(
Explanation:
There are 60 minutes in an hour, therefore 60 * 24 = minutes in a day and, 60 * 24 * 7 = minutes in a week, so 60 * 24 = 1440. and 60* 24 * 7 $$ \rightarrow 1440 * 7 = 10080 $$minutes in a week.

Is it possible to add a scalar to a vector? Why or why not?

We cannot add a vector and a scalar quantities together because they have different dimensions.

Explanation:

1. A vector quantity is defined as a physical quantity which has both magnitude and direction. For example, velocity, displacement etc. A scalar quantity is a quantity which has magnitude only but no direction. For example, distance, speed etc.

2. It is impossible to add the two together because of their different dimensions . This basically means that being a vector quantity a particular physical quantity will have both magnitude and direction. Summing the two quantities together we have to describe the direction of the resultant quantity. As a scalar quantity does not have a direction it would be next to impossible to describe the direction of the resultant.

3. For example, let's take a body moving with a velocity of $$60kms^{-1}$$ north and covering a distance of $$120km$$.

Now, adding the two is not possible as we cannot describe the direction of the resultant quantity.

Is one tenth of a foot a common unit of measurement?

$$ \dfrac{1}{10} $$ of a foot is a very unusual measurement. I am not saying it doesn't exist, only that I've not heard it before.
Explanation :
$$ \dfrac{1}{12} $$ of a foot = $$1$$ inch , $$1$$'' or $$2.54\ cm $$. $$ \dfrac{1}{10} $$ of an inch $$(2.54\ mm) $$ was fairly commonly used.

Convert $$16$$ degree celsius into fahrenheit.

Relationship between Celsius and Fahrenheit is

$$\dfrac{C}{5} = \dfrac{F - 32}{9}$$

$$\dfrac{16}{5} = \dfrac{F - 32}{9}$$

$$F - 32 = \dfrac{16 \times 9}{5}$$

$$F = \dfrac{16 \times 9}{5} + 32$$

$$F = \dfrac{144}{5} + 32$$

$$F = \dfrac{144 + 160}{5} = \dfrac{304}{5} = 60.8^\circ$$

Can someone lend me a hand in explaining sig figs involving different units?
How would I solve and express the answer in sig figs?

Answer:
You multiplied two answers, and one of them has three sig figs. The other has two. So the fewest number of sig figs indicates the number you are less sure about with regards to its precision.
$$5.50 \times 10^{8} mg \times \dfrac{4.0 \times 10^{5} mol}{1 mg}$$

$$= 2.2 \times 10^{13} mols$$
You only get the same number of sig figs from a multiplication or division process as the number you use with the fewest number of sig figs
you can only be as that which you are least sure about, which is the $$4.0 \times 10^{5} mols$$. which only has two sig figs.
In your conversion factor, when you have "per . . . ", that is an exact relationship except for the larger number.
So if you have $$\dfrac{0.9464 L}{quart}$$, the L is not exact, but the quart is, because you're sure
that for every quart, there is some quantity of L that you are using fewer decimal places for than the exact value. Your estimate is based on what number you equate to a single unit of something else, and that would affect your sig figs.

How are astronomical units, light years and parsecs related?

Each is used to measure the very large distance in our universe.
Explanation:
The AU or astronomical unit is the shortest distance of the three. It is the rough distance from the sun to the earth but since our distance to the sun varies from about 92.5 million miles to 93.5 million miles it is not exact. The average, 93 million miles is used. The AU is used strictly to measured distance in our solar system.
The next distance is a light year. A light year is the distance light travels in one year. Light travels at 186,000 miles per second. Multiplied out that means light travels roughly 6 trillion miles in one year. The nearest star is about 4.22 light years away. That comes to roughly 25 trillion miles. The distance in trillions is simply to great for the human mind to grasp and overburdens computers when doing measurements.
Finally there is the Parsec. It is equal to about 3.26 light years. A parsec is a very complex idea. Basically it is used to measure the distances between any two objects beyond our solar system. It is complex because it takes into account the movement of the earth relative to those other two objects to better define the desired result.

Derive the formula for Celsius to Fahrenheit?

Answer
Compare the number of degrees from the freezing point of water to its boiling point on each scale to find a ratio and add in the differences between the freezing points.
Explanation:
The Fahrenheit freezing point of water is $$ 32^{0}F $$and its boiling point is$$ 212 ^{o}F $$
$$ 212 ^{o}F - 32^{o}F = 180 ^{o} F $$ between the freezing point and boiling point of water.
The Celsius freezing point of water$$ 0^{o}C$$and its boiling point is$$100^{o}C $$
$$ 100 ^{o}C - 0^{o}C = 100^{o} C $$ between water's freezing and boiling points.
This results in a ratio for C to F of $$ \dfrac{100}{180} or \dfrac{5}{9} $$ and
this results in a ratio for F to C of $$ \dfrac{180}{100} or \dfrac{9}{5} $$
Then $$ 32^{0}F $$ equal $$ 0^{o}C $$ , so
The formula for $$ ^{o}C to ^{o}F $$ is
$$ \left ( ^{o}C \times \dfrac{9}{5} \right ) + 32 = ^{o} F $$

Can u derive the formula for orbital velocity with proper explanation?

Answer:
$$\Rightarrow v = \sqrt{\dfrac{GM}{r}}$$
Explanation:
Orbital velocity is the speed and direction of an object in orbit.
To derive orbital velocity, we concern ourselves with two concepts:
Gravitational force
Centripetal force
Gravitational force is important, because it is the force that allows orbiting to exist. A central body exerts a gravitational force on the orbiting body to keep it in its orbit.
Centripetal force is also important, as this is the force responsible for circular motion. For deriving a simple equation for orbital velocity, we will assume uniform circular motion. In the case of an orbiting body, the centripetal force is the gravitational force.
This "is" usually equates to an "=". So we should start by saying that the gravitational force $$F_{g}$$ is equal to the centripetal force $$F_{c}$$:
$$\Rightarrow F_{g} = F_{c}$$
Now, we need to know how these forces are defined. Gravitational force is based on the masses of both objects and acts as the inverse of the square of the distance:
$$\Rightarrow F_{g} = \dfrac{GMm}{r^{2}}$$
where G is the gravitational constant, M is the mass of the object applying the force, m is the mass of the orbiting body, and r is the distance between the two objects.
Centripetal force is defined as mass times acceleration, where we are considering centripetal acceleration $$a_{c}$$:
$$\Rightarrow F_{c} = ma_{c} = \dfrac{mv^{2}}{r}$$
where m is the mass of the object undergoing uniform circular motion, v is its speed, and r is the radius of the circle defined by its motion.
Now we equate:
$$\Rightarrow F_{g} = F_{c}$$

$$\Rightarrow \dfrac{GMm}{r^{2}} = \dfrac{mv^{2}}{r}$$
We want to find v:
$$\Rightarrow \dfrac{GM m}{r^{2}} = \dfrac{m v^{2}}{r}$$

$$\Rightarrow \dfrac{GM}{r} = v^{2}$$
Hence :

$$\Rightarrow v = \pm \sqrt{\dfrac{GM}{r}}$$

$$\Rightarrow v = \sqrt{GM}r$$

What is meant by 'terminal velocity' for a skydiver, and what forces are acting when a skydiver is falling at terminal velocity?

When a parachutist first leaves the plane, with the chute not open, the main force acting is gravity. As her speed through the air increases, the air resistance also increases. At 'terminal velocity', which is about 200 km/h, the air resistance force balances the gravitational force and the parachutist stops accelerating and falls at constant velocity.

Once the parachute is open the air resistance is much greater due to the greater surface area, so the new new 'terminal velocity' is much slower, perhaps 20 km/h or so. The forces will again come into balance (when the chute first opens there is a net upward force which slows the downward motion) and the parachutist will fall at the slower velocity.

Actually calculating the value of the air resistance force is easy at either of the terminal velocities, since it is just the same in an upward direction as the gravitational force in the downward direction. It is very hard during any of the accelerations, because it requires understanding the shape of what is falling, the density of air and a number of other variables, and requires fairly sophisticated calculus.

An elastic cord is $$61\ cm$$ long when a weight of $$75\ N$$ hangs from it but is $$85\ cm$$ long when a weight of $$210\ N$$ hangs from it. What is the "spring" constant $$k$$ of this elastic cord?

The spring constant is $$=577\ Nm^{-1}$$
Let the length of the elastic cord at rest $$=lm$$
Therefore,
In the first case, $$k=\dfrac{F_{1}}{\Delta x_{1}}=\dfrac{75}{0.61-l}$$
In the second case, $$k=\dfrac{F_{2}}{\Delta x_{2}}=\dfrac{210}{0.85-l}$$
$$75(0.85-l)=210(0.61-l)$$
$$210l-75l=210\dot \ 0.61-75\dot \ 0.85$$
$$135l=64.35$$
$$l=\dfrac{64.35}{135}=0.48$$
So,
$$k=\dfrac{75}{0.61-0.48}=576.9\ Nm^{-1}$$

A machine gun fires $$10$$ rounds per second. The speed of the bullets is $$300\ m/s$$. What is the distance in the air between the flying bullets?

horizontal distance $$=30\ m$$
I'll assume you mean to say the horizontal distance between them.
After the bullets are launched from the gun, their horizontal motion is constant (idealized projectile motion).
We know that one bullet is fired every $$.1\ s$$ so we essentially need to find the horizontal distance a bullet would travel in $$0.1\ s$$ with the initial spped.
To do this, we use the equation
$$\Delta x=v_{0x}t$$
where
$$\bullet \Delta x$$ is the change in $$x-$$ position, which is equal to the distance between bullets
$$\bullet v_{0x}$$ is the initial horizontal speed of the bullet $$(300\ m/s)$$
$$\bullet t$$ is the time interval $$(0.1\ s)$$
Plugging in values:
$$\overset { distance }{ \overbrace { \Delta x } } =(30\ m/s)(0.1\ s)=30\ m$$

A sprinter runs around a $$440$$ meter circular track in $$49$$ seconds. What is her average speed? What is her average velocity? Can you tell anything about her instantaneous velocity $$5$$ seconds after the start?

Answer
Average speed is 8.98 m/s while average velocity is zero. You can say nothing about the instantaneous velocity after 5 s.
Explanation :
Average speed is based on the distance travelled - 440 metres in this case. Divide this by the time taken to cover the distance, and you have average speed.
$$ 440 m \div 49 s = 8.98 \dfrac{m}{s} $$
Average velocity is based on the displacement of the runner during the lap run - the resultant change in location, which is zero on a circular track.
Finally, the average speed tells us nothing about the instantaneous velocity at any moment. For all we know, he may have stopped to get a rock out of his shoe at this time!

An atom of gold has a mass of approximately $$3.25 \times 10^{-22}$$ grams. What is the mass $$1000$$ atoms of gold?

A mass of an atom of gold has a mass of approximately $$3.25\times 10^{-22}$$ grams,

Mass $$1000$$ atoms of gold would be = $$3.25\times 10^{-22}\times 1000$$

$$=3.25\times 10^{-22}\times 10^{3}$$
$$=3.25\times 10^{(-22+3)}$$

$$= \underline{3.25\times 10^{-19}}$$ grams

A value of 345mm is a measure of?

Answer
A measure of length to three significant digits.
Explanation:
mm millimeters is a measure of distance.
345 has three significant digits.

A particle moves along a straight line with velocity given by $$v(t)= 7 - (1.01)^{-t^2}$$ at time $$t \geq 0$$. What is the acceleration of the particle at time $$t=3$$?

The acceleration when $$t=3$$ is
$$a(3) = \frac{2.3.( \ln 101 - \ln 100)}{101^{3^2}}. 100^{3^2}$$
$$=0.055 \ ms^{-2}$$

Convert 18 km/h to m/s? Answers with steps

Answer
18km/h = 5m/s
Explanation:
To convert km/h to m/s we need to first convert the units.
So 1km / h $$ = \dfrac{1000}{60.60} $$
upon solving this we get 1km / h $$\dfrac{5}{8}$$ ms
now multiply the kmn / h into $$\dfrac{5}{8}$$
you will get the answer as 5m/s

How are density mass and volume related?

They are related by the density triangle.
Explanation:
They are related by the density triangle.
$$d = \dfrac{m} {V}$$
$$m = d \times V$$
$$V = \dfrac{m} {d}$$
Density
Density is defined as mass per unit volume.
$$d = \dfrac{m} {V}$$
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1917446_1906775_ans_e0f950df8ef04ace85aeff12be30bf5a.png

Which are the largest atoms?

A fundamental trend observed for the periodic table is that atomic size increases down a Group, a column of the Periodic Table, yet decreases across a Period, a row of the Periodic Table, from left to right as we face the table.

This fundamental trend is a consequence of Periodicity and two atomic properties. In a given atom, incomplete electronic shells shield the nuclear charge very ineffectively. The result, as we go across a period, the element to the right is a smaller atom due to the increased (and poorly shielded) nuclear charge.

Thus due to periodicity trends, the first group elements are the largest.

How does force change the shape of an object?

Force applied causes deformation in the object. It changes the relative positions of constituent particles in the crystal lattice.

As soon as that happens, the interatomic or intermolecular forces come into play and they, tend to restore the solid back to its the original shape.

This restoring force per unit area is called Stress. When external forces are removed, the internal forces tend to restore the solid back.

This property is called Elasticity.

However, no material is perfectly elastic and what happens is that the body is not able to restore itself completely.

A car traveling $$85\ km/hr$$ strikes a tree. The front end of the the car compresses and the driver come to rest after travelling $$0.80\ m$$. What was the average acceleration of teh driver during the collision?

The acceleration is $$=-348.4 ms^{-2}$$
Explanation:
The initial velocity of the car (driver) is $$u=85 kmh^{-1}$$
$$u=\dfrac{85}{3.6}=23.61 ms^{-1}$$
The distance travelled by the driver is $$s=0.80m$$
The final velocity of the driver is $$v=0 ms^{-1}$$
Apply teh equation of motion,
$$v^2=u^2+2as$$
The acceleration is
$$a=\dfrac{v^2-u^2}{2s}=\dfrac{0-23.61^2}{2.0.80}$$
$$=-348.4 ms^{-2}$$

How do I get the molar mass of urea?

The molecular formula of urea is :$$ NH_2CONH_2$$

Thus the molar mass is : $$14 + 2 +12 +16 +14 +2 = 48 \ g/mol$$

How many atoms in an $$18 \ g$$ mass of glucose?

Molar mass of glucose = 180 g/mol.

Therefore the number of moles in 18 g of glucose : $$\dfrac{18}{180} = 0.1 \ mol $$

The number of atoms in 1 mole of glucose : $$ 6 \times C + 12 \times H + 6 \times O = 24 \times 6.022 \times 10^{23}$$

$$\therefore number \ of \ atoms \ in \ 18 \ g \ glucose = 0.1 \times 24 \times 6.022 \times 10^{23} = 14.4 \times 10^{23} \ atoms $$

How many formula units are in $$0.335$$ g CaO?

Number of formula units can be found by :

$$Formula \ units : moles \times 6.022 \ times 10 ^{23} $$

moles : $$ \dfrac{0.335}{56} = 0.00598 \ moles $$

Here, Molar mass of $$CaO = 56 \ gm/mol$$

$$\therefore Formula \ units = 0.00598 \times 6.022 \times 10^{23} = 3.6 \times 10^{21} $$

Ebonae's fish tank holds 40 gallons. How many quarts does the fish tank hold?

You can solve this by logic.
Each gallon is equal to 4 quarts.
1 gallon = 4 quarts
therefore
40 gallons = 4(40) quarts
40 gallons = 160 quarts

How can acceleration be negative?

Acceleration is a vector...meaning that it has a magnitude (a "number"/size value assigned to it) as well as a direction (typically indicated by a + or - sign)."Negative" acceleration typically happens in two cases. One of them is from slowing down, and one of them is based on frames of references.
1) Slowing down
This "negative" acceleration is actually called deceleration. To show the decrease, mathematically we put a negative sign to indicate this.
2) Frame of reference
So let's say we assign a frame of reference of saying that going right is the POSITIVE + direction, and going left is the NEGATIVE - direction.

Explain how biological preparedness can be applied to taste aversions and phobias?

Evolution has made humans respond more negatively to certain neutral stimuli because of other stimuli that have been associated with them that may be dangerous or harmful

.
Biological preparedness is the principle that certain negative associations are easier to make for the sake of survival of the species, based on human experience in the past.

An example is the snake. On its own as an object it is entirely harmless and would elicit no response from someone who has no experience of snakes, meaning it is a neutral stimulus. However, when a snake bites a human, it becomes a negative stimulus, and the human is conditioned to have a fear of snakes, because it has associated the object of a snake with the effects of its bite.

Through the course of human history it has become easier to associate the snake with its bite, and so some people may have innate fears or phobias of snakes for no apparent logical reason.

Taste aversions may come from the same principle. I have a friend who has problems with migraines, and once ate cheesecake and had a severe migraine afterwards. He loved cheesecake all through his childhood, but now has subconsciously associated it with migraines and gags at the thought of them. This is an example of classical conditioning, because a harmless thing has been associated with a harmful thing and so a conditioned response, such as screaming or gagging, is elicited by a harmless stimulus.
Classical conditioning was described in 1913 by John Broadus Watson, who famously said

"Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I'll guarantee to take any one at random and train him to become any type of specialist I might select - doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations and the race of his ancestors."
He believed that the entirety of human psychology can be explained by classical conditioning, which is a form of behaviourism, and is almost by definition reductive.

How does impulse affect momentum?

Impulse is mathematically equal to the change in momentum

which happens during the action of the impulsive force (the force causing

impulse).

From Newton's second law,

$$\vec{F}=\frac{d \vec{p}}{d t}$$

$$\Rightarrow \vec{F} d t=d \vec{p}$$

Integrating both sides,

$$\vec{F} \int_{t_{0}}^{t} d t=\int_{p_{0}}^{p} d \vec{p}$$

$$\Rightarrow

\vec{F}\left(t-t_{0}\right)=\vec{p}-\vec{p}_{0}$$

By definition, impulse, $$\vec{J}=\vec{F}\left(t-t_{0}\right)$$

Thus, Impulse = Change in momentum

How does the atomic number affect atomic radius?

The atomic number of an element is the number of protons present in the nucleus of an atom of the element. Because of that, we can say that the atomic number represents the positive charge of the atom.

As the positive charge of the atom increases, the atomic radius decreases because the positive charge will bring the electrons (negatively charged) closer to the nucleus. This is called the effective nuclear charge of an atom.

Atomic radius becomes smaller as we move across a row/period in the periodic table because it increases the number of protons. As the number of protons increases, the effective nuclear charge increases across the same period because the electrons are added in the same shell. So, the electrons are pulled closer to the nucleus, and the atomic size decreases across a period.

But, the atomic radius becomes larger as we move down a group or column in the periodic table because it increases the number of energy levels with each successive period. As we move down the group, the number of period increases, which means the number of shells in an atom also increases. So, the extra electrons are added in the next shell with each successive period down a group, and the atomic size increases with an increase in atomic number down the group.

How do chemistry and biology relate?

There is a saying that claims that Biology only works because of Chemistry and Chemistry only works because of Physics.

The biological processes of living organisms depend upon the interactions of the atoms, molecules, and compounds that make up living tissues and the environment in which life takes place.

The structural composition of the living organism begins with atoms making molecules and compounds, molecules and compounds forming organelles, organelles forming cells, cells forming tissues, similar tissues with similar functions for organs, organs function to form systems and systems form the multicellular organisms that roam the planet from fungi to plants and plants to animals. Not to mention all of the unicellular organisms that also interact in the living systems that sustain life on this planet.

We can begin with the fact that the earth's biosphere is about $$75\%$$ water and living cells are also $$75\%$$ water. Water is composed of an atom of Oxygen bond to two hydrogens by sharing an electron with each Hydrogen in a molecular bond that creates a slightly higher positive charge on each hydrogen and a slightly higher negative charge on the Oxygen. These arrangements of the atoms and their charges make water a polar molecule. The fact that water molecules are polar gives them unique properties of adhesion (they like to adhere to surfaces) and cohesion (they like to join together).

These properties of water make it the universal solvent, capable of dissolving almost any material. Makes water less dense as a solid (ice) than as a liquid (water), which is why ice floats in a refreshing glass of iced tea. Water's polarity creates spaces between the molecules to hold dissolved materials like salt in the seawater.

Water is the primary material in cytoplasm and blood which allows for the transport of materials in both unicellular and multicellular organisms. Water is the Hydrogen donor in the energy exchanges that take place in photosynthesis and cellular respiration. The hydrogen and hydroxide molecular bond of water makes it act as both an acid and a base providing Hydrogen ions and hydroxide ions for an infinite number of chemical reactions that take place at the cellular level.

Basically, this is a long-winded answer that hopefully gets each of us to understand that every activity that sustains life on the planet takes place only because of the chemical properties of the atoms, molecules, and compounds involved. Whether it is a plant undergoing photosynthesis by removing carbon dioxide from the atmosphere in order to create glucose and oxygen for aerobic respiration in an animal or the complex ionic dance of the sodium and potassium pump that allows nerves to transmit information, everything living thing depends upon Chemistry for life on earth to continue.

Are atomic mass, formula mass, and molar mass the same thing?

When we write "formula mass", we usually mean the mass associated with 1 mole of such a formula; i.e. Avogadro's number of such a formula. Molar mass is the same thing: Avogadro's number of whatever stuff you have. The ability to successfully calculate equivalent masses of compounds is vital to success in Chemistry.

Atomic mass is the mass associated with a mole of atomic species; this is not always the same as molar mass: a mole of $$O$$ atoms is $$\cfrac12$$ the mass of a mole of oxygen molecules, $$O_2$$ species.

How do you draw $$s, p, d, f$$ orbitals?

An $$s$$ orbital is a sphere. In two dimensions, we draw it as a circle.
A $$p$$ orbital consists of two lobes of electron density on either side of the nucleus.
We usually draw $$p$$ orbitals as figure eights, but we should remember $$p$$ orbitals are really much fatter than in our usual drawings.
Four of the five d orbitals consist of four lobes pointed towards the corners of a square, like a four-leaf clover. The fifth orbital looks like a $$p$$ orbital with a doughnut around its middle.
We usually draw $$d$$ orbitals as skinny teardrops pointing in various directions, but we should remember that the lobes are really much fatter than in the drawing.
The seven f orbitals are even more complex shapes. The ones we see in diagrams are linear combinations of the $$ml = -3$$ to $$+3$$ orbitals. Here is one common set of combinations.
If you absolutely have to draw them, you can draw the shapes as below.
$$\bullet$$ One orbital looks like a $$p$$ orbital with two doughnuts around its middle.
$$\bullet$$ Two orbitals have eight lobes pointing towards the corners of a cube.
$$\bullet$$ Four orbitals have six lobes oriented in various planes (easiest to draw).
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1914126_1907890_ans_ebcd0184e7234c24ae47faec740831b4.jpg

How do you calculate mole fractions?

Mole fraction is a way to express the concentration of different components of a solution.

Let us consider you prepare a solution by dissolving $$n $$ moles of salt in m moles of water.

$$Mole \ fraction \ of \ salt \ in\ solution =\dfrac{ moles \ of \ salt }{( moles\ of\ salt + moles \ of \ water}$$

$$Mole\ fraction\ of\ salt =\dfrac{ n }{ ( n + m)}$$

$$Mole \ fraction \ of\ water = \dfrac{moles \ of \ water }{ ( moles \ of \ salt + moles\ of\ water)}$$

$$Mole\ fraction \ of \ water = \dfrac{m }{ ( n + m)}$$

Every Wednesday Carla runs 2.5 miles. How many feet did she run?

Each mile has 5,280 feet. And so we can find the feet in 2.5 miles this way:
$$2.5\times5280 = 13,200$$ feet

How do you use scientific notation?

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing $$0.0000000056$$, we write $$5.6 \times 10-9$$.

Move the decimal place to the right or left to create a new number from $$1$$ up to $$10$$.
Determine the exponent, which is the number of times you moved the decimal.
Put the number in the correct form for scientific notation.

The exponent in scientific notation is equal to the number of times the decimal point must be moved to produce a number between $$1$$ and $$10$$
Scientific notation is valuable in our world because many jobs use or require it. Most occupations such as chemist, astronomers, and engineers use it on a daily basis when writing down numbers that are to big or to small to be written out in a reasonable amount of time.
Some examples of writing Scientific Notation from Standard Notation

How many inches are in $$\dfrac{1}{4}$$ yard?

Answer:
See a solution process below:
Explanation:
We know the conversion factor of yards to inches is:
1 yard=36 inches
To find how many inches in $$\dfrac{1}{4}$$ yard we can multiply each side of the equation by $$\dfrac{1}{4}$$ giving:
$$\dfrac{1}{4} \times 1 yard = \dfrac{1}{4} \times 36 inhes$$

$$\dfrac{1}{4} yard = \dfrac{36}{4} inches$$

$$\dfrac{1}{4} yard = 9 inches$$
Therefore, there are 9 inches in $$\dfrac{1}{4}$$ yard

How do you find the magnitude of the acceleration of the particle?

$$3.2\dfrac{m}{s^2} $$

Explanation :
$$ \vec{F_{1}} = (3 \hat{i} + 5 \hat{j}) N $$

$$\vec{F_2} = (6\hat{i} - 2 \hat{j}) N $$

Resultant $$ \vec{F_{1}} + \vec{F_{2}} = \vec{F} $$
$$ = [(3 \hat{i} + 6 \hat{i} ) + (5 \hat{j} - 2 \hat{j}) ] N $$
$$ = (9 \hat{i} + 3 \hat{j}) N $$

$$ |\vec{F}| = \sqrt{9^{2} + 3^{2}} = \sqrt{81 + 9} = \sqrt{90} $$
$$ = 9.5\ N $$

Newton's $$2nd$$ Law
$$F = ma $$
$$9.5 = 3 \cdot a $$
$$a = 3.2\ m/s^{2} $$
1914207_1908778_ans_f93c365d97dc4398b43d5b9297305ff2.png

1914207_1908778_ans_f93c365d97dc4398b43d5b9297305ff2.png

How many inches are in 1$$\dfrac{ 1}{3}$$ yards?

Answer:
48 inches
Explanation:
using the conversion
1 yard =36 inches
$$\Rightarrow \dfrac{1}{3} yard = \dfrac{36}{3} = 12 inches$$

$$\Rightarrow 1\dfrac{1}{3} yard = 36 + 12 = 48 inches$$

How many cents is 3 quarters?

Answer
3 quarters is 75 cents.
Explanation:
Each quarter equals 25 cents. If there are three, then we have three sets of 25 cents.
25+25+25=75
Thus, 3 quarters equals 75 cents.

How fast does earth rotate near the equator?

Circumference of Earth is 40075 kilometers.

40075/24=1669.7 kilometers per hour.

Explanation:

Earth rotates it self once in 24 hours So speed at equator is 1669.7 kilometer per hour\

Actual rotation is in 23 houirs 56 minutes and 4 seconds.For making calculation simpsle I took the usual value 24 hours of rotation period..

How many cubic centimeters are in an $$8.00\ oz$$ bottle of cough medicine?

Answer
8 US fluid oz.have 236.56 cubic centimeter. However, 8 British fluid oz. have 227.28 cubic centimeter.
Explanation:
In US fluid oz. each oz. has 29.57 cubic centimeter (or mililiter) of fluid. Hence in 8 oz ., these are $$ 8 \times 29.57 = 236.56 $$ cubic centimeter.
However, British fluid oz. is 28.41 cubic centimeter and hence 8 oz. will have $$ 8 \times 28.41 = 227.28 $$ cubic centimeter

How many $$cm^{3} $$ are the in $$ 1m^{3} $$ ?

Answer
One million
Explanation :
$$ 1 cm ^{3} = ( 1 \times 10^{-2}) .m^{3} = 1 \times 10^{-6} . m^{3} $$
And thus $$ \dfrac{1. m^{3}}{1. cm^{3}} = \dfrac{1.m^{3}}{10^{-6} . m^{3}} = 1, 000, 000 $$

How many inches is in 1 yard?

Answer:
36 inches
Explanation:
Please refer to How many inches is there in 1/8 th of a yard?

How many inches is there in $$\dfrac{1}{8}$$th of a yard?

Answer:
There are $$4\dfrac{1}{2}$$ inches in $$\dfrac{1}{8}$$ yard.
Explanation:
In 1 yard we have 3 feet and in each feet we have 12 inches.
So we have $$3 \times 12 = 36$$ inches in each yard.
Hence in $$\dfrac{1}{8}$$ yard we have $$36 \times \dfrac{1}{8} = \dfrac{9}{2} = 4\dfrac{1}{2}$$ inches.

How many cups are in a gallon?

Answer
According to
1 Gallon [Fluid, US] = 16 Cups [US]

How many cups are in $$\dfrac{1}{2}$$ a gallon?

Answer
See a solution process below:
Explanation:
We know the conversion factor of gallons to cups is:
1 gallon=16 cups
To find the number of cups in $$\dfrac{1}{2}$$ gallon we can multiply each side of the equation by $$\dfrac{1}{2}$$ giving :
$$\dfrac{1}{2} \times 1 gallon = \dfrac{1}{2} \times 16 cups $$
$$\dfrac{1}{2} gallon = \dfrac{16}{2} cups $$
$$\dfrac{1}{2} gallon = 8 cups $$
Therefore , there are 8 cups in $$\dfrac{1}{2} $$ gallon

How many cubic centimeters would you need to have 1 mole of aluminum?

Answer
The mole is a value that can compared to particles (molecules and atoms), volume and mass.
The mole is equal $$ 6.02 x 10 ^{23} $$ molecules, which is known as Avogadro's number. The mole is equal to 22.4 Liters of gas at standard temperature and pressure (STP). And, the mole is equal to the molar mass (gfm) of the element or molecule.
The element aluminum has a molar mass of 26.99 amu. Therefore, a 1 mole sample of aluminum would have a mass of 26.99 grams.
Once we know the mass of the mole of aluminum we can use the density to calculate the volume. The density equation is $$ D = \dfrac{m}{v} $$ , where D = density , 3 = mas and v = volume
The standard density of aluminum is $$ 2.70 \dfrac{g}{cm^{3}}$$

How many feet are in 4 miles?

Answer
4 miles=21,120 feet
Explanation:
1 mile=5280 feet ...just something you need to memo
$$ 4 miles = 4 \times 5280 = 21120 feet $$

How many feet are in 2.4 miles?

Answer
12672
Explanation:
There are 3 feet in a yard and 1760 yards in a mile.
So in 2.4 miles there are:
2.417603=241763=12672 feet

How many feet are in $$\dfrac{1}{2}$$ of a mile?

Answer
See a solution process below:
Explanation:
We know the conversion factor of miles to feet is:
1 mile=5280 feet
To find how many feet in a $$ \dfrac{1}{2} $$mile we can multiply each side of the equation by $$\dfrac{1}{2}$$ giving :
$$\dfrac{1}{2} \times 1 mile = \dfrac{1}{2} \times 5280 feet $$
$$\dfrac{1}{2} mile = \dfrac{5280}{2}feet $$
$$\dfrac{1}{2} mile = 2640 feet $$
There are 2,640 feet in $$\dfrac{1}{2}mile $$

How many feet is 15 miles?

Answer
$$ 15 \times 5280 = 79,200 $$ feet
Explanation :
There is 5280 feet in 1 mile.
This means that 15 miles is:
$$ 15 \times 5280 = 79,200 $$ feet

How many feet are in .55 miles?

Answer
2904 feet
Explanation:
1 mile = 5280 feet
$$ 0.55 miles = 5280 \times 0.55 feet = 2904 feet $$

How many degrees celsius equals one degree fahrenheit?

Answer
Temperature in celsius is $$ - 17.22 ^{\circ} C $$
Explanation :
If F is the temperature in Fahrenheit and C is temperature in Celsius then
$$\dfrac{F - 32}{180} = \dfrac{C -0}{100} $$ or $$ \dfrac{F - 32}{9} = \dfrac{C}{5}$$
Hence if $$ F= 1 $$

$$c=-17.22^{°}$$

How many kilograms are equal to 5,000 grams?

Answer:
5 kilograms
Explaanation:
1000 grams = 1 kilogram
To convert grams to kilograms we divide by 1000
$$\dfrac{5000g}{1000} = 5kg$$

How many kilometers is 1.7 miles?

Answer:
If exact, then 2.7358848 kilometers, so to 2 significant figures that is 2.7 kilometers.
Explanation:
There are exactly 1.609344 kilometers in a mile by definition.
So if the figure 1.7 miles is precise, then in kilometers it is:
1.7×1.609344 = 2.7358848
If the figure given is only accurate to 2 significant figures, then we should only quote the answer to 2 significant figures too.
So 1.7 miles is approximately 2.7 kilometers.

How many degrees Celsius is 67 F?

Answer
19.44 degrees Celsius =67 degrees Fahrenheit
Explanation:
The formula for converting degrees Celsius to degrees Fahrenheit is
$$ ^{\circ} C = (^{\circ} F - 32) \times \dfrac{5}{9} $$
In your case
$$ C = (67 - 32) \times \dfrac{5}{9} $$
$$ C = 19.44^{\circ} C $$

How many degrees = 1 radian?

Answer
$$ 1^{\circ} = \dfrac{\pi}{180} = 0.0175^{\circ} $$
Explanation
Relation between radians and degrees is $$ \pi ^{c} = 180^{\circ} $$
$$ 1^{\circ} = \dfrac{\pi}{180} = 0.0175^{\circ} $$

How many feet in a mile?

Answer
5280 feet
Explanation:
According to British units
1 mile=8 furlongs
(A furlong is a commonly used unit)
And,
1 furlong=660 feet
Then
$$ \rightarrow 1 mile=(8660) feet $$
$$ \Rightarrow = 5280 feet $$

How many km are in 5.6mm?

Answer:
$$5.6 \times 10^{-6} km$$
Explanation:
If you convert to a bigger unit, the number gets smaller.
If you convert to a smaller unit the number gets bigger.
5.6mm is a really tiny distance - less than the distance across a finger nail. This is obviously a REALLY tiny fraction of a Km.
To convert mm to Km, divide by 1000 to get metres, then by 1000 again to get Km.
$$5.6 \div 1000 \div 1000$$ is easier written in scientific notation as it is a tiny fraction of a Km.
$$5.6 \times 10^{-3} \times 10^{-3} = 5.6 \times 10^{-6}$$
1 mm is one millionth part of 1 Km.

How many gallons are in 60 ounces?

Answer
60 fluid ounces are equal to 0.47 gallon.
Explanation:
Use dimensional analysis.
1 gallon = 128 fluid oz
The two conversion factors are:
$$ \dfrac{1 gal}{128 fl oz} and \dfrac{128 fl oz}{1 gal} $$
Multiply the given number of ounces by the conversion factor that cancels ounces and leaves gallons.
$$ 60 fl oz \times \dfrac{1 gal}{128 fl oz} = 0.47 gal $$

How many earth years are in 1 light year?

Answer
An earth year is a unit of time.
A light year is a measure of distance.
Explanation:
A light year is the distance light will travel in a vacuum over the period of one (earth) year.
Since light travels at about 186,300 miles per second, with 86,400 seconds per day and about 365 days per year, that works out at about:
$$ 186300 \times 86400 \times 365 \approx 5, 875 , 000, 000, 000 $$ miles

How many meters are in a yard?

Answer:
0.9144
Explanation:
There are exactly 2.54 cm in an inch.
There are 12 inches in a foot, so 122.54 = 30.48 cm in a foot.
There are 3 feet in a yard, so 330.48 = 91.44 cm in a yard.
There are 100 cm in a meter, so $$\dfrac{91.44}{100} = 0.9144$$ meters in a yard.

How many litres are in a gallon?

Answer:
3.78541 liters in a gallon
Explanation:
In a US gallon, there are approximately 3.78541 liters.

How many gallons are in 101.4 fl oz?

Answer
See a solution process below:
Explanation:
There are 128 fluid ounces in one gallons, so we can write and solve an equation for g (the number of gallons in 101.4 fluid ounces) as:
$$ \dfrac{1 gal}{128 oz} = \dfrac{g}{101.4 oz} $$

$$ \dfrac{1 gal}{128 oz} \times 101 .4 oz = \dfrac{g}{101.4 oz} \times 101.4 oz $$

$$\dfrac{ 1 gal}{128 oz} \times 101.4 oz = \dfrac{g}{101.4 oz} \times 101 .4 oz $$

$$\dfrac{1 gal}{128} \times 101.4 = g $$

$$ \dfrac{101.4 gal}{128} = g $$

$$0.7921875 gal = g$$
$$0.8 gal= g$$ rounded to the nearest 10th of a gallon.
There are approximately 0.8 gallons in 101.4 fluid ounces

How many light years away is the sun from Jupiter?

Answer:
Average Sun-Jupiter distance is 5.206 AU = 0.0000828 light year (ly) = 2612 light seconds (ls), nearly, compared to 499 light seconds, for the Earth.
Explanation:
1 AU - average Earth-Sun distance = 149597871 km. 1 light year = 62900 AU, nearly. 1 light year = 31558150 light seconds.

How many fluid oz. are in a gallon?

Answer
128 oz. =1 gallon
Explanation:
8 oz. = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
$$ 8 \times 2 \times 2 \times 4 oz . = 1 gallon $$
Note that British (including Canadian) measures are different from US measures. The same 128 oz. to 1 gallon holds but ounces are a different size.
US ounce $$ \approx 29.6 ml $$
Imperial (British) ounce $$ \approx 28. 4 ml $$

How many feet is 33 miles?

Answer
See a solution process below:
Explanation:
There are 5,280 feet in 1 mile so we can write a conversion factor as:
1 mile=5280 feet
To find the number of feet in 33 miles multiply each side of the equation by 33
$$ 33 \times 1 mile = 33 \times 5280 feet $$
33 mile=174240 feet
There are 174,240 feet in 33 miles

How many grams are in 2000 mg?

Answer

$$2 g$$
Explanation :
$$ 1 mg = 10^{-3} g $$
$$ 2000 mg = 2000 \times 10^{-3} .g$$
$$ = 2.000 .g $$

How many miles are in $$100$$ feet?

Answer:
0.018939 miles = 100 feet
Explanation:
We convert the 100 feet to miles
$$(100 feet) . \dfrac{1 mole }{5280 feet} = 0.018939 miles$$
God bless....I hope the explanation is useful

How many millimeters are in 50 cm?

Answer
500 millimetres
Explanation:
To convert from centimetres ( cm) to millimetres (mm) use the following conversion.
$$ 1 cm = 10 mm \leftarrow $$ worth remembering
$$ 1 cm \rightarrow 10 mm $$
$$ \Rightarrow 50 cm \rightarrow 50 \times 10 mm = 500 m m $$

How many grams are in 40 hectograms?

Answer
Well hecto $$ \equiv 10^{2} $$......
Explanation :
So we get $$ 40 \times 10^{2}.g. = 4000 .g.$$ i.e 4.0kg.

How many milliliters are in a cubic meter ?

Answer
About a million?
Explanation:
$$ 1mL = 1. .cm^{3} $$ are we agreed on this?But $$ 1. .cm^{3} = \left ( 1 \times 10^{-2} m \right )^{3} $$because the centi prefix $$ \equiv 10^{-2} $$And thus $$ \left ( 1 \times 10^{-2} m \right )^{3} = 1 \times 10^{-2} . m \times 1 \times 10^{-2}. m \times 1 \times 10^{-2} . m = `1 \times 10^{-6}.m^{3} $$
Ans so finally $$ .\dfrac{1 .mL}{1.m^{3}} = \dfrac{1 \times 10^{-6}.m^{3}}{1 . m^{3}} = 10^{-6} $$
Alternatively (finally again) $$ \dfrac{1.m^{3}}{1.mL} = \dfrac{1.m^{3}}{1 \times 10^{-6} m^{3}} = 10^{+6} $$
Thus there are$$ 10^{6}$$ one million, mL in a cubic meter.
We use the same methodology to show that there are 1000L in a cubic meter. A $$ m^{3} $$ is a VERY large volume.

How many micrograms make 1 kg?

Answer:
1 kilogram makes 1,000,000,000 or $$10^{9}$$ micrograms.
Explanation:
1 microgram is one-millionth of standard unit, which is gram here,
Hence, one gram has 1,000,000 micrograms.
As 1 kilogram has 1000 grams,
1 kilogram makes $$1000 \times 1,000,000 = 1,000,000,000$$ or $$10^{9}$$ miccrograms.

How many microliters are in 41.0 mL?

Answer:
41000 microliter
Explanation:
1 ml = 1000 microliter
Using this equality, we will make two conversion factors
$$\dfrac{1 ml}{ 1000 microliter}$$or $$\dfrac{ 1000 microliter}{ 1 ml}$$

$$41 ml \times\dfrac {1000 microliter}{1 ml}$$
41000 microliter

How many meters is 120 cm?

$$120.cm=1.20.m$$
Explanation:
$$1.cm=1 \times 10^{-2}.m$$
Thus $$120.cm=120 \times 1 \times 10^{-2}.m =120.m$$
Centi, micro, milli, and kilo are simply commonly used multipliers to save on the number of $$0000's$$ we have to write.
Micro $$(\mu)$$ means $$\times 10^{-6}$$
Milli $$(m)$$ means $$\times 10^{-3}$$
Kilo $$(k)$$ means $$\times 10^{3}$$
Mega $$(m)$$ means $$\times 10^{6}$$
Deci means $$\times 10^{-6}$$

How many meters in a mile?

Answer:
Exactly 1609.344
Explanation:
There are exactly:
2.54 cm in 1 inc
12 inches in 1 foot
3 feet in 1 yard
1760 yards in 1 mile
Hence there are:
2.541231760 = 160934.4 cm in 1 mile
There are exactly 100 cm in 1 meter
Therefore
$$\dfrac{160934.4}{100} = 1609.344$$ meters in 1 mile.

How many grams are in one atomic mass unit?

Answer
$$ 1a .m.u = 1.6726219 \times 10^{-27} kf $$
Explanation:
1 atomic mass unit (a.m.u.) is the mass of a proton or a neutron which is equal to $$ 1.6726219 \times 10^{-27} kg $$
which is close to the mass that you find in a periodic table.

How many square feet are in $$100m^2$$?

$$1076ft^2$$
Explanation:
First we obtain the conversion of feet to meters. Then we can square that to get the factor for $$\frac{ft^2}{m^2}$$
$$1ft=0.3048m$$
$$1ft^2=0.3048^2=0.0929m^2$$
Now we can use this factor for the desired conversion:
$$\frac{1ft^2}{0.0929m^2}*100m^2=1076ft^2$$

How many millimeters are in an inch ?

Answer
25.4 mm
Explanation:
There are 25.4 millimeters in one inch as given by the photo below:
1891314_1910917_ans_a4f82a499efa461d9a5a97c964953022.PNG

1891314_1910917_ans_a4f82a499efa461d9a5a97c964953022.PNG

How long in meters is 670 nanometers?

Answer:
670 nanometers is $$670 \times 10^{-9}$$ meters or $$6.7 \times 10^{-7}$$ metres in scientific notation or $$0.00000067$$ meters in standard form.
Explanation:
In metric system everything is standardized. In metric system as nano is one-billionth or $$10^{-9}$$
One nanometer is $$10^{-9}$$ meter, hence
670 nanometers is $$670 \times 10^{-9}$$ meters or $$6.7 \times 10^{-7}$$ metres in scientific notation or $$0.00000067$$ meters

How many minutes are in $$1.25$$ hours?

Answer
75
Explanation :
A conversion is just an applied ratio of values.
We know that there are 60 minutes in 1 hour $$ \dfrac{60 m}{1 hr} $$, so to find out how many are in 1.25 hours we arrange the ratios to give us a final answer in minutes.
$$\dfrac{60 m}{1 hr} (1.25 hr) = 75 m $$

How is solubility expressed in units of measurement?

Answer
Thanks for your question on solubility.
Usually, solubility is expressed in grams of solute per milliliters of solution.
Solubility can be expressed in any mass unit per any volume unit. On solubility graphs , solubility is usually expressed in grams of solute per mL of solution.

How many ml is in 2 liters?

Answer
2000ml
Explanation:
To determine the number of millilitres in 2 litres, we need to use a conversion factor.
To convert 2L to mL, multiply 2 L by the conversion factor:
$$ \dfrac{1000 mL}{1 L} $$
Thus :
$$ 2 L \times \dfrac{1000 L}{1 L} $$
The "L" unit cancels out in the numerator and denominator.
$$ 2 L \times \dfrac{1000 mL}{1 L} $$
Solve
$$ 2000 mL $$

How many minutes are in 0.5 hour?

Answer
30 minutes
Explanation :L
1 hours = 60 miniutes
$$ 0.5 hour \times \dfrac{60 minutes}{hour} = 30 minutes $$

How many minutes are there in 2.8 hours?

Answer
168 Minutes
Explanation :
1 Hour = 60 Minutes
So, 2.8 Hours = 2.8×60 Minutes = 168 Minutes

How many nanometers are there in 1 cm?

Answer
1 centimeter has 10,000,000 i.e. 10 million nanometers.
Explanation:
Standard unit in this system is 1 meter.
There are a billion i.e. 1,000,000,000 nano units in a standard unit and hence 1,000,000,000 nanometers in one meter.
As there are 100 centimeters in each meter,
1 centimeter has $$ \dfrac{1 , 000,000,000}{100} = 10,000,000 $$i.e. 10 million nanometers.

How many minutes are in 1 full week?

How many milliliters are equivalent to $$2.7$$ liters?

Answer:
2700mL
Explanation:
The m prefix in mL means milli, i.e. $$\times 10^{-3}$$
And thus $$\dfrac{1. L}{1. mL} = \dfrac{1. L}{1. \times 10^{-3}L} = \dfrac{1}{10^{-3}} = \dfrac{1}{\dfrac{1}{1000}} = 1000, i e. a 10^{3}$$ factors as required.
Note the arithmetic $$\dfrac{b}{a^{-1}} = \dfrac{b}{\dfrac{1}{a}} = a\times b$$ this is an important result for such dimensional analysis, as you can see in the given example.

How long is an eon in years?

Answer:
Eon has a number of meanings. In Astronomy, an eon refers to 1 billion $$(10^{9})$$ years. But it also refers to a very long, unspecified period of time, or specific geologic stages of the Earth
Explanation:
Since this question is posted in Astronomy, I will assume that the answer of eon = $$10^{9}$$ years is the most appropriate, however it is not the most common.
The term eon (or aeon) is frequently used as a term for a very long but un-specified time period, much the same way "forever" and "ages" are used.

In Earth history, stages of the earth's development are divided into four major eons (Hadean, Archean, Proterozoic and Phanerozoic), which are in turn divided into eras and periods. These geologic eons are distinguished by major stages in Earth's geologic history, rather than fixed periods of time.

How many arcseconds are in a degree?

Answer:
There are 3600 arcseconds in 1 degree.
Explanation:
We can use dimensional analysis to convert from degrees to arcminutes, then from arcminutes to arcseconds:
$$1^{\circ}$$
$$= 1^{\circ} . \dfrac{60 arcminutes}{1^{\circ}}$$
$$= 60 arcminutes$$
$$= 60 arcminutes . \dfrac{60 arcseconds}{1 arcminute}$$
$$= 60 . \dfrac{60 arcseconds}{1}$$
$$= 6060 arcseconds$$
$$= 3600 arcseconds$$

How long is 33 inches added to 4 feet 7 inches?

Answer:
It is 88 inches or 7 feet and 4 inches.
Explanation:;
As each feet has 12 inches, 4 feet have $$4 \times 12 = 48$$ inches. Hence 4 feet and 7 inches are 48 + 7 = 55 inches
and adding 33 inches to 4 feet and 7 inches is 33 + 55 = 88 inches.
Now as 12 inches equal to one foot and $$88 = 7 \times 12 + 4$$, we can also write 88 inches as 7 feet and 4 inches.

How many arcseconds are in $$1^{\circ}$$ ?

Answer:
There are 3600 arcseconds in $$1^{\circ}$$
Explanation:
Each degree has 60 arcminutes and each arcminute has 60 arcseconds.
Hence $$1^{\circ}$$ degree has $$60 \times 60 = 3600$$ arcseconds.

How many significant figures are in the measurement 0.0034 kg?

Answer
Two significant figures.
Explanation:
For starters, you should know that non-zero digits are always significant.
So right from the start, you know that this measurement has at least two significant figures, 3 and 4. $$ 0.0034 \rightarrow $$ two non-zero digits = two sig figs
Now, are the zeroes significant as well?
The answer is no. The reason is that zeroes that come after the decimal point are only significant if the number is greater than 1 or if they are sandwiched between two non-zero digits for numbers that are smaller than 1.
In your case, you have a number that is smaller than 1 and the two zeroes are not sandwiched between two non-zero digits, hence they are not significant.
Therefore, your measurement will have 2 significant figures, the two non-zero digits.

How to convert $$ 2.5 $$ radian to degree/minute/second?

1) converting to degree : (Multiply by $$ \frac{180}{\pi}$$)

=$$ 2.5 \times \frac{180}{\pi}=143.31^o$$

2) converting to minutes :( 0.31 \times 60$$)

=$$ 0.31 \times 60=18.6'$$

3) converting into seconds : ( $$ 0.6 \times 60 $$).

=$$ 0.6 \times 60=36"$$

So, $$ 25 $$ radians= $$ 143^o 18'36"$$

How many ounces are equivalent to a quarter of a pound?

Answer
There are 4 ounce in $$ \dfrac{1}{4} $$ pounds

Explanation Express this as a ratio in the form of
$$\dfrac{\text{Count of ounces} }{\text{counts of pounds}}$$

It is known that for 1 pounds there are 16 ounces giving
$$\dfrac{\text{Count of ounces }}{\text{counts of pounds}} \rightarrow \dfrac{16}{1} $$

But what we need is :
$$ \dfrac{\text{Count of ounces}}{\text{counts of pounds}} \rightarrow \dfrac{16}{1} \rightarrow \dfrac{?}{\dfrac{1}{4}} $$
so ? = $$ 16 \div 4 = 4 $$
So there are 4 ounces in $$ \dfrac{1}{4}$$ pounds

How many significant figures are in the measurement 2103.2 g?

Answer
5
Explanation:
The problem provides you with the following measurement
2103.2 g
The first thing you need to do here is to figure out the number of non-zero digits you have in this measurement.
As you know, non-zero digits are always significant, so right from the start you can say that your measurement has at least 4 significant figures, since
$$2103.2 \rightarrow 4 non-zero digits: 2,1,3,2 $$
Now, your measurement also contains a sandwiched zero, i.e. a zero that follows and is followed by a non-zero digit.
More specifically, you have
Sandwiched zeros are always significant, which means that your measurement has 5 sig figs
four non-zero digits: 2,1,3,2one sandwiched zero

How many $$\dfrac{1}{3}$$ cups do you need to make $$\dfrac{1}{2}$$ cup?

Answer:
one and a half $$\dfrac{1}{3}$$ cups make $$\dfrac{1}{2}$$ cup
Explanation:
We need to figure out how much more than $$\dfrac{1}{3}$$ cup is $$\dfrac{1}{2}$$ cup. That translates to this equation:
$$\dfrac{1}{3} + x = \dfrac{1}{2}$$
if we subtract $$\dfrac{1}{3} $$ from both sides we get:
$$x = \dfrac{1}{2} - \dfrac{1}{3}$$
In order to subtract or add fractions we need to make the denominators (the bottom parts) of both fractions equal to each other. In order to do that we find the Least Common Multiple between them. In this case between 2 and 3. It is 6, which is 2 times 3. Now we multiply the bottom and top of each fraction by the number in that multiplication above that is missing to get to 6, like this:
$$x = \dfrac{1 . 3}{2 . 3} - \dfrac{1 . 2}{3 . 2}$$
Notice that we multiply the $$\dfrac{1}{2}$$ by 3 in the top and bottom because we need 3 to make 2 time something equal to 6, and that we multiply the $$\dfrac{1}{3}$$ by 2 in the top and bottom for the same reason,
Once we make those multiplications we get:
$$x = \dfrac{3}{6} - \dfrac{2}{6}$$
$$x = \dfrac{1}{6}$$
We can see from the previous calculations that $$\dfrac{1}{1}$$ is equal to $$\dfrac{2}{6}$$, and that $$\dfrac{1}{6}$$ is half of $$\dfrac{2}{6}$$, so, in order to make $$\dfrac{1}{2}$$cup you need a whole $$\dfrac{1}{3}$$ cup plus half of it.

How long is $$\dfrac{7}{10}$$ of a mile, in feet?

Answer:
3696 feet
Explanation:
Each mile has 8 furlongs. Each furlong has 220 yards and each yard has 3 feet.
Therefore each mile has $$8 \times 220 \times 3 = 5280$$ feet and $$\dfrac{7}{10}$$ mile will have
$$5280 \times \dfrac{7}{10}$$
$$= 5285280 \times \dfrac{7}{110} = 3696$$ feet

How many base SI units are there?

There are seven fundamental units of measurement:

Length(meters)

Second (time)

kilogram (mass),

Ampere (electric current),

Kelvin (temperature),

Candela (luminous intensity),

Mole (amount of a substance).

Derived units are combinations of the fundamental units. There are many examples, such as metres/second (speed), newtons (force), watts (power) and pascals (pressure).

How many quarts are in 12 cups?

$$1 cup =0.25$$ quarts,
$$ x = 12 cups .\dfrac{0.25 qt}{1 cup}$$
$$ x = 12 cups .\dfrac{0.25 qt}{1 cup} $$
$$ x v= 12 .\dfrac{025 qt}{1} $$
x = 3 quarts
there are 3 quarts in 12 cups.

How many quarters does an hour have?

Answer
4 the hour a quarter past the hour, half-hour, a quarter till the hour.
Explanation:
An quarter of an hour is 15 mins.
$$ \dfrac{60}{15} = 4 $$ so there are 4 quarters in an hour.
15 mins past the hour is the first quarter.
Another 15 mins equals 30 mins.
$$15+15=30$$
$$ \dfrac{30}{60} = \dfrac{1}{2} $$
so half an hour is the second quarter
Another 15 mins equals 45 mins
$$15+15+15=45$$
he
$$60-45=15$$
so 15 mins before the hour is the third quarter.
Another 15 mins equals the hour
$$15+15+15+15=60$$
60 mins = an hour
so the hour itself is the fourth quarter.

How many ounces is $$0.2\, lbs$$?

$$ 1 lb = 16 ounces $$
$$ \Rightarrow 0.2 lb = 16 \times 0.2 = 3.2 $$ ounces

How many ounces in 1/8 pounds?

Answer
2 Ounces
Explanation:
1 pound = 16 ounces
Dividing both the sides by 8
1/8 pounds = 16 /8 ounces
2 ounces.

How many ounces are in one and a half quarts?

Answer
48 ounces.
Explanation:
1 quart is 31.99 ounces.
So,
$$ 1.5 \times 32 = 48 $$

How many quarts are in 10 gallons ?

$$1\ gal = 4\ qt$$
$$ 10 \times 1 gal = 10 \times 4qt $$
$$10\ gal = 40\ qt $$
There are 40 quarts in 10 gallons.

How many ounces is in 500 mL?

$$1 mL=0.033814$$ ounces
To find the number of ounces in 500 mL multiply each side of the equation by 500
$$ 500 \times 1 mL = 500 \times 0.033814 $$ ounces
$$ 500 mL = 16.907 $$ ounces
There are approximetely 17 ounces in 500 mL

How many ounces in 1/4 of a pound?

$$\because$$ 1 pound = 16 ounces.
Hence $$ \dfrac{1}{4} $$ pounds $$ = \dfrac{16}{4} =4\ ounces$$ ounces

How many centimeters are in 7.2 inches?

Answer:
18.29 centimeters
Explanation:
There are 2.54 cm in 1 in. Since we are converting inches to centimeters, the conversion factor will be $$\dfrac{2.54 cm}{1 in}$$
$$\therefore 7.2 in \times \frac{2.54 cm}{1 in} = 18.288 \approx 18.29 cm$$

How many pints are equivalent to 3 gallons?

2 cups: 1 pint;
2 pints: 1 quart;
4 quarts: 1 gallon.
Therefore there are $$ 2 \times 4 = 8 $$ points in 1 gallon
Therefore there are $$ 8 \times 3 $$ points in $$ 1 \times 3 $$ gallons
or 24 pints in 3 gallons.

How many seconds are in $$3.5$$ years?

$$110 451 600$$ (using $$365.25$$ days as the average number in a year)

$$\text{Explanation}$$

Here's how you do it:

$$3.5\,years \times \dfrac{365.25\,days}{year} \times \dfrac{24\,hour}{day} \times \dfrac{60 \,minutes}{hour} \times \dfrac{60\,seconds}{minute}$$

$$=110451600 Sec$$

How many seconds are there in $$35$$ minutes?

Answer
$$ 35 minutes \times \dfrac{60 seconds}{1 minutes} $$
$$ = 2100 seconds $$

How many pints are in 7 quarts?

Answer
14
Explanation:
A quart is 2 pints.
So $$ 7 $$ quarts is $$ 7 \times 2 = 14 $$ pints

How many seconds are there in 2.5 hours?

Answer
In 2.5 hrs. there are 9000 seconds.
Explanation:
There are 60 minutes in an hour and 60 seconds in each minute.
therefore, there are $$ 60 \times 60 = 3600 $$seconds in each hour.
Hence in 2.5 hrs. there are $$ 3600 \times 2.5 = 9000$$ seconds

How many centimeters are in $$3$$ inches?

Answer:
Each inch is 2.54 centimeters, hence in 3 inches
there are $$2.54 \times 3 = 7.62$$ centimeters.

How many seconds are in a 24 hour day?

Answer
Well there are 60 seconds in a minute and 60 minutes in an hour and 24 hours in a day. Thus:
60 X 60 X 24=86,400 seconds in a day

How much is $$3$$ Kelvin?

$$3K$$ is $$−270^0C$$, just $$3$$ degrees above absolute zero,

Explanation:

$$3K$$ is one hundredth of room temperature on the Kelvin scale, which represents absolute temperatures.

It is the background temperature of the universe.

How many yards are in a tenth of a mile?

There are $$176$$ yards in $$1$$ tenth of a mile.

Explanation:

If $$1$$ mile is $$1760$$ yards, then $$1$$ tenth of a mile is $$1$$ divided by $$10$$ which equals $$0.1$$, if you multiply $$0.1$$ by $$1760$$ you get $$176$$ which is the number of yards that are in $$1$$ tenth of a mile. $$10$$ divided by $$1760$$ is $$176$$.

How many centimeters are in a inch?

Answer:

1 in = 2.54 cm

Explanation:

As shown here, as well as in many other sources

Note that unlike many other unit conversions which are approximations, the 1 in = 2.54 cm is exact.

How many yards are in a $$1/4$$ of a mile?

$$440$$ yards.

Explanation:

$$1$$ mile = $$1760$$ yards.

$$\frac{1}{4}$$ mile = $$\frac{1}{4}\cdot1760$$ yards.

$$\frac{1}{4}\cdot1760=\frac{1760}{4}$$

$$=440$$

How many yards are in $$5$$ miles?

The conversion factor for miles to yards is:

$$1mi=1760$$ yds

To find the number of yards in $$5$$ miles, multiply each side of the equation by $$5$$ giving:

$$5*1mi=5*1760yds$$

$$5mi=8800yds$$

There are $$8,800$$ yards in $$5$$ miles.

How many yards in a mile?

A yard is equal to $$0.000568182$$ miles.

Explanation:

There are $$1,760$$ yards in a mile. In fractional form it looks like this:

$$(\frac{1mi}{1,760yd})$$

How many yards go into one and three fourths miles?

One and three fourths miles have $$3080$$ yards.

Explanation:

Each mile has $$8$$ furlong and each furlong has $$220$$ yards

so each mile has $$8*220=1760$$ yards and as $$1\frac{3}{4}$$ miles are

$$\frac{4}{4}+\frac{3}{4}=\frac{7}{4}$$ miles.

$$1\frac{3}{4}$$ miles have,

$$\frac{7}{4}*1760=3080$$ yards.

How many centimeters are there in 2 kilometers?

1 kilometer means 1000 meters
and 2 kilometers means $$2 \times 1000 = 2000$$ meters
Similarly centi stands one hundredth and one centimeter is one-hundredth of a meter i.e. each meter has 100 centimeter
Therefore 2000 meters are $$2000\times 100 = 2000,000$$ centimeters
Hence, there are 200,000 centimeters in 2 kilometers.

How many centimeters are there in $$1.23 \times 10^{-6}$$ kilometers?

Each kilometer has 1000 meters and each meter has 100 centimeters.
Hence each kilometer has $$1000 \times 100 = 100000 = 10^{5}$$ centimeters.
Therefore $$1.23 \times 10^{-6}$$ kilometer will have
$$1.23 \times 10^{-6} \times 10^{-6 + 5} = 1.23 \times 10^{-1}$$ or $$0.123$$ centimeters

How many yards are in $$7$$ miles?

$$12320$$ yards.

Explanation:

There are $$1760$$ yards in one mile, therefore you need to multiply $$1760$$ by $$7$$ to find the number of yards in $$7$$ miles.

How much is $$325 F$$ in $$^0C$$?

$$325^0F=162\frac{7}{9}^0C$$

Explanation:

Boiling point of water is $$212^0F=100^0C$$

Freezing Point of water is $$32^0F=0^0C$$

Difference between boiling and freezing is $$180F^0=100C^0$$

$$325^0F$$ is $$325-32=293F^0$$ above freezing.

$$293F^0*\frac{100C^0}{180F^0}=162\frac{7}{9}C^0$$

$$325^0F$$ is $$162\frac{7}{9}C^0$$ above freezing or $$162\frac{7}{9}^0C$$

How much is $$90 C$$ in Fahrenheit?

$$194F$$

Explanation:

The conversion for Celsius to Fahrenheit is:

$$F=\frac{9}{5}C+32$$

Plug in the C value, resulting in:

$$F=(\frac{9}{5}\cdot90)+32$$

$$F=\frac{810}{5}+32$$

$$F=162+32$$

$$F=194$$

How much is $$70$$ degrees Fahrenheit in Celsius?

$$70^0F=21.\bar{1}^0C$$

Explanation:

To convert Fahrenheit to Celsius, the normal method is to subtract $$32$$ then divide by

$$1.8$$ ( i.e, $$\frac{9}{5}$$)

So in our example

$$\frac{5}{9}(70-32)=\frac{5}{9}(38)=\frac{190}{9}=21.\bar{1}$$

How much is $$10 kg$$ in pounds?

Here is a conversion that I set up (using $$1$$ lb = $$453.6 g$$):

$$10kg(\frac{1000g}{1kg})(\frac{1lb}{453.6g})=22.0462lbs$$

How much is $$168 cm$$ in feet and inches?

$$168 cm$$ are equal to approximately $$5$$ feet and $$6$$ inches.

Explanation:

Each inch is equal to $$2.54 cm$$.

Therefore, each cm is equal to $$\frac{1}{2.54}=0.3937$$ inches.

Hence, $$168cm$$ are equal to $$168*0.3937=66.1416$$ inches.

As each feet has $$12$$ inches $$5$$ feet are eual to $$12*5=60$$ inches.

And hence $$168$$ cm are equal to $$5$$ feet and $$6.1416$$ inches or rounding it say $$5$$ feet and $$6$$ inches.

How much is $$23kg$$ in pounds?

$$23kg=51lb$$

Explanation:

$$1kg=2.205lb$$

$$23kg*\frac{2.205lb}{1kg}=51lb$$

How to convert L to $$ dm^3$$ and ml to $$ cm^3$$ ?

$$ dm^3 $$ is cubic decimetres

A decimetre is 10 cm - if you cube 10 cm you get $$ 10 \times 10 \times 10 = 1000 cm^3 $$ which is 1 litre.

ml are millilitres or "thousandths of a litre". Therefore 1 ml is the same as $$ 1cm^3 $$

Please prove $$1\ debye = 10^{-18} \ esu \ cm = 3.335 \times 10^{30} \ C - m$$ ( coulomb meter),

Dipole moment $$(\mu)$$ between two charges separated by distance $$d$$ is

$$\mu = q \times d$$

Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of $$10^{-10} $$ statcoulomb (generally called e.s.u. (electrostatic unit) in older literature), which were separated by $$1$$ angstrom $$(= 10^{-8}\ cm)$$

$$1$$ Debye = $$10^{-10} esu \times 10^{-8}\ cm $$

$$ = 10^{-18}\ esu\ cm $$

$$ = 10^{-18}\ esu\ cm \times \dfrac{3.335 \times 10^{-10}\ C}{\text{esu}} \times \dfrac{10^{-2}\ m}{cm} $$

$$ = 3.335 \times 10^{-30}\ cm $$

How to you convert $$ 5 $$ radians to degrees?

$${\textbf{Step-1: Use formula radian to degree.}}$$

$${\text{We know that,}}$$

$$1\text{ rad}=\dfrac{180^0}{ \pi }$$

$${\text{Let 5 rad}}$$ $$=x^0$$

$${\textbf{Step-2: By law of proportion.}}$$

$$\therefore \dfrac{1}{5} = \dfrac{\dfrac{180}{ \pi }}{x}$$

$$\therefore x=5 \times (\dfrac{180}{ \pi })$$

$$\therefore x=(\dfrac{900}{ \pi })$$

$$\therefore x \approx 287^0$$

$${\textbf{Hence , 5 radians to degree is }} \mathbf{287^\circ}$$

How much is $$63 kg$$ in pounds?

$$138.6$$ Pounds.

Explanation:

We know:

$$1$$ kg = $$2.20$$ Pounds.

$$63$$ kg = $$2.20\cdot63$$ Pounds

$$63$$ Kg = $$138.6$$ Pounds.

What are polar coordinates used for in real life?

Useful applications in physics and engineering.

Explanation:

From a physicist's point of view, polar coordinates (randθ) are useful in calculating the equations of motion from a lot of mechanical systems.

Quite often you have objects moving in circles and their dynamics can be determined using techniques called the Lagrangian and the Hamiltonian of a system. Using polar coordinates in favor of Cartesian coordinates will simplify things very well.

Hence, your derived equations will be neat and comprehensible .

Besides mechanical systems, you can employ polar coordinates and extend it into a 3D ( spherical coordinates ). This will help a lot in doing calculations on fields . Example: electric fields and magnetic fields and temperature fields.

In short, polar coordinates make calculation easier for physicists and engineers. Thanks to that, we have better machines and better understanding on electricity and magnetism (essential for generating power).

PS: Knowing the why's and the how's in school is important even if you are not going to use them in real life. The point is that we have to set ignorance aside and appreciate the things we take for granted. Life as we know it will never be the same without math, science and even literature. Kudos for asking this question!

What are the steps of the scientific method?

Make an observation
Form a question
Form a hypothesis
Conduct an Experiment
Analyse the Data and Draw a Conclusion

Explanation:

The scientific method aims to explain natural phenomena. All of the steps can occur in a different order but mostly in the order above. Scientists throughout history have used the same method to answer questions they don't understand. Sometimes you have to repeat the scientific method if you observe something else, or if the data doesn't support the hypothesis.

Mr. Brady's new car get sixty miles to the gallon. In the metric system gas consumption is measured in liters per $$100$$ kilometers, how do you make the conversion?

Gas consumption is $$100$$ kilometers to $$3.92$$ liters

Explanation:

To convert gas consumption from miles per gallon to liters per $$100$$ kilometers, we should first know

$$(1)$$ the relation between gallon and liters - this is $$1$$ gallon is equal to $$3.78541$$ liters and

$$(2)$$ relation between miles and kilometers - this is $$1$$ gallon is equal to $$1.60934$$ kilometers.

Hence $$60$$ miles to $$1$$ gallon is equivalent to

$$60 \times 1.60934$$ kilometers to $$3.78541$$ liters

or $$1$$ kilometers to $$\dfrac {3.78541}{60 \times 1.60934} = 0.0392\ liters$$

or $$100$$ kilometers to $$0.0392 \times 100=3.92$$ liters

What determines when a system reaches equilibrium? What observations can be made about a system once equilibrium has been established?

Equilibrium point is the point where the rate of forward reaction is equal the rate of backwards reaction, therefore the concentrations of the products and reactants stay the same and do not change once they reach equilibrium.
1919007_1913759_ans_7a1ef0b2e1be4074b492665a8daae793.png

1919007_1913759_ans_7a1ef0b2e1be4074b492665a8daae793.png

What did Leibniz contribute to the development of calculus?

Gottfried Wilhelm Leibniz was a mathematician and philosopher. Many of his contributions to the world of mathematics were in the form of philosophy and logic, but he is much more well known for discovering the unity between an integral and the area of a graph. He was primarily focused on bringing calculus into one system and inventing notation that would unambiguously define calculus. He also discovered notions such as higher derivatives, and analysed the product and chain rules in depth.

Leibniz mainly worked with his own invented notation, such as:

$$y=x$$ to denote a function, in this case, $$f(x)$$ is the same as $$y$$

$$\frac{dy}{dx}$$ to denote the derivative of a function

$$\int y dx$$ to denote an antiderivative of a function

So, for example, the product rule looks like this:

Let $$y=uv$$, where $$u$$ and $$v$$ are both functions

Then $$\frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}$$

The diameter of an atoms is approximately $$ 1.10 ^{-8} cm $$ . What is this diameter when expressed in nanometers ?

A nanometer is $$ 10 ^{-9} $$ meters
If you covert 1 cm into $$ 10^{-2} $$ meters , then $$ 10 ^{-8} $$ meters would becomes $$ 10 ^{-10} $$ meters, and $$ 10 ^{-10} $$ meters converted to nanometers (times $$ 10 ^{9} $$ ) would be 0.11 nanometers.

What are the appropriate units for the Sun's luminosity?

Smaller unit is watt. Astronomical unit ( that prefer to call LAU ) is Sun's IAU ( International Astronomical Union $$\mathrm{I}$$ )
value of 3.826 watts

Explanation

Luminosity of a star or a group of multitude of far distant
stars (galaxy ), appearing as a small light-emitting disc, is the

total amountf of energy emitted in a unit of time.

The unit of measurement, for the rate of this energy
transfer, is joule second or watt, in short.

Sun's (IAU) luminosity $$L_{\text {Sun}}=3.826 \times 10^{26}$$
watts.

In my notation, this is the astronomical unit 1 LAU $$=3.826
\times 10 ^{26}$$ watts

Luminosity of the nearest star Proxima Centauri is. $$0.0017 $$ LAU., as given in

On the blueprint of a house, $$48$$ millimeters represents $$7$$ meteres. The length of the living room is $$60 $$ millimeters on the blueprint. What is the actual length of the living room?

$$x=8.75 m$$

Explanation:

Use direct proportion to compare the length on the blueprint with the actual length.

$$\dfrac{48 mm}{7m} =\dfrac{60 mm}{x m} \dfrac{\leftarrow \ blue print}{\leftarrow \ lengths}$$

$$x=\dfrac{7 \times 60}{48}$$

$$x=8.75m$$

One inch equals $$2.54$$ centimeters. How do you find the length of a newborn, in inches, if it measures $$45.7$$ centimeters?

$$45.7\ cm=17.99\ inches$$

Explanation;

As $$2.54\ cm$$ is equal to $$1$$ inch

$$\therefore \ 1\ cm$$ is equal to $$\dfrac{1}{2.54}=\dfrac{100}{254}\ inch$$

and $$45.7\ cm$$ is equal to $$\dfrac{100}{254} \times 45.7$$

$$=\dfrac{100}{254} \times \dfrac{457}{10}$$

$$=\dfrac{10.100}{254} \times \dfrac{457}{1.10}$$

$$=\dfrac{4570}{254} \cong17.99\ inches$$ (using calculator)

Is one joule per second equivalent to one watt?

Yes, one Watt is defined as $$1$$ Joule of energy per $$1$$ second.

Power is defined as work per unit of time

$$Power =\dfrac{work\ done}{time\ needed}$$

The SI units of work and time are Joules and seconds, respectively. One Watt was defined as a power of $$1$$ Joule per second.

Power

Definition: the rate at which work is done

Formula: Power $$=$$ work done $$/$$ time interval

Unit: Watt $$=Joule/ second$$

$$1$$ watt of power is expended when $$1$$ Joule of work is done in one second

What is SI unit conversion?

Metric unit conservation are completed to convert a measurement made in one metric unit to another metric unit.
are completed to convert a measurement made in one metric unit to another metric unit.

What is megahertz a measurement of?

Frequency.

What do quantitative and qualitative measurements mean in science?

Quantitative means measuring a quantity - putting a value to something. For example, we might measure the rate of a reaction by seeing how many seconds it takes for a change to happen, such as a piece of magnesium ribbon to dissolve in acids of different concentrations.

Qualitative means without determining a value. We might be making an observation, for example, silver gives a yellow precipitate with $$NaNO_3$$, but a white precipitate with $$NaCl$$, or making observations like lithium compounds produce a red flame color while sodium compounds produce a yellow flame color.

What is Radian Measure?

Imagine a circle and a central angle in it. If the length of an arc that this angle cuts off the circle equals to its radius, then, by definition, this angle's measure is 1 radian. If an angle is twice as big, the arc it cuts off the circle will be twice as long and the measure of this angle will be 2 radians. So, the ratio between an arc and a radius is a measure of a central angle in radians.

For this definition of the angle's measure in radians to be logically correct, it must be independent of a circle.
Indeed, if we increase the radius while leaving the central angle the same, the bigger arc that our angle cuts from a bigger circle will still be in the same proportion to a bigger radius because of similarity, and our measure of an angle will be the same and independent of a circle.

Since the length of a circumference of a circle equals to its radius multiplied by $$ 2 \pi $$, the full angle of $$ 360^0 $$ equals to $$ 2 \pi $$ radians.

From this we can derive other equivalencies between degrees and radians:

$$ 30^0 = \frac { \pi}{6} $$

$$ 45^0 = \frac { \pi}{4} $$

$$ 60^0 = \frac { \pi}{3} $$

$$ 90^0 = \frac { \pi}{2} $$

$$ 180^0 = \pi $$

$$ 270^0 = 3 \frac { \pi}{2} $$

$$ 360^0 = 2 \pi $$

What is the difference between morphology and physiology?

Morphology is a branch of biology that studies the structure of organisms and their features. Physiology is a branch of biology that studies the normal functions of organisms and their parts.

What is the difference between intensional orientation and extensional orientation?

"Intensional" is a subjective view. "Extensional" is a more objective "fact-based' view.

Explanation:

Intensional orientiation would be thinking first about popular labels. For example, you may think that anything labeled "i-YouPick" is a good product without knowing anything about the actual device.

An extensional orientiation would look at the actual items or events, and then make your own decision or apply an appropriate label.

For example, an intensional orientation might assume that the "AntiFa" groups are about liberty and freedom. But an extensional orientation would recognize elements and characteristics in the groups that are identical with those that they purport to oppose.

The term intensional orientation (the “s” is intentional) refers to the tendency to view people, objects, and events in terms of how they’re talked about or labeled rather than in terms of how they actually exist.

Extensional orientation is the opposite: It’s a tendency to look first at the actual people, objects, and events and then at the labels—a tendency to be guided by what you see happening rather than by the way something or someone is talked about or labeled.

What is the Fahreheit equvialent of $$15$$ degrees celsius ?

$$^{o} F= \left( ^{o} C . \dfrac{9}{5} \right)+32$$

$$^{o} F= \left( 15 . \dfrac{9}{5} \right)+32$$

$$^{o} F=27+32$$

$$^{o} F=59$$

What is the correct order from shortest to longest for these units of measure?Angstrom, astronomical unit, centimeter, kilometer, lightyear, micron, nanometer, parsec?

Starting from the Shortest.
Explanation:
Starting from the Shortest.
1. $$ Angstrom \rightarrow 10^{−10} m $$
2. $$ Nanometer \rightarrow 10^{−9} m $$
3. $$ Micron \rightarrow 10^{−6} m $$
4. $$ Centimeter \rightarrow 10^{−2} m $$
5. $$ Kilometer \rightarrow 10^3m $$
6. $$ Astronomical Unit \rightarrow 1.496 \times 10^11m $$
7. $$ Light-year \rightarrow 9.461 \times 10^{15} m $$
8. $$ Parsec \rightarrow 3.26 light-years , or \; 3.08 \times 10^{16} m $$

What is the basic SI unit of density?

The derived SI unit for density is $$\dfrac{kg}{m^3}$$

Explanation:

Density is an SI derived unit. It is derived from the SI fundamental unit for mass, the kilogram, and the SI fundamental unit for length, the meter.

Density is the mass per unit of volume. The SI derived unit for volume is cubic meters. So the derived SI unit for density is $$\dfrac{kg}{m^3}$$.

What is systemic physiology?

Physiology of one system (i.e. cardiovascular, respiratory system)

What is the Kelvin temperature scale?

Essentially, it is a temperature scale based on Absolute zero.

Explanation:

Definition

The Kelvin scale is unique in a few ways from Fahrenheit and Celsius. Primarily, it is based on the measurement of absolute zero. This is a theoretical and highly debated point at which all atoms stop moving (but molecules still vibrate). The scale has no negative numbers because

0 is the lowest Kelvin temperature. When referencing the scale, it is generally best to use K, instead of degrees. For example, water freezes at 273.15 K and boils at 373.15 K.
1921741_1915960_ans_990966b3532441ddba5074039d69d49c.jpeg

1921741_1915960_ans_990966b3532441ddba5074039d69d49c.jpeg

What SI units are used to measure density?

Density = mass / volume

Unit of density = unit of mass / unit of volume

Unit of density = $$ kg/m^3 $$

What period corresponds to $$ 500 Hz$$?

Definitions:

Hz=cycles/second

Period = time required for 1 cycle

$$ 500 Hz=\frac{500 cycles}{second}$$

or written in an equivalent form:

$$ 500 Hz \rightarrow $$ a ratio of $$ 500 $$ cyles:$$ 1 $$ second

or $$ 1$$ cycle: $$ \frac{1}{500}$$ second

So the period is $$ \frac{1}{500}=0.002$$ second.

What is the temperature $$-34^0C$$ expressed in kelvin?

$$239.15k$$
Explanation:
$$273.15K=0^0C$$
So to convert from $$^0C$$ to $$K$$, add $$+273.15$$ to $$^0C$$ to convert to $$K$$.
$$+273.15+(-34)=+239.15K$$

What is the distance from earth to the sun in scientific notation?

So the distance between the earth and the sun is $$150$$ million kilometers. In scientific notation, you have to find the number between $$1$$ and $$10$$, then multiply it by $$10^{x}$$. So the number between $$1$$ and $$10$$ in $$150,000,000$$ is $$1.5$$, and a number of decimal points is $$8$$. So the answer is $$1.5⋅10^{8}$$.

What SI units are used to measure power?

The watt (W) is the SI derived unit for power. It comes from the SI base units.

Velocity is the rate at which an object travels.

$$ v = \frac {distance}{time } = \frac {d}{t} $$

The units of acceleration are metres per second squared $$ ( m.s)^2 $$

Force is any influence that tends to change the motion of an object. Force = mass × acceleration.

f=ma.

The newton (N) is the force needed to accelerate up a mass of 1 kg by $$ 1 . m. s^2 $$

$$ 1 N = 1 kg ms^2 $$Work is the action of a force through a distance.

$$ w = f \times d $$

Energy is the ability to do work. It has the same units as work. The SI unit for energy is the joule (J). 1 J = 1 N⋅m.

Power is the measure of how much energy or work is used per unit time.

$$ Power = \frac {energy}{time} $$

The SI unit of power is joules per second (J/s) or Watts (W).

In summary,

$$ 1W = 1J/s = 1 N.m/s = 1.kg m^2 . s^{-3 } $$

What is the temperature, in degrees Celsius, that is equivalent to a temperature of $$40^0F$$?

$$4.44$$ Degrees Celsius.
Explanation:
The formula to convert Fahrenheit to Celsius (or Vice Versa) is,
$$F=(\frac{9C}{5})+32$$
Here C is the Temperature in Celsius Degrees and F is temperature in Fahrenheit Degrees.
For your problem the equation should be,
$$40=(\frac{9C}{5})+32$$
Put $$40$$ instead of F because the value in hand is temperature in Farhenheit.
$$\frac{(40-32)5}{9}=C$$
Then take all the constant term to one side and keep the variable on other side.
After calculating, we get the value of the variable
$$C=4.4$$
So the answer is $$4.4$$ Degrees Celsius, which is equivalent of $$40$$ degrees fahrenheit.

What is the mass of a $$132\ lb$$ human in kilograms?

$$60\ kg$$
Explanation :
Simple,
$$1\ kg = 2.2\ lb$$
Since we are to find $$kg$$
$$x\ kg = 132\ lb $$

Put it like this
$$ \dfrac{1}{2.2} = \dfrac{x}{132} $$

$$x = \dfrac{132}{2.2} $$

$$x = 60$$

Thus, the mass of a $$132\ lb$$ human is $$60\ kg$$

What is the basic unit of length in the SI system?

The meter.
Explanation:
The meter was first defined as a fixed ratio of the longitude of the earth. It is now defined by both a standard meter and by the wavelengths of light.

How do you convert 7.8 km to miles?

$$\text{Explanation}$$

$$5\text{miles}=8\text{km OR mile =8/5km Or 1 km =5/8 mile}$$

$$\text{ For the same distance, the number of miles is less than the number of km.}$$

$$7.8\text{km}\times \dfrac {5}{8}=4.875\text{miles}$$

$$\text{Or by direct proportion}:$$

$$\dfrac {\text{miles}}{\text{km}}=\dfrac{x}{7.8}=\dfrac{5}{8}$$

$$x=\dfrac{7.8\times 5}{8}$$

$$x=4.875\text{miles}$$

Why is the metric system important?

The metric system is used by nearly everyone on Earth.

Explanation:

Without the metric system, we'd have a difference International System of Units, the metric system is important because $$1mm$$ is $$0.1cm,\ 1\ cm$$ is $$0.01 m$$, with the imperial system the conversion is tedious.

What units of measurement are used to describe wavelengths?

Wavelength is defined as the length of one whole oscillation or wave cycle.

Note how this is a length. This means we used our standard units for length, which are metres (m).

In reality, we might use slightly different units based on the type of wave we're talking about. For visible light, we might use nanometres ($$10^{-9}m$$) - but this still comes back to metres for calculations.

What units can measure density?

$$\frac{\text{Mass}}{\text{Volume}}$$

So we can have the quotient of any mass units and any units of volume. Given that $$m^3$$ are an impossibly large volume, chemists typically use $$g \cdot mL^{-1}$$ or $$g \cdot L^{-1}$$.

What metric unit is used to measure distance?

Meter (m)

Explanation:

The meter is the standard measure of distance in metric units.

Depending on the area of study, prefixes will be added to make the magnitude more relevant to the subject. For example, some unit conventions will use IPS (inch pound second), or MKS (meter kilogram second), indicating that the measurements will be in this convention, simply for the sake of making the magnitude more reasonable to the application.

What is the unit used to measure period called?

The time period of a wave (or any other periodic phenomena) is measured in units of time, i.e. in seconds.

A mile is $$5280\text{ ft}$$ long. $$1\text{ ft}$$ is approximately $$0.305 m$$. How many meters are there in a mile? How many kilometres $$\text{(km)}$$ are there in a mile?

$$\text{This is the conversion from miles to meters}:$$

$$1 \text{mile}.\dfrac{5280 \text{ft}}{1\text{mile}}.\dfrac{0.305m}{1\text{ft}}=5280\times 0.305m=1610\text{meters}$$

$$\text{This is the conversion from miles to km}:$$

$$1\text{mile}.\dfrac{5280\text{ft}}{1\text{mile}}.\dfrac{0.305m}{1\text{ft}}.\dfrac{1\text{km}}{1000m}=\dfrac{5280\times0.305}{1000}\text{km}=1.610\text{km}$$

What is the unit symbol for a nanometre?

$$nm$$.
Explanation:
We have the following:
$$1m$$ - metre / meter
$$1cm=10^{−2}m$$ - centimetre / centimeter
$$1mm=10^{−3}m$$ - millimetre / millimeter
$$1\mu m=10^{−6}m$$ - micrometre / micrometer
$$1nm=10^{−9}m$$ - nanometre / nanometer

Why is the scientific method important to follow?

Answer
Because if you follow this method it helps prevent you from thinking things what ain't so.
Explanation:
Anyone can make a mistake. It is too easy to make assumptions, to believe what you want to believe, to ignore data that conflict with what you think. And as human beings, scientists can be all too guilty of these errors.
The scientific method is a way to prevent these mistakes. It doesn't always work, but it demonstrably has had some successes. So firstly observe phenomena; what is happening? Secondly, ask questions; why is that occurring the way that it is? Thirdly, formulate an hypothesis; this is what I think is happening. Fourthly, develop a testable prediction; if this is true for A, will it be true for B? Fifthly, do experiments to test your prediction; is it true for B, and C, and D? Sixthly, was it true? If yes, then develop an hypothesis by generalization. Seventh (perhaps most importantly!); attempt to falsify your hypothesis. Here, you ask the questions, what experiments could I (and others) do, and what results would I anticipate, that would show my analysis and understanding to be faulty?
If you can do all these things and still have a handle on and an understanding of results, then formulate a theory and book a flight to Stockholm. The scientific method thus relies on experiment; it is not performed in isolation. You may draw a particular conclusion from a set of experimental results, which MAY be different to the conclusion reached by another researcher. Nevertheless, your experimental results, and that of the other researcher, should substantially agree.

Who invented gravity ?

It was discovered and the theory of it formulated by Isaac Newton (possibly drawing on Robert Hooke) around the year $$1686$$ or so.

Explanation:

Gravity was discovered, not invented, but the theory of universal gravitation is usually attributed to Isaac Newton, but he may have got at least some of it from Robert Hooke.

What is linear mass density?

Linear mass density is the amount of mass per unit length.

Just as ordinary density is mass per unit volume, linear density is mass per unit length. Linear densities are usually used for long thin objects such as strings for musical instruments.

EXAMPLE:

Suppose we have a $$0.80 mm$$ diameter guitar string made of carbon steel (density = $$7.860 g/cm^3$$). What is the linear mass density of the string?

SOLUTION

Step 1: Find the volume of a length (say, $$1 m = 100 cm$$) of the string.

$$V=\pi r^2l$$

The radius of the string is half the diameter.

$$r=\frac{0.80mm}{2}=0.40mm=0.040cm$$

$$V=\pi r^2l=\pi*(0.040cm)^2*100cm=0.503cm^3$$

Step 2: Find the mass of the wire.

Mass = $$0.503cm^3*\frac{7.860g}{1cm^3}=3.95g$$

Step 3: Find the linear mass density.

Linear mass density = $$\frac{mass}{length}=\frac{3.95g}{1m}=4.0g/m$$

Which of the following are vectors and which are scalars: distance, mass, time, weight, volume, density, speed, velocity, acceleration, force, temperature and energy?

$$\text{Explanation};$$

$$\text{Vector}$$ quantities have $$\text{both}$$ magnitude and direction.

$$\text{Scalar}$$ quantities have $$\text{only}$$ magnitude.

$$\text{Distance}$$ is a scalar quantity. It refers only to how far an object has travelled. For example, $$4$$ feet is a distance; it gives no information about direction. To say an object travelled 4 feet is somewhat ambiguous. To say the object travelled $$4$$ feet west, for example, would be a displacement, and would then be a vector quantity. It gives a more complete picture of what happened.

$$\text{Mass}$$ is a scalar quantity. Simply put, it refers to how much matter an object is made up of. It has magnitude but gives no indication of the direction in any sense. The vector counterpart to mass is the weight.

$$\text{Weight}$$ is a vector quantity. Weight is a force, and forces are vectors, i.e. having both magnitude and direction. Perceived weight of an object at rest on earth is given by $$W=\overrightarrow{F}_g=mg$$, the product of the mass of the object and the free-fall acceleration constant, $$g$$, or simply equal to the force of gravity acting on the object. The force of gravity acts downward.

$$\text{Time}$$ is a scalar quantity (as far as we are concerned at this level). It gives information about the magnitude, i.e. how much time, but no information about direction.

$$\text{Volume}$$ is a scalar quantity. It refers to the amount of space that an object occupies and therefore has magnitude, but gives no information about direction.

$$\text{Density}$$ is a scalar quantity, having only magnitude and giving no information about direction. We can also reason that because density is equal to mass divided by volume and both mass and volume are scalar quantities, density must also be a scalar quantity.

$$\text{Speed}$$ is a scalar quantity, having only magnitude and giving no information about direction. For example, $$40m/s$$ is a speed, it tells us how fast an object is travelling, but nothing about which direction the object is travelling in. The vector counterpart to speed is velocity.

$$\text{Velocity}$$ is a vector quantity. Velocities have both magnitude and direction. For example, $$40m/s$$ NE is a velocity.

$$\text{Acceleration}$$ is a vector quantity. Acceleration has both magnitude and direction. For example, $$9.8m/s^2$$ downward or $$−9.8m/s^2$$ vertically is an acceleration.

$$\text{Force}$$ is a vector quantity. Force has both magnitude and direction. Weight is an example of force given above. Another is the force of friction, which has some magnitude and acts in the direction opposite that of motion.

$$\text{Temperature}$$ is a scalar quantity. Measurement of temperature has magnitude but gives no information about direction.

$$\text{Energy}$$ is a scalar quantity. It gives information about the magnitude, e.g. how much energy an object has, but none about direction.

Why $$[CuCl_4]^{2-}$$ has a flattened tetrahedral structure, not regular tetrahedron and $$[CoCl_4]^{2-}$$ is tetrahedron?

From the electron configuration of the atoms:

$$Cu: [A r] 3 d^{10} 4 s^{1}$$

$${Co}:[Ar]3 d^{7} 4 s^{2}$$

Take away two electrons and you have the +2 oxidation states

for both:

$$Cu^{2+}:[Ar]3d^94s^0$$

$$Co^{2+}:[Ar]3d^74s^0$$

Therefore, we have a $$d^9-d^9$$ complex in $$[CuCl_4]^{2−},[CuCl_4]^{2−}$$,

and a $$d^7-d^7$$ complex in $$[CoCl_4]^{2−},[CoCl_4]^{2−}$$

How many inches is in 5 yards?

Use dimensional analysis.
$$ 1 \text{yard}= 36 \text{inch} $$
There are two conversion factors:
$$ \dfrac {1\text{yd}}{36 \text{in} } $$ and $$ \dfrac { 36 \text{in }}{1 \text{yd}} $$
Multiply $$5$$ yards by the conversion factor the cancels yards and keeps inches.
$$ 5 \text{yd} \times \dfrac {36\text{ in}}{1 \text{yd} }= 180 \text{inch} $$

Why do scientists prefer the SI units over the old English system of measurement?

There are several reasons why $$\mathrm{Sl}$$ is preferred to the old English system of measurement:

1. SI is not based on the arbitrary construct of the human body; rather, on precise and definite standards.

2. Sl uses base $$10,$$ just like our number system, so it is much easier to learn, remember, and convert between units.

3. The prefixes used in $$\mathrm{Sl}$$ are from Latin and Greek and they refer to the numbers that the terms represent. (For example,"kilo" as in "kilogram" means $$1000$$ and "milli" means $$1 / 1000$$ ). You can now easily calculate the number of millimeters in a kilometer. (how many inches in a mile?)

4. Sl units are interrelated in such a way that one unit is derived from other units without conversion factors. E.g. $$1 N$$ (Newton) is the force needed to give $$1 k g$$ (kilogram) of mass an acceleration of $$1 \frac{m}{s^{2}}$$
Try that with the 'English' units.

5. Sl is used in most places around the world, so our use of it allows scientists from disparate regions to use a single standard in communicating scientific data without vocabulary confusion.

$$0.4$$ miles is how many feet?

$$0.4\text{miles}=2,112\text{ feet}$$

$$\text{Explanation}$$

$$1\,\text{mile}=5280 \text{feet}$$

$$0.4 \text{miles}=0.4\times 5280=2,112 \text{feet} $$

An average human body temperature is $$98.6^{\circ}F.$$ What is average human body temperature in Kelvins?

The formula we are going to use is $$;T_C=\dfrac{T_F-32}{1.8}$$ and $$T_K=T_C+273.$$

First, we neet to convert Fahrenheit to celsius, because the Celsius scale has the same magnitude as Kelvin except $$0^{\circ}C$$ is set as the freezing point of pure water and $$100^{\circ}C$$ as the boiling point of pure water.

$$T_C=\dfrac{T_F-32}{1.8}$$

$$=\dfrac{98.6-32}{1.8}$$

$$=\dfrac{66.6}{1.8}$$

$$=37$$

Now we add $$273$$ to the $$37^{\circ}C$$

$$T_K=T_C+273$$

$$37+273$$

$$=310$$

$$\text{Therefore, the average body temperature in kelvin is 310}$$

How many quarts are in $$10$$ gallons?

The conversion factor for gallons to quarts is:

$$1\text{gal}=4\text{qt}$$

To find how many quarts in $$10$$ gallons multiply each side of the equation by $$10;$$

$$10\times 1 \text{gal}=10\times 4\text{qt}$$

$$10\text{gal}=40\text{qt}$$

There are 40 quarts in 10 gallons.

Why is a universal system of measurement necessary in science?

A universal system reduces the confusion when different systems of measurement are used and makes it easy to compare measurements taken by different persons.

Here’s a real-world example of the confusion that can occur.

In 1983 an Air Canada Boeing 767 temporarily had no working fuel gauges, so the ground crew resorted to calculating the 767's fuel load by hand. They used a procedure similar to calculating the volume of oil in a car by taking a dipstick reading. This gave them the volume. But airlines measure the amount of fuel by mass. They needed the density of jet fuel to make the proper calculations. The ground crew used 1.77 lb/L as the density, as they had on all other planes in the fleet. But the brand new 767 was metric and used 0.8 kg/L as the density. The plane had only about half the fuel the crew believed they had. The plane ran out of fuel and sank too fast to reach its destination. Only a nearby abandoned Air Force base was a possible landing spot. The crew made a remarkable dead-stick glider landing. There were only minor injuries to the passengers as they used the emergency exits on the plane.

What is mu in physics?

Answer
$$ \mu$$can describe a lot of quantities. Sometimes it's used in kinematics for coefficients of friction, or even in particle physics for the reduced mass of a particle.

Why do catalysts affect collision theory?

Catalyst provides an alternative reaction pathway with a lower activation energy.

As the collision theory says in order for particles to react they must collide with the correct orientation and sufficient energy, with a lower activation energy. So catalyst provides, a lower activation energy.

How many ounces are in 1/4 of a gallon?

Did you know you can manipulate units of measurement in the same way you can numbers. Use this as a guide on how to do the calculation.

32 fluid ounces in $$ \frac {1}{4} $$ gallon

YES I KNOW THIS IS PREALGEBRA!!

16 oz = 1 pint

8 pints = 1 gallon

Let the word ounces be represented by z

Let the word pints be represented by p

Let the word gallons be represented by g

So every time you see z it means the word ounces

So every time you see p it means the word pint

So every time you see g it means the word gallon.

Using ratio

We can write the ounces to pints ratio as z:p

I much prefer to use the fraction format and you will see why.

We can write the ounces to gallons ratio as $$ \frac {z}{p} $$ .....ratio (1)

We can write the pints to gallons ratio as $$ \frac {p}{g} .$$ .......ration (2)

Our target is to get the ratio of ounces to gallons $$ \rightarrow \frac {z}{g} $$

Look what happens when we have Ratio(1) $$ \times $$Ratio(2)

$$ \frac {z}{P} \times \frac {p}{g} \rightarrow \frac { z \times p}{ p \times g } \leftarrow \frac { ounces \times pints}{pints \times gallons} $$

Using an example: $$ 2 \times 3 $$ gives the same answer as$$ 3 \times 2 $$ So we can swap things round when multiplying

Thus we have:

$$ \frac {z \times p}{ p \times g} \rightarrow \frac { z \times p}{ g \times p} \rightarrow \frac {z}{g} \times \frac {p}{p} = \frac {z}{g} $$

The $$ \frac {p}{p} $$ is the equivalent of 1 and anything multiplied by 1 does not change in value.

Use the same approach as above on the numbers:

$$ \frac {z}{p} \times \frac {p}{g} \rightarrow \frac { 16z }{1p} \times \frac {8p}{1g} $$

$$ \rightarrow \frac {16z}{1 p} \times \frac {8p}{1g } $$

$$ \rightarrow \frac { 16z \times 8}{ 1 \times 1g} $$

$$ \frac { ounces}{gallons} \rightarrow \frac{128 z}{ 1 g } $$

So for a quater of a gallon we have:

$$ \frac { ounces }{ gallons} \rightarrow \frac { 128z \times \frac {1}{4} }{ 1 g \times \frac {1}{4} } = \frac { 32z}{ \frac {1}{4} g } $$

$$ \frac {1}{4} ( 16 \times 8 ) = 16 \times 2 = 32 $$

How do you convert $$105$$ degrees fahrenheit to celsius?

To convert from Fahrenheit to Celsius, use the formula:
$$ T_0C = (T_0F - 32) \times \dfrac {5}{9} $$
Substitute $$ T_0F $$ as $$105$$ and solve for $$ T_0C $$
$$ T_0C = ( T_0F - 32) \times \dfrac {5}{9} $$
$$ T_0C = ( 105 -32) \times \dfrac {5}{9} $$
$$ T_0C = 73 \times \dfrac {5}{9} $$
$$ T_0C \approx 40.56^0 C $$

What are units of measurement?

Answer
Measuring, by definition, is a process of comparing the value of something we observe with some standard of measure we commonly agree to be our unit of measurement.
For instance, we commonly agree to measure a length by comparing it with a length of some object we agreed to be a unit of length. So, if the length of our object is 3 times greater than the length of the unit of length, we say that the measure of length of our object equals to 3 units of measurement.
Different objects of observation require different units of measurement. Unit of measurement of an area is different from unit of measurement of electric resistance. But for each type of observable object we have our own unit of measurement, so each object (time, weight, length, force, pressure, speed etc.) can be measured.
The most common system of units employed by the international scientific community is the International system of units (Le Systme international d'units, or SI). There are seven SI base units, and all physical quantities can be measured in terms of combinations of these seven units:
the meter for distance,
the kilogram for mass,
the second for time,
the ampre for electric current,
the kelvin for temperature,
the mole for amount of substance, and.
the candela for intensity of light.

How do atmospheric pressure and elevation affect boiling point?

As elevation increases, atmospheric pressure and boiling point decrease.

Does the coefficient of restitution change?

Answer
It depends on what you mean by "change.
The coefficient of restitution is based on the surface properties of the ball and surface it collides with. So for a given ball the coefficient will be different for different surfaces it collides with, in this sense it changes. A good example of this is a tennis racquet. The face of a racquet can be divided into different sectors, each has its own coefficient of restitution. The central sector a little above the handle has the highest coefficient. This is what players term the "sweet spot".
Another way that the coefficient can change for a given ball is that over time its internal structure may degrade. This is more the case with balls that are made out of rubber / plastic. Hence worn out balls are replaced during games where appropriate.

How do you convert milliliters to liters?

This is a case of the metric system. To convert from "milli-" to the standard unit, such as meters or litres, we divide by $$1000.$$

One millilitre is equal to a thousandth of a litre, and one litre is equal to one thousand millilitres.

In numbers, that is:

$$ 1mL = 0.001 L = 10^{-3} L $$

$$ 1 L = 1000 mL = 10^3 m L $$

How do you convert $$2.3$$ cm to mm?

We all know that $$1cm$$ is equals to $$10mm$$.

Therefore,

$$1cm=10mm$$

multiply $$2.3$$ on both sides

$$ 2.3 \times 1 cm = 2.3 \times 10 mm $$

$$ 2.3 cm = 23 mm $$

How do you convert 90 inches to yards?

1 yard = 3 feet

1 foot = 12 inches

Therefore 1 yard = 36 inches

90 inches = $$ \frac { 90}{36} $$ yards or 2.5 yards

Why are astronomical units used?

Answer:
astronomers use the unit astronomical unit (A>U>)to measure distances between planets and between Sun and planets and other bodies in solar system.
Explanation:
One astronomical unit is is the average distance between sun and earth. It is149597870 kilometers..It is convenient tttttttto use it in solar system.

How much is 70 degrees Fahrenheit in Celsius?

Answer
$$ 70^{o}F = 21.\bar{1}^{o} C $$
Explanation
:To convert Fahrenheit to Celsius, the normal method is to subtract 32 then divide by
$$ 1.8 \left ( i.e \dfrac{9}{5} \right )$$
So in our example:
$$ \dfrac{5}{9} (70 - 32) = \dfrac{5}{9} (38) = \dfrac{190}{9} = 21.1 $$
Alternatively, since $$ - 40^{o}F = - 40^{o}C $$we can convert by adding 40, multiplying by $$ \dfrac{5}{9} $$then subtracting 40:
$$ \dfrac{5}{9} (70 + 40) - 40 = \dfrac{5}{9} (110) - 40 = \dfrac{550}{9} 40 61.1 - 40 = 21 . 1 $$
The reverse conversion from Celsius to Fahrenheit can be done by either of the following:
Multiply by $$\dfrac{9}{5} $$then add 32.
Add 40, multiply by $$ \dfrac{9}{5} $$ then subtract 40

To convert a temperature in degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by $$\dfrac{9}{5} $$ and then add $$ 32^{\circ}$$ ls a temperature in degrees Celsius proportional to its equivalent temperature in degrees Fahrenheit?

Answer
No, a Celsius temperature is not proportional to its equivalent Fahrenheit temperature.
Explanation:
The formula is
$$ F = \dfrac{9}{5} C + 32 $$
F increases as C increases and F decreases as C decreases, but the relation is not a direct proportionality.
In mathematics, a direct proportion has the form
y=mx,
where m is a constant.
$$ F = \dfrac{9}{5} C $$
If the formula had been
it would have been a direct proportion.
However, the addition of the +32 term makes the formula no longer a direct proportion.

How do you convert the measurement of 2 days into seconds?

Answer
Do a chain multiplication........
explanation :
$$ 2 .day \times 24 .h. day^{-1} \times (60 .min . h^{-1}) \times (60 .s. min^{-1}) = 2 \times 24 \times 60 \times 60 .s. $$

How many nanometers are there in 1 cm?

Standard unit in this system is 1 meter.

There are a billion i.e. 1,000,000,000 nano units in a standard unit and hence 1,000,000,000 nanometers in one meter.

As there are 100 centimeters in each meter,

1 centimeter has $$ \frac { 1000000000}{100} = 10000000 $$ ie $$ 10 $$ million nanometeres

How do you convert $$ 45^{o}C $$ to Fahrenheit?

Answer
Recall the formula to convert this.
$$ T_{C} = \dfrac{5}{9} (T_{F} - 32) $$
Of course, $$ T_{C} $$is the temperature in$$ ^{o}C $$and TF is the temperature in $$^{o}F $$
Let's test this to make sure. I know that $$ 100 ^{o} C = 212^{o} F $$
is the boiling point of water, so let's see if that works.
$$ T_{C = \dfrac{5}{9}} ( 212 - 32) $$
$$ = \dfrac{5}{9} ( 180) $$
$$ = 5 . 20 = 100 ^{o} C $$
Yep. Now use it on $$ 45 ^{o} C $$
$$ 45 = \dfrac{5}{9} (T_{F} - 32) $$
$$ \dfrac{405}{5} = T_{F} - 32 $$
$$ 81 + 32 = 113^{o} F = T_{F} $$

What is 29 degrees celsius in fahrenheit?

Answer
Fahreheit temperature $$ = \left ( 29 \times \dfrac{9}{5} \right ) + 32 = 84.2 ^{\circ} F $$
Explanation :
The numbers to remember are 5, 9 and 32
Fahrenheit are the lager number when comparing like temperature for like. So to convert Centigrade to Fahrenheit, you need to make the numbers bigger. Thus you multiply by $$ \dfrac{9}{5} $$ To go from Fahrenheit to centigrade you are making the numbers smaller so you multiply by \dfrac{5}{9} $$
All you need to remember now is that freezing point for each is different.
Centigrade freezing point is $$0^o$$
Fahrenheit freezing point is $$32^o $$
Using this information to answer your question
We are going from Centigrade to Fahrenheit so it is small number to large. So we have $$ \times \dfrac{9}{5} $$
We are changing freezing point from 0 on 1 scale to 32 on a different scale so we now have:
$$\times \dfrac{9}{5} + 32 $$
Fahrenheit temperature $$ = \left ( 29 \times \dfrac{9}{5} \right ) + 32 = 84.2^{\circ} F $$

How do you convert 360 degrees to radians?

Answer
$$ 360^o = 2 \pi $$ radians
Explanation :
$$ 360^o$$ represents a complete revolution, tracing out an arc of $$ 2 \pi $$ radians.
A radian is the angle subtended by an arc of length equal to the radius and the complete length of the circumference is $$ 2\pi r $$ , where r is the radius.
So a complete circular arc subtends $$ \dfrac{2\pi r }{r} = 2\pi $$

How to calculate rotational speed?

Rotational speed $$\omega$$ can be evaluated considering the change in angular displacement $$\theta$$ with time $$t$$.

$$\omega=\frac{\theta}{t}$$

Practically this can be a bit dfficult so what we do to measure the rotational speed of, say, a motor shaft is to visually count the number of rotations per minute.

We observe a point on the rim of the rotating shaft and we count the number of rotations (say 10) and check the time elapsed.

We divide the number of rotations by the time and get the rotational speed in, say:

$$\frac{revolutions}{minute}$$

Now, we can improve a bit by considering that during a complete revolution the angular displacement will be $$2\pi$$ radians so we can convert it into something we can use in mathematical evaluations:

$$1\frac{rev}{min}=\frac{2\pi}{60}\frac{rad}{s}=0.105\frac{rad}{s}$$

So now we can go from revolutions per minute to angular dsplacement $$\theta$$ per second.

Consider an example:

the shaft of a motor rotates $$1800\frac{rev}{min}$$ Through how many radians does it turn in $$18 s$$?

The rotational speed in radians per second that corresponds to $$1800\frac{rev}{min}$$ is:

$$\omega=(1800\frac{rev}{min})(0.105\frac{\frac{rad}{s}}{\frac{rev}{min}})=189\frac{rad}{s}$$

Since, $$\omega=\frac{\theta}{t}$$, in $$18s$$ the shaft turns through:

$$\theta=\omega t=189\cdot18=3402rad$$

How long would it take to bicycle 45 miles at an average speed of 15 miles per hour?

3 hours

What is the Fahrenheit equivalent of 15 degrees Celsius?

$$15$$ degrees Celsius $$= 59$$ degrees Fahrenheit.

$$\text{Explanation}$$

Multiply the $${^\circ}C$$ temperature by $$1.8$$. Add $$32$$ to this number.This the answer in $${^\circ}F$$

$${^\circ}F=({^\circ}C.\dfrac{9}{5})+32$$

$${^\circ}F=(15.\dfrac{9}{5})+32$$

$${^\circ}F=27+32$$

$${^\circ}F=59$$

How many moles are there in 28 grams of $$CO_2$$?

As molar mass of $$CO_2$$ is 44g/mol

Moles = $$\dfrac{Given \ mass}{Molar\ mass}$$

number of moles= $$\dfrac{28}{44}= 0.636 moles$$

What function do Protons, Neutrons, and Electrons have in an atom?

The proton in the positively-charged particle and the number of protons give the atom's element name. Each element has a different amount of protons.
Neutrons are responsible for combining with protons in the nucleus together to be held by the strong force. Too many neutrons in an atom will result in radioactive decay due to the neutrons' force overpowering the strong force.

Electrons are the weirdest particles. They are the smallest ones, and have a mass of
$$\dfrac{1}{1836}$$ of a proton or a neutron. They are negatively-charged, and the valence electrons are responsible for the reactivity of an atom.

How many gallons are in 101.4 fl oz?

There are approximately 0.8 gallons in 101.4 fluid ounces.

What is a quantitative measurement and what is a qualitative measurement?

$$\text{Quantitative}$$ measurement relates to measurement of data that can be represented in a numerical or statistical output.

$$\text{Qualitative}$$ measurement generally relates to the coding of text based data (written responses or transcribed interviews) into connections or themes.

A stone is dropped freely, while another thrown vertically downward with an initial velocity of 2m/s from the same point, simultaneously. What is the time required by them to have a distance of 22 m between them ?

Answer
t=11 s
Explanation:We're asked to find the time t when the distance between the two stones, which we'll call $$ \Delta y $$ is $$ 22 m $$
The equation for the position of stone 1 (the one dropped from rest) is
$$ \Delta y_{1} = - \dfrac{1}{2} gt^{2} $$
(the initial y-velocity $$v_{0y} $$ is 0)
and that of stone 2 (the one launched downward) is
$$ \Delta y_{2} = v_{0y} t - \dfrac{1}{2} gt^{2} $$
At any given time, the position of stone 2 will always be farther than that of stone 1, because it was launched with an initial velocity downward. Since we want to find when the distance between them is 22 m, we can say
$$ \Delta y_{2} = \Delta y_{1} - 22 m $$ (minus because it's farther downward)
Substituting the above equations for $$ \Delta y_{2} and \Delta y_{1} $$ we have :
$$ \left ( - 2\dfrac{m}{s} \right ) t - \left ( 4.9\dfrac{m}{s^{2}} \right ) t^{2} = \left ( - 4.9 \dfrac{m}{s^{2}} \right ) t^{2} - 22 m $$
$$\left ( - 2\dfrac{m}{s} \right ) t = - 22 m $$
$$ t = 11 m $$
Thus, the distance between the objects will be 22 meters after 11 seconds.
We can check to see if this answer is correct by finding their positions at time t=11 s:
Distance between them $$ = \Delta y_{1} -\Delta y_{2} = - 593 m - ( - 615 m) $$
$$ = 22 m $$

What are the seven fundamental units?

The SI units for the seven fundamental measurable qualities are:

$$A$$, ampere, a unit of electrical current
$$cd$$, candela, a unit of luminous intensity
$$K$$, kelvin, a unit of absolute temperature
$$kg$$, kilogram, a unit of mass
$$m$$, meter, a unit of distance
$$mol$$, mole, a unit of quantity/counting
$$s$$, second, a unit of time

How do you find the slope and y intercept of y = x?

Comparing it with y = mx +c

we get, The slope is m = 1.

Find the number of atom present in $$PO_4^{ -3}$$ ions ?

Answer:
5 atoms
Explanation:Total number of atoms
= Number of Oxygen atoms + Number of Phosphorus atoms
=4+1
=5 atoms in one ion of $$(PO_{4})^{-3}$$

How do you estimate carrying capacity of a population?

Carrying capacity is the maximum number of organisms that a habitat can support based on its resources & beyond carrying capacity it can not support more individuals.

It can be calculated by using this equation:
$$ \dfrac{dN}{dt} = rN \left [ \dfrac{ K - N}{K} \right ] $$
where,
N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity

Why is the rusting of an iron pole not a physical change ?

In fact, the rusting of iron is quite clearly an example of chemical change.

Explanation:

Chemical change involves the formation of new substances and the making and breaking of strong chemical bonds.

Rust is nothing but Iron Oxide; a new substance formed out of the reaction. The color of the surface of the iron also changes. Hence, rusting of iron is a chemical change.

The cells of unicellular organisms are what?

Most unicellular organisms are bacteria, archaebacteria, and such, with that being said it is a prokaryotic cell.

What units of measurement are used for the combined gas law?

for $$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

In SI units, p is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins (the Kelvin scale is a shifted Celsius scale, where 0.00 K = −273.15 °C, the lowest possible temperature).

What is the chemical formula for ATP?

The molecular formula C₁₀H₁₆N₅O₁₃P₃ may refer to: Adenosine triphosphate (ATP).

A wrench with a length of 54cm is being used to unscrew a 6cm bolt. If a torque of 90Nm is needed to overcome the friction keeping the bolt in place, what is the minimum torque that must be applied to the wrench to unscrew the bolt?

Answer:
'What is the minimum force that must be applied'
$$166 \dfrac{2}{3}$$
Explanation:
Did you know that you can and may treat units of measurement in the same way you do the numbers
Known: 54 cm = 0.54 m
Let the unknown applied force be x Newtons
$$0.54m \times xN = 90Nm$$
Divide both sides by 0.54m
$$\dfrac{0.54 m}{0.54} \times xN = \dfrac{90 \times N \times m}{0.54 \times m}$$
$$1 \times xN = 166\dfrac{2}{3}N$$

Which Among The Following Algorithms Is Designed Based On The Feistel Cipher?

Feistel Cipher is not a specific scheme of block cipher. It is a design model from which many differentblock ciphers are derived. DES is just one example of a Feistel Cipher. A cryptographic system based on Feistel cipher structure uses the samealgorithm for both encryption and decryption.

What Is Density ????

Answer
Explanation:
Density is a physical characteristic, and is a measure of mass per unit of volume of a material or substance. It is a measurement of the amount of matter in a given volume of something.
The higher an object's density, the higher it's mass per unit of volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less dense substance (such as water).

How does calculus relate to chemistry?

Generally, calculus may relate to chemistry when you work with thermodynamics and kinetics.
One simple thermodynamics example is the idea of entropy, which is a measure of disorder in a system. A Physical Chemistry definition of entropy is:
$$dS = \dfrac{\delta q_{rev}}{T} (Eq . A)$$
where S is entropy, q is heat flow, and T is temperature.
At a constant pressure and temperature (such as during a phase transition), it can be written like this:
$$dS = \dfrac{\delta q_{rev , p}}{T} = \dfrac{dH}{T} (Eq . B)$$
where H is enthalpy. Remember that we're at constant pressure. Now, if you take the partial derivative of entropy with respect to temperature at a constant pressure for Eq. B, you've got the General Chemistry definition of heat capacity---capacity for heat flow at a constant pressure! This is written as CP(T). You get:
$$\left ( \dfrac{\delta S}{\delta T} \right )_{P} = \left ( \dfrac{\delta T}{\delta T} \right )_{P} \dfrac{1}{T} = \dfrac{Cp(T)}{T} (Eq . C -1)$$
If you rewrite this further and take the integral, you get:
$$dS = \dfrac{Cp(T)}{T} dT (Eq. C-2)$$
or
$$\Delta S = S(T_{2}) - S(T_{1}) = \int_{T_{1}}^{T_{2}} \dfrac{Cp(T)}{T} dT (Eq . D)$$
So if you know the specific heat capacity, then for example, you can figure out its entropy at 500K if you know its entropy at room temperature (298K) and you assume the heat capacity varies negligibly within the temperature range. The standard state entropy of reaction $$(\Delta S^{\circ}_{R})$$ can be used for this, for instance.
One more slightly involved example is when you derive half lives from rate laws in kinetics (you may see this in AP Chemistry, or in Physical Chemistry). So maybe you start with the following "classic" decomposition reaction:
$$N_{2}O_{4} \rightarrow 2NO_{2}$$
Since there is only one reactant, you know it is first order. You can write the rate law for this as:
$$r(t) = \dfrac{1}{2} \dfrac{d[NO_{2}]}{dt} = - \dfrac{1}{1} \dfrac{d[N_{2}O_{4}]}{dt} = k[N_{2}O_{4}]$$
If you rearrange this and separate variables, you get:
$$-\dfrac{1}{[N_{2}O_{4}]}d[N_{2}O_{4}] = kdt$$
then if you integrate this:
So from this you would know that the half life for a substance that is decomposing by itself (such as radioactive decay, which is first order) is independent of its initial concentration.

What is the correct order from shortest to longest for these units of measure?Angstrom, astronomical unit, centimeter, kilometer, lightyear, micron, nanometer, parsec?

Starting from the Shortest.
Explanation:
Starting from the Shortest.
1. Angstrom $$=10^{−10}m$$
2. Nanometer $$=10^{−9}m$$
3. Micron $$=10^{−6}m$$
4. Centimeter $$=10^{−2}m$$
5. Kilometer $$=10^{3}m$$
6. Astronomical Unit $$=1.496*10^{11}m$$
7. Light-year $$=9.461*10^{15}m$$
8. Parsec $$=3.26$$ light-years, or $$3.08*10^{16}m$$

which of the following sets of concurrent forces may be in equilibrium?
$$ 1) F_1 = 3N , F_2 =5N , F_3= 1N $$
$$2) F_1 =3N , F_2=5N , F_3= 6N$$

Answer
"Forces are in equilibrium when they form a triangle
We know that the sum of these three forces is zero
$$\vec{A} + \vec{B} + \vec{C} = 0 $$ For a triangle the sum of the two sides is always greater than the third side
Therefore, $$F_1 = 3N; F_2 = 5N; F_3 = 6N$$
$$F_1 + F_2 > F_3$$
$$F_2 + F_3 > F_1$$
$$F_3 + F_1 > F_2^{"}$$
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1923001_1927008_ans_84860452ec684ea29f29ca4171080f37.PNG

Displacement is scalar or vector quantity ?

Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

It is completely represented by magnitude and direction both.It also follows vector algebra.

The force of gravity is measured in units called ____________ (Newtons/watts).

The Force of gravity is measured in unit called Newton/kg or Newton.$$kg^{-1}$$

Give a physical quantity which has no units ?

Answer
Lots of things can potentially have no units, it often means the quantity is a ratio.
Explanation:
Strain is a good example, because it is the ratio of original length to extended length, the units cancel and it is dimensionless. This is the correct term for 'having no units'.
Coefficients of friction also fall into this category.

Give two real life examples of gradient divergence and curl.

Off the top of my head, every radio and TV broadcast, almost every electric motor or dynamo, almost every transformer operates according to Maxwell’s equations, which are all based on gradient, divergence and curl. All of these are designed using Maxwell’s equations.

So, for that matter, are almost all fields. Einstein’s law of gravity is a “div” equation. Fields permeate physics, and vector calculus describes what happens to fields.

Grad, div and curl are also fundamental for fluid flow, particularly compressible mediums (gasses). And our society operates on fluid flow - from pipelines to jet engines.

Define the term speed. what are its various units? is it a scalar or vector quantity?

Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of 100 km in 1.0 h, its speed is 100.0 km/1.0 h = 27.8 m/s, where the speed is a derived scalar quantity obtained by dividing distance by time.

What is delphi technique explain with suitable example ?

The Delphi technique is a group communication method where a panel of experts arrive at a consensus over a series of questions and discussions. It is used for estimating or forecasting. First, select a suitable facilitator and experts with relevant knowledge, and make sure the problem is defined well.

What is the relation between Joule and calorie?

The calorie was originally defined as the amount of heat required at a pressure of $$1$$ standard atmosphere to raise the temperature of $$1$$ gram of water $$1^{o}$$ Celsius. Since $$1925$$ this calorie has been defined in terms of the joule, the definition since $$1948$$ being that one calorie is equal to approximately $$4.2$$ joules.

How many seconds are there in one week

Answer
Number of seconds in a week =
1 min = 60 secs
$$ 1 hr = 60 \times 60 = 3600 secs $$
$$ 1 day = 24 \times 3600 = 86400 secs $$
$$1 week = 86400 \times 7 = 604800 secs$$
Hence, there are 604800 secs in a week.

Write the two basic principal in physics.

A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. ... Examples of principles are Newton's Laws, Work-Energy theorem, and Impulse-Momentum Theorem.

the principal of thrusts in physics are unification and reduction. in unification, Diverse phenomena of nature are expressed in few terms of laws and concepts. for example, the law of gravitation. It explains falling of objects on earth, planetary motion, motion of moon, etc.

Difference between bust and chest measurement

Answer
The chest measurement is just below your breasts. The bust measurement is the largest point around your bust, it can be useful to include your cup size as well.
Another common mistake is waist and hip measurement. Waist is the narrowest portion of your waist, not where your pants waistband is. Hips will be the widest portion of your hips.

Definition of Motion

In physics motion is the phenomenon in which an object changes its position over time. Motion is mathematically described in terms of displacement, distance , velocity, acceleration, speed and time.

What is the science and what is physically?

Physical science is the study of the inorganic world. That is, it does not study living things. (Those are studied in biological, or life, science.) The four main branches of physical science are astronomy, physics, chemistry, and the Earth sciences, which include meteorology and geology.

What is orbit and orbital?

Orbit is a well defined circular path around the nucleus in which an electron revolves. It represents the planar motion of an electron. Orbits do not have directional characteristics. an orbit can accommodate electrons equal to $$2n^2$$ where $$n$$ represents the principle quantum number. Orbital atomic theory and quantum mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.

Convert $$1$$ lakh into Million.

$$1$$ Lakh = $$100$$ Thousands
= $$1$$ followed by $$5$$ Zeros
= $$100,000$$.
$$10$$ Lakhs = $$1$$ Million
= $$1$$ followed by $$6$$ Zeros
= $$1,000,000$$.

So, $$1 lakh =0.1 Million$$

11.25m into mm, converted as directed

$$11250\ m$$

Step-by-step explanation:

$$1\ cm = 10\ mm$$

$$1\ m = 100\ cm$$

$$1\ m = 1000\ mm$$

therefore $$11.25\ m = 11.25 ^{\ast} 10^{3} $$

$$ = 11250\ mm $$ or $$11.25 ^{\ast} 10^{3} $$

Convert into hour 1 hour 20 min

1 hour 20 minutes $$= 60 + 20 $$ minutes

$$= 80 $$ minutes

$$\dfrac{80}{60} = \dfrac{4}{3}$$ hours

What is the smallest particle of matter - a)atom b)molecule Pls explain the answer.

Explanation:
a) Atom :- An atom is the smallest unit of ordinary matter that forms a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across.
b) Molecules....
The smallest unit into which a substance can be divided without changing its chemical nature

Good book for organic chemistry?

for theory. you may go with following
1. Soloman's and frhyles
2. Paula Y bruice
3. Peter sykes (best)
and for questions you can go with
MS Chouhan(elementary )
MS chauhan (advanced)
Himanshu pandey..
for theory use foreign authors only..

Who is the Isaac Newton

Isaac Newton was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.

Define Momentum. It is a scalar and vector quantity ? give its unit and dimension

Momentum of a body can be defined as the product of mass of the body and velocity of the body. It means momentum of a body is directly proportional to the mass of the body. Momentum of a body is also directly proportional to the Velocity of the body. The SI unit of momentum is kilogram metre per second.

It is a vector quantity.

What can't be measured? is it not important ? Justify.

If You Can't Measure It, You Can't Improve It. Management thinker Peter Drucker is often quoted as saying that "you can't manage what you can't measure." Drucker means that you can't know whether or not you are successful unless success is defined and tracked.

Find Time(In hrs.)

Speed = 20 kilometer per hour(km/h)
Distance = 100 Kilometer(km)

$$Speed=\dfrac{\text{Distance}}{\text{Time}}$$

$$Time = \dfrac{100}{20} = 5$$ hrs

Explain with the help of an activity that matter is made up of particles

There is a content match. The idea that all matter is made up of particles is stated explicitly a few times in the Student Edition. Most of the instances are brief mentions made in the body of the text. The idea that "all forms of matter are made up of tiny particles that are in constant motion" is introduced as the particle model of matter . Thereafter, the idea of particles is used to explain a few properties of substances (such as hardness and phases of matter). Before being introduced to the structure of the atom, students are reminded that all matter in the universe is made up of tiny particles: "A glass of water, for example, has many water particles, each too small to see" . The text continues by defining atoms as the building blocks of matter:

How are given mass, molar mass and number of moles related to each other?

$$n=m/M$$

$$n$$ = no of moles

$$m$$ = given mass

$$M$$ = molar mass

Molar mass of a substance is nothing but the mass of 1 mole of the substance.

All the important definition of chapter 1 for class 10 Science 1st chapter chemistry.

Chemical reaction is which in which new substances with new properties are formed.

Chemical equations-- When chemical reaction is denoted in the forms of symbols is called chemical equations.

Oxidation reaction are those in which oxygen addition takes takes and removal of hydrogen takes place

Reduction reaction are those in which removal of oxygen and addition of hydrogen takes place.

Why is the unit of temperature called a fundamental unit?

Kelvin is a fundamental unit! It's a lot easier to measure temperature than to measure the motion of component particles. Hence, we can accept it as a fundamental quantity. Time is said to be a fundamental unit because it is not dependent on one or more units.

A student studies that convex lens always forms virtual image irrespective of its position. What causes the convex mirror to always form a virtual image?

Convex mirror always form virtual images because the focal point and the centre of curvature of the convex mirror are imaginary points and that cannot be reached. So image is formed inside the mirror and cannot be projected on a screen.

Examples of scalar and vector quantities list.

Scalar quantities:

mass
length
time
speed
temperature
electric current

Vector quantities:

force
velocity
acceleration
displacement
magnetic induction

What is the effect of temperature on molarity?

Answer
Molarity is affected by the temperature . molarity is the ratio between number of moles of solute to the volume of solution in litres and as on increasing temperature the volume increases and hence with the increase in temperature the molarity of solution decreases .
molarity is directly proportional to the temperature

Write the relationship between kilowatt-hour and joule

The relationship between " kWh " and " Joules " are :

$$1 \ kWh= 1000 \ Watt \times [60 \times 60] \ seconds$$

$$1 \ kWh = 10^3 \ W \times 3600 \ s$$

$$1 \ kWh = 3.6 \times 10^6 \ J$$

What is the unit of electric potential?

volts.
In the International System of Units (SI), electric potential is expressed in units of joules per coulomb (i.e., volts), and differences in potentialenergy are measured with a voltmeter.

Define Latent heat of vaporisation.

Latent heat of vaporization is the amount of heat required by a substance to get vaporised, i.e., to get converted into gaseous state. For example, the latent heat of vaporization of water is $$2268 J/g$$ or $$540 Cal/g$$.

List two properties that liquids have in common with solids.

1] Both liquids and solids have definite shape.

2] Both liquids and solids consists of molecules.

The relationship and strength of the four fundamental forces (gravitational, electromagnetic, weak nuclear, And strong nuclear)

The Four Fundamental Forces of Nature are:

Gravitational Force - Weakest force; but infinite range. (Not part of standard model)
Weak Nuclear Force - Next weakest; but short range.
Electromagnetic Force - Stronger, with infinite range.
Strong Nuclear Force - Strongest; but short range.

Gravitational Force

The gravitational force is weak, but very long ranged. Furthermore, it is always attractive. It acts between any two pieces of matter in the Universe since mass is its source.

Weak Nuclear Force

The weak force is responsible for radioactive decay and neutrino interactions. It has a very short range and. As its name indicates, it is very weak. The weak force causes Beta decay ie. the conversion of a neutron into a proton, an electron and an antineutrino.

Electromagnetic Force

The electromagnetic force causes electric and magnetic effects such as the repulsion between like electrical charges or the interaction of bar magnets. It is long-ranged, but much weaker than the strong force. It can be attractive or repulsive, and acts only between pieces of matter carrying electrical charge. Electricity, magnetism, and light are all produced by this force.

Strong Nuclear Force

The strong interaction is very strong, but very short-ranged. It is responsible for holding the nuclei of atoms together. It is basically attractive, but can be effectively repulsive in some circumstances. The strong force is ‘carried’ by particles called gluons; that is, when two particles interact through the strong force, they do so by exchanging gluons. Thus, the quarks inside of the protons and neutrons are bound together by the exchange of the strong nuclear force.

Change of gaseous state directly to solid state without going through liquid sate is called _____________________ .

sublimation.

Do we sweat more on a dry day or humid day ? Justify your reason.

We sweat more on dry day because more the dryness of the atmosphere, more is the evaporation which results in sweating.

The absolute scale of temperature is Kelvin. Water freezes at 273 K. and boils at 373 K. hence find out the value of 40-degree Celsius temperature in the Kelvin scale.

1945800_1933987_ans_da8df621052c4ff484ca15cb6be3754a.jpg

What is hygrometer?

Hygrometer is an instrument that is used to measure humidity in the atmosphere.

Compare and contrast action-reaction forces and balanced forces.

Balanced forces, which are also equal and opposite, cancel out because they act on the same object. Action andreaction forces, in contrast, act on different objects, so they don't cancel out. In fact, they often result in motion. ... Compare and contrast action-reaction forces and balanced forces.

Why do we see water droplets on the outer surface of a glass containing ice cold water?

Because of the evaporation from the surface of the glass containing ice cold water.

Time taken to fix a broken build is measured using _________.

Time taken to fix a broken build is measured using build repair rate

Write the $$SI$$ units of resistance?

The ohm (symbol:$$\Omega $$) is the $$SI$$ derived unit of electrical resistance,named after German physicist Georg Ohm

The standard unit of mass is the _______.

The standard unit of mass is the kilogram

What is the relationship between astronomical unit and light year

One light year is almost six trillion miles. And an astronomical unit is the average distance between the earth and the sun. So the distance to the sun is by definition one AU. A parsec is the distance at which one astronomical unit subtends an angle of one second of arc.

+ Solution

Write any three points of difference between $$'G $$' and $$'g'$$.

Acceleration due to gravity $$(g)$$
1. The acceleration produced in a body freely falling under the gravitational pull of the Earth is known as gravitational due to gravity.
2. The value of 'g' is different at different places on the Earth.
3. The value of 'g' on the surface of Earth is $$9.8 m/s^2$$.
Universal Gravitational Constant $$(G)$$
1. The gravitational force between two bodies of unit masses separated by a unit distance is known as Universal Gravitational Constant.
2. The value of 'G' is same at all the places on the Earth.
3. The value of 'G' = $$6.67 * 10^{-11} Nm^2 / kg^2$$ throughout the universe.

Define atomic mass unit?

A unit of mass used to express atomic and molecular weight, equal to one twelfth of the mass of an atom of carbon-12

What is the full form of physics?

Physics was named so since it chiefly manages the investigation of phenomena and happenings in our surroundings which we can see or feel. In spite of the fact that the subject advances it came to a smaller-scale level; however prior it was just learned at the large scale level.

The word 'physics' originates from the Greek 'learning of nature,' and all in all, the field intends to break down and comprehend the natural phenomena of the universe.

Examples of periodic and non periodic changes

Changes which take place in a definite interval of time are called periodic changes whereas changes which are irregular and not determined with definite time are called non periodic changes.

Day and night, changing phases of the moon, beating of heart, clock striking an hour are all examples of periodic motion whereas water becoming ice, burning of matchstick etc are non periodic changes.

Acceleration is a vector quantity ,which indicates that its value

Acceleration is defined as " the change in the velocity of a moving object with respect to time" is called acceleration. It is the result of all the forces acting on the object. Acceleration is a vector quantity because it has both "magnitude" and "direction".
When you slow down while moving a vehicle velocity decreases and hence acceleration also decrease and its value becomes"negative". similarly, when you speed up your car the increases in velocity increases the acceleration and its value will be "positive".
Since its a vector quantity so its value can be either "positive" or "negative".

Name the forces acting on the car sticking to an electromagnet in a Junkyard. Which one of them is larger?

Magnetic fore is more larger because it is able to pull the car towards itself. Answer: When the car is sticking to the electromagnet magnetic force and gravitataional force is acting on the car. Magnetic force is more larger because it is able to pull the car towards itself.

Atomic radius is measured in ...

Picometers is used to measure the atomic radius

A particle start from rest on circular path with constant tangential acceleration. Find the ratio of centripetal acceleration to the tangential acceleration after one revolution.

$$a_r=\frac{v^2}{r}$$
$$s=2\pi r$$
$$u=0$$
$$v^2=u^2+2a_ts$$
$$v^2=2a_ts$$
$$a_t=\frac{v^2}{2s}$$
$$=\frac{v^2}{2(2\pi r)}=\frac{v^2}{4\pi r}$$
$$\frac{a_r}{dt}=\frac{v^2/r}{v^2/4\pi r}$$
$$=4\pi$$

How many feet are in a football field that is 100 yards?

Answer
300 ft
Explanation :
Since 1 yard = 3 feet, we can multiply 100 yd by $$\dfrac{3 ft}{1 yd} $$ We are essentially multiplying by 1, but doing so allows us to cancel out the yd unit so that we are left with only ft.
$$ \dfrac{100 yd}{1}.\dfrac{3 ft}{1 yd} = 300 ft $$

What is the unit of viscosity? Please explain.

The viscosity of a fluid is a measure of its resistance to flow.
We usually think of the viscosity of a liquid as its "thickness".
For example, we say that honey is "thicker" (has a higher viscosity) than water.
One way to measure viscosity is to place the fluid between two flat parallel plates and slide one plate past the other.
In terms of the above diagram, the formula for viscosity η is
$$ \eta = \frac { F \delta }{Av } $$
Thus the units of visocity are $$ \frac { N \times m}{ m^2 \times m . s^{-1} }= N.sm.m^{-2} = P a.s $$
If a fluid is placed between two $$ 1m^2 $$ plates that are 1 m apart and one plate is pushed sideways with a force of 1 N and it moves at a velocity of $$ 1 m/s^{-1} $$ then the fluid has a viscosity $$ \eta = 1 Pa.s $$
Many chemists still use an old unit of viscosity, the poise (P), named after the French physician Jean Poiseuille.
It is convenient unit because $$ 1m Pa.s = 1cP $$
For example , the viscosity of water at $$ 20^0 C $$ is $$ 1.002 mPa.s $$ or $$ 1.002 cP $$
Honey has a viscosity of about $$ 10 Pa.s $$ or $$ 10000cP $$

One year on Mercury is equal to $$87.97$$ Earth days. One year on Pluto is three times the length of one Mercury year minus $$16.21$$ days. How long is one year on Pluto?

This is a tricky one as there may be some ambiguity about $$16.21$$ days which is: to which planet is the day attributed? Also the units are tricky. They behave the same way

numbers do!!!

Assumption $$1$$

From the sentence part "of one Mercury year minus $$16.21\ days"$$ I am assuming that the days are Mercury days. From $$year$$ minus $$16.21\ days"$$ I am assuming

that they are directly linked. Thus the days are directly attributable to the Mercury year.

Assumption $$2$$

Our annual cycle is split up into $$365\ units$$ of cycles in one solar year ( a day). The other planets will circle the sun at different speeds but will experience the equivalent

effects our planet does. However, these will be at different rates. Thus for each planet their year may also be split up into $$365$$ rotational units.

Building the initial equationBuilding the initial equation

We are talking about units of measurement in both days and years. So let the generic unit for day be $$d$$ and the generic unit for year be $$y$$. This gives us:

Let the year unit of measurement for Mercury be $$y_m$$

Let the day unit of measurement for Mercury be $$d_m$$

Similarly for Earth we have $$y_e$$ and deye and $$d_e$$

And for Pluto we have $$y_p$$ and $$d_p$$

Another potential ambiguity.

Consider the question in parts:

"One year on Mercury is $$87.97$$ on earth

$$\rightarrow 1 y_m=87.97 d_c...(1)$$

No doubt about teh meaning!

"One year on Pluto is $$3$$ times one year on Mercury minus $$16.21$$ days"

Does this mean: $$1y_p=3(1 y_m-1621 d_m)$$

Or does it mean:$$1y_p=3(1 y_m)-1621 d_m$$

Assuming this is the case: $$1y_p=3(1 y_m-1621 d_m) ...(2)$$

Substitute $$(1)$$ in $$(2)$$ giving:

$$1y_b=3(87.97d_c- 16.21 d_m)...(3)$$

To convert $$16.21 d_m$$ into $$d_c$$

From $$(1)\ 1y_m=87.97d_c \rightarrow 365d_m =87.97d_c$$

Divide both sides by $$365$$ giving:

$$1d_m =\dfrac{87.97}{365} d_c$$

$$1y_p=3 \left( 87.97d_c -\dfrac{16.21 \times 87.97}{365} d_c \right) ...(3_a)$$

I get $$1y_o \approx 252.19d_c$$ But we need this in years

So $$1y_p \approx \dfrac{252.19}{365} y_c \approx 0.69 y_c$$

A car derives north for $$35$$ minutes at $$85\ km/hr$$ and then stop for $$15$$ mins. The car continues north travelling $$130\ km$$ in $$2$$ hours. What is the total displacement and average velocity?

Total displacement : $$179.6\ km$$
Average velocity : $$63.4\ km/h$$
Explanation:
Since it's travelling in the same direction for the entire duration of its journey, the total displacement of teh car is dimply the distance form the starting point.
In the first part of its journey, the car travelled for $$35$$ minutes at a speed of $$85\ km/h$$.
Convert the time from minutes to hourse to get
$$35 min \dfrac{1 h}{60 min}=0.5833\ h$$
This means that the car covered
$$0.5833 h\dfrac{85 km}{1 h}=49.6 km$$
The car stopes, then continous along its current direction, covering $$130\ km$$ in $$2\ hours$$. The total displacement of the car will thus be
$$d_{total }=49.6+130=179.6\ km$$
The average velocity is simply the total displacement divided by the total time of travel. In your case, the total time will be
$$t_{total}=0.5833\ h+ \underbrace { 0.25h }_{ =15 min } +2h=2.833\ h$$
The average velocity is
$$\bar v=\dfrac{179.6 km}{2.833 h}=63.4\ km/h$$

How do intermolecular forces affect evaporation?

The larger the intermolecular forces in a compound, the slower is its evaporation rate.

In order of decreasing strength, the important intermolecular forces in a compound are:

Hydrogen bonds $$>$$ Dipole-dipole attractions $$>$$ London dispersion forces

They all depend on the fact that a polar molecule has both positive and negative charges. The positively charged part of one molecule aligns with the negatively charged part of another molecule.

These forces of attraction hold polar liquids together.

If the molecules are held tightly together by strong intermolecular forces, few of the molecules will have enough kinetic energy to separate from each other.

They will stay in the liquid phase, and the rate of evaporation will be low.

If the molecules are held loosely together by Van der Waal's forces, many of them will have enough kinetic energy to separate from each other.

They will escape from the liquid phase, and the rate of evaporation will be high. So, the greater the intermolecular force in a compound, the slower will its rate of evaporation.

Aneesha travels at a rate of $$50$$ miles per hour. Morris is traveling $$3$$ feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?

A reasonable estimate of Morris's speed would be $$58$$ miles/ hour
The phrasing of the question implies that there should have been a list of values to choose from but no such list was provided.
$$3\dfrac{feet}{second}=3\dfrac{feet}{second}\times 60\dfrac{seconds}{minute}\times 60 \dfrac{minutes}{hour}$$
$$3\times (60\times 60)=3\times 3600$$ which is a little more that $$10,000$$
So $$3\dfrac{feet}{second}$$ is a little more that $$10,000\dfrac{feet}{hour}$$
There are $$5,280$$ feet in a mile.
then we have an estimated speed difference of
$$\dfrac{10,000 \dfrac{feet}{hour}}{5,000 \dfrac{feet}{mile}}=2\dfrac{miles}{hour}$$
So Morris is traveling at approximately $$2\dfrac{miles}{hour}$$ less than Aneesha's given $$60\dfrac{miles}{hour}$$ or at approximately $$58\dfrac{miles}{hour}$$
As point of interest, using a spreadsheet to calculate the difference in traveling at $$60$$ miles per hour versus $$58$$ miles per hour gave a value of $$2.93\bar{3}$$ feet per second; pretty close to the requested $$3$$ feet per second.

How was it determined that a parsec is $$ 3.26 $$ light years?

Parallax is an effective way to measure distance to nearby stars because it relies on geometry. When astronomers use parallax, they are measuring how a star appears to move against its background. The unit parsec refers to the distance that an object would have to be from the Earth to have a parallax angle of $$ 1 $$ arc-second.

In the figure above, the angle, $$ \alpha $$ is the angle that is measured by the Earth on opposite sides of the sun. The parallax angle, $$ p $$ is half of this angle.

$$ p=\frac{1}{2}\alpha$$

If we defines $$ p $$ to be $$ 1 $$ arc-second, then our object will be $$ 1 $$ parsec away. Since light from the sun takes $$ 8 $$ minutes and $$ 20 $$ seconds to reach the Earth,. we know that;

$$ 1 AU=8.33 $$ light minutes

We can use this information to convert our parsec into light years with the tangent formula.

$$ tan(p)=\frac{8.33 \quad light \quad minutes}{d}$$

Or;

$$ d=\frac{8.33 \quad light\quad minutes}{tan(p)}$$

If we convert $$ p $$ to radians, than we can use the small angle approximation, $$ tan(\theta)\approx \theta$$.

$$ 1 arc-second=4.85 \times 10^{-6} $$ radians

Plugging this in for $$ p $$ and using the small angle approximation;

$$ d=\frac{8.33 \quad light\quad minutes}{4.85\times 10^{-6}}$$

=$$ 1.72 \times 10^6 $$ light-minutes

=$$ 3.26 $$ light years

1913938_1912067_ans_ffaecc5fbb464a2c88cce602b67057b7.png

What is a clever way to remember anthimeria and periphrasis?

In rhetoric, anthimeria, traditionally and more properly called antimeria - antí- "against, opposite" and méros- "part")

Ok, first think about its use,
It involves using one part of speech as another. So the word opposite comes to mind, even if a little.
Now divide the word anthi and meria.
Anti means opposite or against and it is already present in the word "anthi" and just try to remember the meria part.
Example of a use of anthimeria-
The clever man snaked its way out of the hassle.
We all know snake is a noun yet it is used as a verb in this sentence.

Periphrasis the use of separate words to express a grammatical relationship that is otherwise expressed by inflection, e.g. did go as opposed to went and more intelligent as opposed to cleverer.
Again break the word into peri and phrasis.

Phrase means a group of words without a finite verb and is readily present in phrasis and peri means near or around, so a group of words having the same or nearly same meaning is used to substitute another word in periphrasis. So it is easy to remember this way.

SI unit of potential energy?

Please understand that the SI unit for potential energy is the same as the SI unit for all energy, the Joule.

The Joule in SI base units is defined as:

$$J = \dfrac{kg \cdot m^2}{s^2}$$

Please consider the equation for kinetic energy.

$$K.E. = \dfrac{1}{2}mV^2$$

The units for V is $$\dfrac{m}{s}$$

Square that $$\dfrac{m^2}{s^2}$$

Multiply by the units for mass:

$$\dfrac{kg \cdot m^2}{s^2}$$

Let's consider Gravitational potetial energy:

$$P.E. = mgh$$

The units for m is kg:

$$P.E. = kggh$$

The units for g is $$\dfrac{m}{s^2}:$$

$$P.E. = kg\dfrac{m}{s^2}h$$

The units for h is m:

$$P.E. = \dfrac{kg \cdot m^2}{s^2}$$

Lets look at $$E = mC^{2}$$

The units for m is kg:

$$E = kgC^{2}$$

The units for C is $$\dfrac{m}{s}$$ square it $$\dfrac{m^2}{s^2}$$

$$E = \dfrac{kg \cdot m^2}{s^2}$$

I hope that this helps you to understand that the SI unit for all types of energy is, the Joule.

What is one atmosphere of pressure?

One atm. is the same (per definition) as $$101325$$ pa. This
approximately the same as $$10^{5}$$ pa which is $$1$$ bar.

Explanation:

The standard atmosphere is defined as $$101325$$ pa. As you can
see, this is pretty close to $$10^{5}$$ pa which is equal to $$1$$ bar.

Keep in mind that pressure is defined as the force exerted
on a certain area. Therefore the SI unit of pressure $$p a$$ is the same as $$N
\cdot m^{-2}$$.

What is the SI unit of electric charge?

Answer
The S.I unit is the Coulomb (C)
Explanation:
It is approximately $$ 6.242.10^{18} e $$(e being the charge of a proton)

What bases are purines?

The two purine bases in humans are adenine and guanine.
In DNA, they pair with their complementary pyrimidine bases, thymine and cytosine, respectively.
In RNA, they pair with their complementary pyrimidine bases, uracil and cytosine, respectively.
Adenine (A) and guanine (G).
Thymine (T), uracil (U), and cytosine (C)
When we have a base pair, a purine base and its complementary pyrimidine base hydrogen-bond.
Example: AT Pair
Example: GC Pair
1929468_1913966_ans_cd9bac11e4bb4898a4d024f1cdd5c957.png

1929468_1913966_ans_cd9bac11e4bb4898a4d024f1cdd5c957.png

What are the $$6$$ models of the atom?

There are five basic atomic models which have contributed the structure of the atom itself.

Explanation:

They are:

1. John Dalton's atomic model: Dalton´s Billiard Ball (Solid Sphere) Model.

2. J.J. Thomson's model: Plum Pudding model.

3. Ernest Rutherford's model: Nuclear model.

4. Niels Bohr's model: Planetary model.

5. Erwin Schrödinger's model: Electron Cloud Model/Quantum Model.
6. Wave mechanical model.

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On a scale drawing, $${1}/{4}$$ inch $$=1$$ foot. What are the dimensions on the scale drawing for a room that is $$18$$ feet by $$16$$ feet?

We are told in the scale drawing is:
$$\dfrac{1}{4}\ inch=1\ feett$$
To find how many inches to make the length of the room at $$18$$ feet multiply each side of teh equation by $$18$$
$$18 \times \dfrac{1}{4}\ inch=18 \times 1\ feet$$
$$\dfrac{18}{4}\ inches=18\ feet$$
$$\dfrac{16+2}{4} inches=18\ feet$$
$$\left( \dfrac{16}{4}+\dfrac{2}{4}\right) inches=18\ feet$$
$$\left( 4+ \dfrac{1}{2}\right) \ inches =18\ feet$$
$$4\dfrac{1}{2} \ inches =18\ feet$$
To find how many inches to makes the width of the room at $$16$$ feet multiply each side of the equation by $$16$$
$$16 \times \dfrac{1}{4}\ inches =16 \times 1\ feet$$
$$\dfrac{16}{4} \ inches =16\ feet$$
$$4\ inches =16\ feet$$
To draw teh room to scale you would draw a rectangle:
$$4\dfrac{1}{2}\ inches $$ by $$4$$ inches

What is the unit used for Water Vapor?

Grams per kilogram.
Explanation:
When measuring water vapor, the relatively humidity is only a ratio of the amount of water vapor to the maximum amount of water vapor so there isn't really a unit. The absolute humidity can be determined by finding the relative humidity and then looking at the temperature. When you determine this you fin out how many grams of water vapor are in the air per kilogram of air.

What is the SI unit used to measure amount of substance?

Answer
The amount of a substance, ie., the number of moles there is, is measured in mol.
Explanation:
1 mol of a substance is the amount of that substance which contains the same number of particles as 12 g of carbon12.
For solids, the number of moles can found using the following formula:
$$ moles = \dfrac{mass}{molar mass} $$
For liquids, the number of moles can found using the following formula:
$$ moles = cons . \times vol $$
For gases, 1 mol occupies $$ 24 dm^{3} $$ at 278 K and 1 atm of pressure

Water is leaking out of an inverted conical tank at the rate of 10,000 cm$$^3$$/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 6m and the diameter at the top is 4m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2m, how can I find the rate at which water is being pumped into the tank.?

Answer:
(see below for solution method)
Explanation:
Start by ignoring the leakage and determine the rate of inflow required to achieve the specified rate of height (depth) of water increase.
Later we'll use the fact that
Actual inflow rate
= Inflow Rate for Increased Depth + Leakage Rate
For the given cone the ratio of r adius to h eight is $$\dfrac{1}{3}$$ so
$$t = \dfrac{1}{3}h$$
The formula for the volume of a cone:
$$V = \dfrac{\pi r^{2}h}{3}$$ becomes $$V = \dfrac{\pi h^{3}}{27}$$
$$\dfrac{dV}{dh} = \dfrac{\pi h^{2}}{9}$$
We are interested in the change in Volume with respect to time and note that
$$\dfrac{dV}{dt} = \dfrac{dV}{dh} . \dfrac{dh}{dt}$$
Using the value we've already calculated for $$\dfrac{dV}{dh}$$ and the supplied value of 20 cm/min (at a height of h=200 cm)
we get:
$$\dfrac{dV}{dt} = \dfrac{\pi (200 cm)^{2} . (20 cm)}{9 min}$$
$$= \dfrac{800000 \pi}{9} cm^{3} / min$$
or roughly
$$279,252.7 cm^{3}$$ / min
This is the Inflow Rate Required to Cause Height Increase and
ignores the Rate of Leakage
The Actual Inflow Rate needs to be the sum of these two:
$$279,252.7 cm^{3} / min + 10,000 cm^{3} / min$$
$$= 289, 252.7 cm^{3} / min$$

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Write the SI unit of co efficient of static friction

As we know the units of force are newton and normal is also a force, hence its unit is also newton. The two forces units will cancel each other. Therefore, the coefficient of friction has no unit. It is a unit less and dimensionless quantity.

Give some examples of electrostatic force

"Electrostatic force:

The electrostatic force is the force that exists between electrically charged particles or objects at rest.

Examples of electrostatic forces:

When we run a piece of paper with the oil in our head with the help of a comb produces electrostatic force.
Balloons get attracted to another balloon when one of them are rubbed with hair.
When I do iron my silk or cotton cloth and keep it right in front of me, they just cling on to my body.
Lightning is also another example of electrostatic force."

A circular curve of highway is designed for traffic moving at $$92 km/h$$. When assumed the traffic consists of cars without negative lift ?
(a) If the radius of the curve is $$150 m$$, what is the correct angle of banking of the road?

(b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at $$92 km/h$$?

(a) $$\theta=23.9^0$$ rounded to first place of decimal
(b) $$\mu_{s(min)}=0.44382$$

Explanation:
a) In the figure below
Let $$mg$$ be weight of car,

$$r$$ radius of curve it is traveling,

$$\theta$$ be the banking angle of the road,

$$v$$ its maximum velocity with which it can travel safely while negotiating through the curve,

$$N$$ be the normal reaction, and

$$\mu_s$$ be coefficient of friction between the road and the its tyres.

We know that while in circular motion the centripetal force acting on the car

$$=\dfrac{mv^2}{r}$$

And force due to friction is given as $$=\mu_sN$$

Assuming car to be situated at the origin, Force equations in the $$x$$ and $$y$$ direction at this maximum speed for the car are

$$\dfrac{mv^2}{r}=N\sin\theta+\mu_sN\cos\theta$$ and

$$mg+\mu_sN\sin\theta=N\cos\theta$$

For designing of banking angle of the curved roads, worst case is considered.

$$\mu_s$$ is set = $$0$$.

Very low values of $$\mu_s$$ could be encountered in the event of rain, snow, mud, oil spillage on the road when road becomes slippery.
Above equations reduce to

$$\dfrac{mv^2}{r}=N\sin\theta$$ and $$mg=N\cos\theta$$

Dividing first with second we obtain
$$\dfrac{\frac{mv^2}{r}}{mg}=\dfrac{N\sin\theta}{N\cos\theta}$$

or, $$\tan\theta=\frac{v^2}{rg}$$

Given $$v=92km/hr$$ converted in $$m/s=\dfrac{92*1000}{3600}=25.5$$

Inserting all values in above expression

$$\tan\theta=\dfrac{(25.5)^2}{150*9.81}=0.44382$$

$$\theta=23.9^0$$ rounded to first place of decimal.

(b) If curves are not banked, implies that $$\theta=0$$.

This makes $$\sin\theta=0$$ and $$\cos\theta=1$$.

Now the general expressions reduce to

$$\dfrac{mv^2}{r}=\mu_sN$$ and $$mg=N$$

Insert value of $$N$$ in first and solve for $$mu_{s(min)}$$,

minimum coefficient of friction required between tyres and road that would keep traffic from skidding out of the curve:

$$\dfrac{v^2}{r}=\mu_{s(min)}g$$

$$\mu_{s(min)}=\dfrac{v^2}{rg}$$
We observe that this is equal to value of $$\tan\theta$$ calculated in (a) above.

$$\mu_{s(min)}=0.44382$$.

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How does Newton's second law relate to inertia ?

Newtons second law states:

A larger resultant force acting upon an object, the greater acceleration that object has. Meaning force and acceleration are directly proportional to each other $$(f \propto a),$$ and acceleration is inversely proportionate to the mass of an object.

This is shown through the formula:

$$f = ma$$ where f =Force in Newtons, N, m = Mass in Kilograms, Kg and a = Acceleration in $$m/s^2.$$

This, therefore, can be arranged to find Mass, or Acceleration, using that acceleration is inversely proportionate to the mass of an object.

Inertia is 'The tendency for motion to remain unchanged', basically the measurement that objects move at the same velocity, or not at all. This links to Newton's first law that until acted upon a resultant force, objects moving and not moving will stay moving at that velocity.

Inertial mass is the measurement for how difficult it is to change the velocity for the object. Using the previous Newtons second law formula:

$$F = ma -> M = \dfrac{f}{a}$$

$$\therefore$$ it is linked as Inertia and Intertial mass is found out using Newton's second law as previously stated.

How to calculate the force of gravitational attraction between a person (mass $$=75\ kg$$) & Earth (mass $$5.98\times 10^{24}\ kg$$ and mean radius $$6.37\times 10^{6}m$$) ?

The gravitational force can be calculated with the formula:
$$F_{g}=\dfrac{GMm}{R^{2}}$$
where:
$$F_{g}=$$ gravitational force
$$G=$$ gravitational constant
$$M=$$ mass of Earth
$$m=$$ mass of object
$$R=$$ distance from the earth's centre to the object's centre
Substitute your know values into the formula to determine the gravitational force.
Assuming that the person is standing on the surface of the Earth, the value of $$R$$ would be the radius of the Earth.
$$F_{g}=\dfrac{GMm}{R^{2}}$$
$$F_{g}=\dfrac{\left(6.67\times 10^{-11}\dfrac{N\cdot m^{2}}{kg^{2}}\right)\left(5.98\times 10^{24}kg\right) (75\ kg)}{\left(6.37\times 10^{6}m\right)^{2}}$$
$$F_{g}=737.24\ N$$
$$F_{g}=740\ N$$

Basic Science - Class 8 General Knowledge - Extra Questions

Why do water pipes, in hilly areas, often burst on a cold frosty night?

What is a 'formula' in Chemistry?

Why is a small space left between each set of two rails of a railway line?

How are positive and negative charges produced during a thunderstorm?

Why does not moon have an atmosphere?

Are the lead pencils made of lead?

Why is Miner's Safety Lamp a safe lamp?

The process of electric _______ between clouds and the earth or between different clouds causes _______.

Why is a person in a moving vehicle thrown forward when the vehicle stops suddenly?

Describe the achievements of Horticulture Development Programme.

Why does milk turn sour?

Why is it easier to roll a barrel than to pull it along the road?

What is the temperature $$32$$ degrees Fahrenheit in degree Celsius?

Is chemistry a physical science?

Why is Organic chemistry important? What are the applications of this branch of chemistry? Who uses it? How is it used?

How is electric discharge fatal for human beings?

Why does Earth have day and night?

If it is noon at one location on Earth, what time is it at a location directly on the other side of Earth?

Where is the Moon in its orbit at the time of solar eclipse?

The footprints on the moon were made in the early 1970 s. How do the footprints, you think look today and why?

Match column-I with column-II and select the correct answer using the codes given below:

When the Moon is full, where is it in its orbit around Earth?

Why is the path of water curved on coming out of horizontal jet?

CONCEPTUAL QUESTIONS Are there more nanoseconds in a second than the number of seconds in a year?

What is ecosystem? Write briefly about its components and their interdependence.

A drop of water or mercury on a clean glass plate is circular in shape. Why?

When a moving train slows down quickly, will a passenger tend to fall backward or forward. Explain why?

x and y displacements of a particle are given as x(t) = a $$sin \omega t$$ and y(t) = a $$sin 2\omega t$$. Its trajectory will look like :

An object is placed at a distance of 10 cm from a concave mirror of focal length 20 cm.a) Draw ray diagram for the formation of image b) Calculate the image distancec) state 2 characteristics of the image formed.

A particle is moving along a circular path of radius $$R$$ in such a way that at any instant magnitude of radial acceleration & tangential acceleration are equal. If at $$t=0$$ velocity of particle is $$v_{0}$$, then find the time period of first revolution of the particle .

What is chemistry?

What is the difference between distance and displacement?

What is the $$S.I$$ unit of electric potential?

Why force is a vector quantity?

What does it mean for a species to be in stasis?

Why is acceleration measured in meters / seconds squared?

Which is warmer -30C or -30 F?

Why are peroxisomes important in cells?

Why is the number of protons and electrons equal in an atom?

Why is meiosis not a part of the cell cycle?

Why are standard units of measurement important to scientists?

Why is impulse a vector?

Why do the phospholipids surrounding the cell form a bilayer?

Why is the atomic model useful?

Why are SI units helpful?

Whats $$ 45 $$ degrees F. in celcius?

What quantum numbers refer to a 4d orbital?

What scientists study the history of life on earth?

When the pressure on a gas increases, will the volume increase or decrease?

What is the strongest of the four fundamental forces?

What $$SI$$ units are used to measure power?

Which has the larger atomic radius: $$ Cl - $$ or $$K + $$ ?

What is the study of cells called?

What property of an object determines how much inertia it has?

What property is unique to stem cells?

What is thermochemistry?

What is the percentage by mass of ammonium nitrate?

What is the percentage composition of N, H and O in ammonium nitrate,$$ NH_4NO_3 $$?

What is the pressure conversion factor for torr to kpa?

What is the main component of the cell membrane? Why is the main component?

What is the SI unit of mass ?

What is the weight in lbs of a 75-kg person?

What is the relationship between pressure and volume ?

What kind of organism has pseudopods?

What is time?

What is the number of significant figures in each of the following?$$ 10.0005 g $$$$ 0.003423 mm $$$$ 2900 +100 ft $$$$ 8.9 \times 10^5 L $$

What is the nucleon number?

What is the number of neutrons in $$$^{10}_5 B $$ ?

What is the mass of $$HCl$$ in a $$500\ mL$$ sample of $$6.0\ M\ HCl$$?

What is the isotope symbol for an atom that contain $$82$$ protons and $$125$$ neutrons?

What is the number of moles in $$ 36 g $$ of $$ H_2O $$?

What is instantaneous rate of change formula?

What is the number of protons in an atom of carbon-12?

What is the mass of $$Cl$$ in $$21\ g$$ of $$NaCl$$?

What is the percent by mass of oxygen in $$ Mg (NO_3)_2 $$?

What is the difference between organism, population, community, ecosystem, biome and biosphere ?

What is the conversions of grams to mL?

What is the conversion factor between km/hr and m/s?

What is the difference between a therapist, psychologist, psychiatrist, and a counselor?

The process of electric _ between clouds and the earth or between different clouds causes _.

CONCEPTUAL QUESTIONS
Are there more nanoseconds in a second than the number of seconds in a year?

An object is placed at a distance of 10 cm from a concave mirror of focal length 20 cm.
a) Draw ray diagram for the formation of image
b) Calculate the image distance
c) state 2 characteristics of the image formed.

What is the number of significant figures in each of the following?
$$ 10.0005 g $$
$$ 0.003423 mm $$
$$ 2900 +100 ft $$
$$ 8.9 \times 10^5 L $$