CBSE Questions for Class 11 Engineering Physics Units And Measurement Quiz 9 - MCQExams.com

When a wave traverses a medium the displacement of a particle located at x at a time is given by y = a sin (bt - cx), where a, band are constants of the wave, which of the following is a quantity with dimensions?
  • $$\displaystyle \frac {y}{a}$$
  • $$bt$$
  • $$cx$$
  • $$\displaystyle \frac {b}{c}$$
If energy (E) , force (F) and linear momentum (P) are fundamental quantities, then match the following and give correct answer.
AB
Physical quantityDimensional formula
a) Mass
d) $$\displaystyle { E }^{ 0 }{ F }^{ -1 }{ p }^{ 1 }$$
b) Length
e) $$\displaystyle { E }^{ -1 }{ F }^{ 0 }{ p }^{ 2 }$$
c) Time f) $$\displaystyle { E }^{ 1 }{ F }^{ -1 }{ p }^{ 0 }$$
  • a-d, b-e, c-f
  • a-f, b-e, c-d
  • a-e, b-f, c-d
  • a-e, b-d, c-f
What is the dimensional formula of Inductance?
  • $$[ML^2T^{-2}A^{-2}]$$
  • $$[ML^2TA^{-2}]$$
  • $$[ML^2T^{-1}A^{-2}]$$
  • $$[ML^2T^{-2}A^{-1}]$$
If $$x=at+b{ t }^{ 2 }$$ where $$x$$ is measured in $$m$$ and $$t$$ in $$s$$, then the dimension of $$\left( { b }/{ a } \right) $$ is:
  • $$[L{ T }^{ -2 }]$$
  • $$[L{ T }^{ -1 }]$$
  • $$[T]$$
  • $$[{ T }^{ -1 }]$$
The dimensions of $$\displaystyle \frac { a }{ b } $$ in the equation $$\displaystyle P=\frac { a-{ t }^{ 2 } }{ bx } $$ where $$P$$ is pressure, $$x$$ is distance and $$t$$ is time, are:
  • $$\displaystyle \left[ { M }^{ 2 }{ LT }^{ -3 } \right] $$
  • $$\displaystyle \left[ { MT }^{ -2 } \right] $$
  • $$\displaystyle \left[ { LT }^{ -3 } \right] $$
  • $$\displaystyle \left[ M{ L }^{ 3 }{ T }^{ -1 } \right] $$
The moon is observed from two diametrically opposite points on earth. The angle subtended at the moon by the two directions of observations is $$1^o 54'$$. Given the diameter of the earth to be about $$2.276 \times 10^7 m$$, compute the distance of moon from the earth.
  • $$1 \times 10^8 m$$
  • $$6.84 \times 10^8 m$$
  • $$6.84 \times 10^{10} m$$
  • $$38.4 \times 10^8 m$$
The mass of the electron is given $$9.1\times 10^{-31} kg$$. Find the order of magnitude of the number of electrons of $$1 kg$$.
  • $$10^{31}$$
  • $$10^{-30}$$
  • $$10^{30}$$
  • $$10^{-31}$$
What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us ?  
  • $$2.7\times 10^{25} m$$
  • $$ 10^{25} m$$
  • $$10^24 m$$
  • $$3\times 10^{25} m$$
The radius of proton is $$0.6\times 10^{-15} m$$. What is the order of magnitude of it volume?   
  • $$10^{-47} m^3$$
  • $$10^{-44} m^3$$
  • $$10^{-45} m^3$$
  • $$10^{-46} m^3$$
What is the order of magnitude of one light year? 
  • $$10^{15} m$$
  • $$10^{10} m$$
  • $$9.2 \times 10^{15} m$$
  • $$10^{16} m$$
The sun's angular diameter is measured to be $$1920 ''$$. The distance of the sun from the earth is $$1.496 \times 10^{11} m$$. What is the diameter of the sun?
  • $$1 \times 10^9 m$$
  • $$1.39 \times 10^9 m$$
  • $$13.9 \times 10^9 m$$
  • $$139 \times 10^9 m$$
The radius of the sun is $$7\times 10^8 m$$ and its mass is $$2\times 10^{30} kg$$. What is the order of magnitude of density of the sun?
  • $$1.4\times 10^3 kg/m^3$$
  • $$ 10^7 kg/m^3$$
  • $$1.5\times 10^3 kg/m^3$$
  • $$10^3 kg/m^3$$
The given rectangular shaped object pictured is being measured. Its left end is perfectly lined up with "0 m" on the measuring tape. Which of the following is the best and most precise length of the green, rectangular shaped object that can be obtained, using the measuring tape?
494917_fe1ca69055e84d81a3e6941df27b2bb2.png
  • 2.0 m
  • 2.4 m
  • 2.37 m
  • 2.377 m
  • 2.5 m

 Students A, B and C measure the diameter of a wire using three different screw gauges of least count  0.01 cm, 0.05 cm and 0.001 cm respectively. Each one makes 10 measurements.The measurements will be more precise for 
  • A
  • B
  • C
  • all
The radius of the earth is given $$6.4\times 10^6 m$$. What is the order of magnitude of the size of the earth? 
  • $$10^6 m$$
  • $$6 \times 10^6 m$$
  • $$10^7 m$$
  • $$5 \times 10^6 m$$
State whether the given statement is TRUE or FALSE.
The total height of 10 identical coins each of thickness 0.5 cm placed one over the other will be 50 mm.
  • True
  • False
Which of the following is not a characteristic of the standard unit?
  • It should be of convenient size
  • It should change with respect to space and time
  • It should not be perishable
  • It should be easily reproducible
Match the following:

Column - I

Column - II
A
Deca
p
$$10^3$$
B
Hecto
q
$$10^6$$
C
Kilo
r
$$10^1$$
D
Mega
s
$$10^2$$
E
Giga
t
$$10^8$$


u
$$10^9$$
  • A-r, B-s, C-p, D-q, E-u
  • A-s, B-r, C-p, D-q, E-u
  • A-r, B-s, C-u, D-q, E-p
  • A-q, B-s, C-p, D-r, E-u

A star has a parallax angle p of 0.723 arcseconds. What is the distance of the star?
  • 1.38 parsecs
  • 2.38 parsecs
  • 3.38 parsecs
  • 4.38 parsecs
Two stars $$S_1$$ and $$S_2$$ are located at distances $$d_1$$ and $$d_2$$ respectively. Also if $$d_1>d_2$$ then which of the following statements is true?
  • The parallax of $$S_1$$ and $$S_2$$ are same.
  • The parallax of $$S_1$$ is twice as that of $$S_2$$.
  • The parallax of $$S_1$$ is greater than parallax of $$S_2$$
  • The parallax of $$S_2$$ is greater than parallax of $$S_1$$
If the angular distance between the stars turns out to be approximately 1100 arcseconds, or 0.30 degrees. The moon appears to shift 0.3 degrees when we observe it from two vantage points 2360 km apart, then find the distance of the moon from the surface of the earth.Given angular diameter of moon is 0.5 degrees.


550354_c52435ed368e4ce6806fc17c9821a5d0.png
  • 450642 km
  • 450392 km
  • 325684 km
  • 480264 km
A star is $$1.45\ parsec$$ light years away. How much parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?
  • $$2\ Parsec$$
  • $$0.725\ Parsec$$
  • $$1.45\ Parsec$$
  • $$2.9\ Parsec$$
Which of the following is a possible dimensionless quantity?
  • Velocity gradient
  • Pressure gradient
  • Displacement gradient
  • Force gradient
$$ 5\times 10^7 \mu s$$ is equivalent to ____
  • 0.5 s
  • 5 s
  • 50 s
  • 500 s
The dimension of $$\dfrac{h}{mv}$$ is: ($$h$$$$=$$ planks constant, $$m$$= mass, $$v$$=velocity)
  • $$M$$
  • $$L$$
  • $$T$$
  • none of the above
The dimensional formula of coefficient of viscosity is
  • $$[MLT^{-1}]$$
  • $$[M^{-1}L^{2}T^{-2}]$$
  • $$[ML^{-1}T^{-1}]$$
  • none
A physical quantity $$Q$$ is found to depend on observables $$x, y$$ and $$z$$, obeying relation $$Q=\dfrac{x^{2/5}z^{3}}{y}$$. The percentage error in the measurements of $$x, y$$ and $$z$$ are $$1\%$$, $$2\%$$ and $$4\%$$ respectively. What is percentage error in the quantity $$Q$$ will be :
  • $$5\%$$
  • $$4.5\%$$
  • $$11\%$$
  • $$7.75\%$$
The equation of state of a gas is given by $$\begin{pmatrix}P+\dfrac{a}{v^3}\end{pmatrix} (V-b^2) = cT$$, where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively
  • $$ML^8T^{-2}$$ and $$L^{3/2}$$
  • $$ML^5T^{-2}$$ and $$L^{3}$$
  • $$ML^5T^{-2}$$ and $$L$$
  • $$ML^6T^{-2}$$ and $$L^{3/2}$$
The ratio of the dimensions of Planck constant and that of moment of inertia has the dimensions of
  • Time
  • Frequency
  • Angular momentum
  • Velocity
$$ML^{-1}T^{-2}$$ is the dimensional formula of
  • force
  • coefficient of friction
  • modulus of elasticity
  • energy
Parallax angles _______ $$0.01/ arcsec$$ are very difficult to measure from Earth.
  • more than
  • less than
  • equal to
  • greater than or equal to
If a star is $$5.2\times 10^{16}\ m$$ away. What is the parallax angle in degrees?
  • $$1.67 \times 10^{-4}$$ degrees
  • $$1.67 \times 10^{-5}$$ degrees
  • $$0.67 \times 10^{-4}$$ degrees
  • $$2.3 \times 10^{-4}$$ degrees
Two  quantities X and Y have different dimension. Which mathematical operation given below is physically meaningful?
  • $$X+Y$$
  • $$X-Y$$
  • $$\dfrac{X}{Y}$$
  • None of these
Four students measure the height of a tower. Each student uses different methods and each measures the height many times. The data for each are plotted. The measurement with the highest precision is:
632872_c589d49ce8a744d1ae7eabec4f873563.png
  • I
  • II
  • III
  • IV
The dimensions formula of ( velocity $$)^2  /$$ radius are the same of that of :
  • Planck's constant
  • Gravitational constant
  • Dielectric constant
  • None of these
If the dimensions of length are expressed as a $$G^x \cdot C^y \cdot h^z$$, where G, C and h are the universal gravitational constant, speed of light and plank constant respectively, then value of x,y,z will be :
  • $$x=1, y=-\dfrac{3}{2}, z=\dfrac{1}{2}$$
  • $$x=\dfrac{1}{2}, y=\dfrac{1}{2}, z=\dfrac{3}{2}$$
  • $$x=\dfrac{1}{2}, y=-\dfrac{3}{2}, z=\dfrac{1}{2}$$
  • $$x=-\dfrac{3}{2}, y=\dfrac{1}{2}, z=\dfrac{1}{2}$$
Someone is weighing some box as 25 ____. Fill in the blank with appropriate answer.
  • Kilogram
  • Meter
  • Seconds
  • Joules
The Quantum Hall Resistance $$R_{H}$$ is a fundamental constant with dimensions of resistance. If $$h$$ is Planck's constant and $$e$$ the electron charge, then the dimension of $$R_{H}$$ is the same as.
  • $$e^{2}/h$$
  • $$h/e^{2}$$
  • $$h^{2}/e$$
  • $$e/h^{2}$$
The dimensional formula for Young's modulus is :
  • $$ [ ML^{-1} T^{-2} ] $$
  • $$ [ M^{0} LT^{-2} ] $$
  • $$ [ MLT^{-2} ] $$
  • $$ [ ML^{2} T^{-2} ] $$
The quantity which has the same dimensions as that of gravitational potential is
  • latent heat
  • impulse
  • angular acceleration
  • planck's constant
  • specific heat capacity
The frequency of vibration of the string is given by 
$$v=\dfrac {p}{2l}\left [ \dfrac {F}{m} \right ]^{1/2}$$
Here, p is the number of segments in the string and l is the length. The dimensional formula for m will be
  • $$[M^0LT^{-1}]$$
  • $$[ML^0T^{-1}]$$
  • $$[ML^{-1}T^{0}]$$
  • $$[M^0L^0T^{0}]$$
The physical quantity that does not have the dimensional formula $$[ML^{-1}T^{-2}]$$ is
  • force
  • pressure
  • stress
  • modulus of elasticity
  • energy density
The dimensional formula of $$\dfrac {1}{\mu_{0}\epsilon_{0}}$$ is
  • $$[M^{0}LT^{-2}]$$
  • $$[M^{0}L^{-2}T^{-2}]$$
  • $$[M^{0}LT^{-1}]$$
  • $$[M^{0}L^{2}T^{-2}]$$
The dimension of $$\displaystyle \frac{a}{b}$$ in the equation $$\displaystyle p = \frac{a-t^2}{bx}$$ where p is pressure, x is distance and t is time is
  • $$\displaystyle [LT^{-3}]$$
  • $$\displaystyle [ML^3 T^{-1}]$$
  • $$\displaystyle [M^2 L T^{-3}]$$
  • $$\displaystyle [MT^{-2}]$$
Number of particles is given by $$n=-D\cfrac { { n }_{ 2 }-{ n }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 2 } } $$ crossing a unit area perpendicular to X-axis in unit time, where $${ n }_{ 1 }$$ and $${ n }_{ 2 }$$ are number of particles per unit volume for the value of $$x$$ meant to $${x}_{2}$$ and $${x}_{1}$$. Find dimensions of $$D$$ called as diffusion constant :
  • $$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ 2 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ -4 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ }{ T }^{ -3 } \right] \quad $$
  • $$\left[ { M }^{ 0 }{ L }^{ 2 }{ T }^{ -1 } \right] $$
Express 0.006006 into scientific notation in three significant digits:
  • $$6.01 \times 10^{-3}$$
  • $$6.0006 \times 10^{-3}$$
  • $$6.00 \times 10^{-3}$$
  • $$6.0 \times 10^{-3}$$
The dimensions of capacitance are :
  • $$\displaystyle \left[ { ML }^{ -2 }{ Q }^{ -2 }{ T }^{ 2 } \right] $$
  • $$\displaystyle \left[ { M }^{ -1 }{ L }^{ 2 }{ T }^{ -2 }{ Q }^{ 2 } \right] $$
  • $$\displaystyle \left[ { M }^{ -1 }{ L }^{ 2 }{ T }^{ -2 }{ Q }^{ -2 } \right] $$
  • $$\displaystyle \left[ { M }^{ -1 }{ L }^{ -2 }{ T }^{ 2 }{ Q }^{ 2 } \right] $$
If $$L,C$$ and $$R$$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $${C}^{2}LR$$ is :
  • $$\left[ { M }^{ }{ L }^{ -2 }{ T }^{ -1 }{ I }^{ 0 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 3 }{ I }^{ 0 } \right] $$
  • $$\left[ { M }^{ -1 }{ L }^{ -2 }{ T }^{ 6 }{ I }^{ 2 } \right] $$
  • $$\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ 2 }{ I }^{ 0 } \right] $$
The dimensional formula of modulus of elasticity is
  • $$\displaystyle \left[ { ML }^{ -1 }{ T }^{ -2 } \right] $$
  • $$\displaystyle \left[ { M }^{ 0 }{ LT }^{ -2 } \right] $$
  • $$\displaystyle \left[ { MLT }^{ -2 } \right] $$
  • $$\displaystyle \left[ { ML }^{ 2 }{ T }^{ -2 } \right] $$
The dimensions of $$\dfrac {\alpha}{\beta}$$ in the equation $$F = \dfrac {\alpha - t^{2}}{\beta v^{2}}$$, where $$F$$ is force, $$v$$ is velocity and $$t$$ is time, is :
  • $$[MLT^{-1}]$$
  • $$[ML^{-1}T^{-2}]$$
  • $$[ML^{3}T^{-4}]$$
  • $$[ML^{2}T^{-4}]$$
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