CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 4 - MCQExams.com

The magnitude of acceleration due to gravity decreases
  • as the height from the surface of the earth increases
  • as the depth from the surface of the earth increases
  • as one moves from the pole of the earth to its equator
  • All the above
The escape velocity of a body on a planet depend on 
  • acceleration due to gravity on the planet
  • the radius of the planet
  • the mass of the planet
  • All the above
The escape velocity from a planet of mass (M), radius (R) and acceleration due to gravity (g) is given by:
  • $$2\sqrt {\dfrac {GM}{R}}$$
  • $$\sqrt {2gR}$$
  • $$\sqrt {\dfrac {2gM}{R}}$$
  • $$\sqrt {\dfrac {2GM}{R}}$$
Choose the correct statement(s). The acceleration due to gravity 'g' decreases if
  • we go down from the surface of earth
  • we go up from the surface of earth
  • we go from the equator towards the poles on the surface of the earth
  • the rotational velocity of the earth is increased
A spring balance is graduated on sea level. If a body is weighted at consecutively increasing heights from earth's surface, the weight indicated by the balance :
  • Will go on increasing continuously
  • Will go on decreasing continuously
  • Will remain same
  • Will first increases and then decreases
The ratio of escape velocity of a tennis ball to that of a basket ball on the surface of the earth is
  • 1:1
  • 1:2
  • 2:1
  • 4:1
Gravity meters measures in units of mGal where 1 Gal (or 1 galileo) is the C.G.S unit of acceleration due to gravity. A gravity meter shows a reading of +300 mGal at a place where the normal 'g' is 9.78 $$m s^{-2}$$. The correct 'g' at that place where the reading was taken is _____ $$m s^{-2}$$.
  • 9.777
  • 9.783
  • 9.750
  • 9.810
The distance from the surface of the earth at which above and below the surface acceleration due to gravity is same will be
  • $$\displaystyle h = \frac{\sqrt{5}- 1}{2} R$$
  • $$\displaystyle h = \frac{\sqrt{3} - 1}{2}R$$
  • $$\displaystyle h = \frac{\sqrt{3} - 1}{3} R$$
  • None of these
At what altitude will the acceleration due to gravity be $$25\%$$ of that at the earth's surface $$($$given radius of earth is $$R)$$?
  • $$\dfrac{R}{4}$$
  • $$R$$
  • $$\dfrac{3R}{8}$$
  • $$\dfrac{R}{2}$$
A satellite in earth orbit experiences a small drag force as it enters the earth's atmosphere. Two students were asked consequence of this
Student-A : The satellite would slow down as, it spirals towards earth due to work of frictional force.
Student-B : The satellite speed up due to earths gravitational pull as it spirals towards earth.
  • A is correct, B is wrong
  • B is correct, A is wrong
  • both are correct
  • both are wrong
When a satellite moves around the earth in a certain orbit, the quantity which remains constant is:
  • angular velocity
  • kinetic energy
  • areal velocity
  • potential energy
Satellites A and B are orbiting around the earth in orbits of ratio $$R$$ and $$4R$$ respectively. The ratio of their areal velocities is
  • $$1 : 2$$
  • $$1 : 4$$
  • $$1 : 8$$
  • $$1 : 16$$
Two planets  $$A$$  and $$B$$  have the same material density. If the radius of  $$A$$  is twice that of B, then the ratio of the escape velocity $$\displaystyle \dfrac{V_A}{V_B}$$ is
  • $$2$$
  • $$\sqrt{2}$$
  • $$\dfrac{1}{ \sqrt{2}}$$
  • $$\dfrac{1}{2}$$
A (nonrotating) star collapses onto itself from an initial radius R$$_i$$ with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration a$$_g$$ on the surface of the star as a function of the radius of the star during the collapse?
126498_f7c939a8a5964d43ac44b1172e9a317a.png
  • a
  • b
  • c
  • d
Let $$\omega$$ be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth a below earth's surface at a pole $$(d << R)$$ The value of $$d$$ is
  • $$\displaystyle \dfrac{\omega^2 R^2}{g}$$
  • $$\displaystyle \dfrac{\omega^2 R^2}{2g}$$
  • $$\displaystyle \dfrac{2\omega^2 R^2}{g}$$
  • $$\displaystyle \dfrac{\sqrt{Rg}}{g}$$
Select the correct choice(s)
  • The gravitational field inside a spherical cavity, within a spherical planet must be non zero and uniform.
  • When a body is projected horizontally at an appreciable large height above the earth, with a velocity less than for a circular orbit, it will fall to the earth along a parabolic path.
  • A body of zero total mechanical energy placed in a gravitational field will escape the field
  • Earth's satellite must be in equatorial plane.
A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $$V$$. Due to the rotation of planet about its axis the acceleration due to gravity $$g$$ at equator is  $$\dfrac{1}{2}$$ of $$g$$ at poles. The escape velocity of a particle on the pole of planet in terms of  $$V$$.
  • $$V_e = 2V$$
  • $$V_e = V$$
  • $$V_e = V/2$$
  • $$V_e = \sqrt{2}V$$
The condition for a uniform spherical mass $$m$$ of radius $$r$$ to be a black hole is [$$G= $$gravitational constant, $$g=$$ acceleration due to gravity].
  • $$\displaystyle\left [ \dfrac{2Gm}{r} \right ]^{1/2}\leq c$$
  • $$\displaystyle\left [ \dfrac{2gm}{r} \right ]^{1/2}= c$$
  • $$\displaystyle\left [ \dfrac{2Gm}{r} \right ]^{1/2}\geq c$$
  • $$\displaystyle\left [ \dfrac{gm}{r} \right ]^{1/2}\geq c$$
A particle of mass $$10 g$$ is kept on the surface of a uniform sphere of mass $$100 kg$$ and radius $$10 cm$$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere 
  • $${\displaystyle 13.34\times 10^{-10}J}$$
  • $${\displaystyle 13.33\times 10^{-10}J}$$
  • $${\displaystyle 6.67\times 10^{-9}J}$$
  • $${\displaystyle 6.67\times 10^{-10}J}$$
Find the height above the surface of the earth where weight of a body becomes half.
  • $$\displaystyle \frac{R}{2}$$
  • $$(\sqrt{2} - 1) R$$
  • $$\displaystyle \frac{R}{(\sqrt{2} + 1)}$$
  • $$\displaystyle \frac{R}{\sqrt{2}}$$
A body is projected up with a velocity $$2$$ times the escape velocity $$v_{e}$$  from the surface of the earth. The velocity of the body at a point  far away the earth's attraction is
  • $$v_{es}$$
  • $$\sqrt{7} v_{es}$$
  • $$\sqrt{2} v_{es}$$
  • $$\sqrt{3} v_{es}$$
A planet of radius $$R = 1/10 \times $$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $$R/5$$ on it and lower a wire of the same length and of linear mass density $$10^{-3} kgm^{-3}$$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $$= 6 \times 10^6 m$$ and the acceleration due to gravity on Earth is $$10 ms^{-2}$$)
  • $$96 N$$
  • $$108 N$$
  • $$120 N$$
  • $$150 N$$
A planet revolves about the sun in elliptical orbit. The arial velocity $$\displaystyle \left ( \frac{dA}{dt} \right )$$ of the planet is $$4.0 \times 10^{16} m^2/s$$. The least distance between planet and the sun is $$2 \times 10^{12}$$m. Then the maximum speed of the planet in km/s is
  • 10
  • 20
  • 40
  • none of these
The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth d below the surface of the earth.When both $$h$$ and d are much smaller than the radius of earth,then which one of the following is true?
  • $$a=h/2$$
  • $$d=3h/2$$
  • $$d=2h$$
  • $$h=d$$
A $$75 kg$$ astronaut is repairing Hubble telescope at a height of $$600 km$$ above the surface of the earth. Find his weight there.
  • $$740 N$$
  • $$700 N$$
  • $$650 N$$
  • $$610 N$$
If the orbital speed of moon is increased by $$41.4\%$$ then moon will
  • leave its orbit and will escape out.
  • fall on earth.
  • attract all bodies on earth towards it.
  • have time period equal to 27 days.
At what height over the earth's pole does the freefall acceleration decreases by 1% ?
  • $$64 km$$
  • $$16 km$$
  • $$8 km$$
  • $$32 km$$
Find the work done to take a particle of mass m from surface of the earth to a height equal to $$2R$$.
  • $$2$$ $$mg R$$
  • $$\displaystyle \frac{mg R}{2}$$
  • $$3 mg R$$
  • $$\displaystyle \frac{2mgR}{3}$$
Let $$V$$ and $$E$$ denote the gravitational potential and gravitational field at a point. It is possible to have
  • $$V = 0$$ and $$E= 0$$
  • $$V = 0$$ and $$E\neq 0$$
  • $$V \neq 0$$ and $$E = 0$$
  • $$V \neq 0$$ and $$E\neq 0$$
The escape velocity for a planet is $$v_e$$. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its centre. Its speed at the centre of the planet will be
  • $$v_a$$
  • $$1.5 v_e$$
  • $$\sqrt{1.5} v_e$$
  • $$2 v_e$$
Let $$V_G$$ and $$E_G$$ denote gravitational potential and field respectively, the it is possible to have
  • $$V_G = 0, E_G = 0$$
  • $$V_G \neq 0, E_g = 0$$
  • $$V_G = 0, E_g \neq 0$$
  • $$V_G \neq 0, E_G \neq 0$$
Use the assumptions of the previous question. An object weighed by a spring balance at the equator gives the same reading as a reading taken at a depth d below the earth's surface at a pole $$(d << R)$$. The value of $$d$$ is
  • $$\displaystyle \dfrac{\omega^2 R^2}{ge}$$
  • $$\displaystyle \dfrac{\omega^2 R^2}{2g}$$
  • $$\displaystyle \dfrac{2\omega^2 R^2}{g}$$
  • $$\displaystyle \dfrac{\sqrt{Rg}}{\omega}$$
Find the height at which the weight will be same as at the same depth from the surface of the earth.
  • $$\displaystyle \frac{R}{2}$$
  • $$\sqrt{5} R - R$$
  • $$\displaystyle \frac{\sqrt{5} R - R}{2}$$
  • $$\displaystyle \frac{\sqrt{3}R - R}{2}$$
A small mass $$m$$ is moved slowly from the surface of the earth to a height $$h$$ above the surface. The work done (by an external agent) in doing this is
  • $$mgh$$, for all values of $$h$$
  • $$mgh$$, for $$h < < R$$
  • $$\dfrac{1}{2} $$ mgR, for h $$=$$ R
  • $$- \dfrac{1}{2} $$ mgR, for h $$=$$ R
Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun
  • is zero in any small part of the orbit.
  • is zero in some parts of the orbit.
  • is zero in one complete revolution.
  • is zero in no part of the motion.
A spaceship is released in a circular orbit near the Earth's surface. How much additional velocity will have to be given to the spaceship in order to escape out of this orbit?
  • $$3.28 \quad m/s$$
  • $$3.28 \times 10^3 m/s$$
  • $$3.28 \times 10^7 m/s$$
  • $$3.28 \times 10^{-3} m/s$$
The gravitational potential difference between the surface of a planet and a point $$20 m$$ above the surface is $$2 Joule/Kg$$. If the gravitational field is uniform then the work done in carrying a $$5 Kg$$ body to a height of $$4 m$$ above the surface is
  • $$2 Joule$$
  • $$20 Joule$$
  • $$40 Joule$$
  • $$10 Joule$$
The magnitude of the potential energy per unit mass of an object at the surface of the earth is given $$U$$. Then, the escape velocity for the object is given by
  • $$v_e = 2U$$
  • $$v_e = \sqrt{U}$$
  • $$v_e = \sqrt{2U}$$
  • $$v_e = (2U)^2$$
The value of G for two bodies in vacuum is $$6.67 \times 10^{-11} N-m^2/Kg^2$$. Its value in a dense medium of density $$10^{10} gm/cm^3$$ will be:
  • $$6.67 \times 10^{-11} N-m^2 /Kg$$
  • $$6.67 \times 10^{-31} N-m^2 /Kg$$
  • $$6.67 \times 10^{-21} N-m^2 /Kg$$
  • $$6.67 \times 10^{-10} N-m^2 /Kg$$
The potential energy of a rocket of mass $$100\ kg$$ at height $$10^7\ m$$ from earth surface is $$4 \times 10^9\ Joule$$. The weight of the rocket at height $$10^9$$ will be
  • $$4 \times 10^{-2} N$$
  • $$4 \times 10^{-3} N$$
  • $$8 \times 10^{-2} N$$
  • $$8 \times 10^{-3} N$$
A tunnel is dug along a diameter of earth. The force on a particle of mass $$m$$ and distance $$x$$ from the centre in this tunnel will be :
  • $$\displaystyle \frac{GM_e m}{R^3 x}$$
  • $$\displaystyle \frac{GM_e mR^3}{x}$$
  • $$\displaystyle \frac{GM_e mx}{R^2}$$
  • $$\displaystyle \frac{GM_e mx}{R^3}$$
At a height $$h$$ above the surface of earth, the change in value of $$g$$ is same as that at a depth $$x$$ below the surface on the earth. Both $$x$$ and $$h$$ are very small in comparison to the radius of the earth. Then,
  • $$x = h$$
  • $$x = 2h$$
  • $$2x = h$$
  • $$x= h^2$$
The value of acceleration due to gravity at height $$h$$ from earth surface will become half its value on the surface if (R $$=$$ radius of earth)
  • $$h = R$$
  • $$h = 2R$$
  • $$h = (\sqrt{2} - 1)R$$
  • $$h = (\sqrt{2} + 1)R$$
If the change in the value of $$g$$ at height $$h$$ above earth surface is the same as that at depth $$x (x \quad or\quad h < R_e),$$ then
  • $$x = h^2$$
  • $$x = h$$
  • $$x = \dfrac{h}{2}$$
  • $$x = 2h$$
At some planet, $$g = 1.96\ ms^{-2}$$. If it is safe to jump from a height of  $$2\ m$$ on earth, then the corresponding safe height on that planet is
  • $$2\ m$$
  • $$5\ m$$
  • $$10\ m$$
  • $$20\ m$$
If $${ W }_{ 1 }$$, $${ W }_{ 2 }$$ and $${ W }_{ 3 }$$ represent the work done in moving a particle from $$A$$ to $$B$$ along three different paths $$1$$, $$2$$ and $$3$$, respectively, (as shown in the figure) in the gravitational field of a point mass $$m$$, find the correct relation between $${ W }_{ 1 }$$, $${ W }_{ 2 }$$ and $${ W }_{ 3 }$$
158161.jpg
  • $${ W }_{ 1 }>{ W }_{ 2 }>{ W }_{ 3 }$$
  • $${ W }_{ 1 }={ W }_{ 2 }={ W }_{ 3 }$$
  • $${ W }_{ 1 }<{ W }_{ 2 }<{ W }_{ 3 }$$
  • $${ W }_{ 2 }>{ W }_{ 1 }>{ W }_{ 3 }$$
If $$g$$ is same at a height $$h$$ and at a depth $$d$$, then
  • $${ R }={ 2d } $$
  • $${ d }={ 2h } $$
  • $${ h }={ d } $$
  • none
A missile is launched with a velocity less than the escape velocity from earth. The sum of its kinetic energy and potential energy is
  • positive
  • negative
  • zero
  • may be positive or negative depending on the direction of projection
If the escape velocity from the surface of a spherical planet is given by $$2 \displaystyle \sqrt{\frac{GM}{K}}$$, where $$M$$ is the mass of the planet and $$K$$ is a constant, then the radius of the planet is
  • $$\dfrac{K}{2}$$
  • $$K$$
  • $$2K$$
  • $$4K$$
The distances from the centre of the earth, where the weight of a body is zero and one-fourth that of the weight of the body on the surface of the earth are (assume $$R$$ is the radius of the earth)
  • $$0$$, $$\displaystyle \frac { R }{ 4 } $$
  • $$0$$, $$\displaystyle \frac { 3R }{ 4 } $$
  • $$\displaystyle \frac { R }{ 4 } $$, $$0$$
  • $$\displaystyle \frac { 3R }{ 4 } $$, $$0$$
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