gravitation revision

02 Oct 2024

1) If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a
height equal to the radius of the earth R, is
1) 12 mgR 2) 2mgR 3) mgR 4) 14 mgR

2) The gravitational force of the earth on the moon is F. Then the gravitational force of the moon on the earth is
1)F 2)F/2 3)F/4 4)zero

3) If a graph is plotted between T 2 and r3 for a planet, then its slope will be (where Ms is the mass of the sun)
2
4π
1) GM 2) GM
4π
s
3)4πGMs 4)GMs
s

4) The radius of the Earth is about 6400 km and that of Mars is about 3200 km. The mass of the Earth is about 10 times the mass of Mars. An object
weighs 200 N on the surface of Earth. Its weight on the surface of Mars would be
1)6 N 2)20 N 3)40 N 4)80 N

5) The intensity of the gravitational field at a point situated at a distance of 8000 km from the centre of the earth is 6 N/kg. The gravitational potential at
that point is (in Joule/kg)
1)8 × 106 2)2.4 × 103 3)4.8 × 107 4)6.4 × 1014

6) Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute from the centre of earth with a speed v such
that it will just reach the earth's surface then v is equal to :

3)√
gR
1)√gR 2)√2gR 4)None of these
2

7) Two spheres each of mass M and radius R are separated by a distance of r. The gravitational potential at the midpoint of the line joining the centres of
the sphere is
1)− GM
r
2)− 2GM
r
3)− GM
2r
4)Zero

8) The escape velocity from the centre of a uniform ring of mass M and radius R is:

1)√ 2GM
R
2)√ GM
R
3)√ GM
2R
4)2√ GM
R

9) The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. It's the escape velocity from the earth is v, then the
escape velocity from the planet is :
1)√3 v 2)√2 v 3)√5 v 4)√12 v

10) The orbital velocity of a satellite at a height R above the surface of Earth is v. The escape velocity from the location is
1)√2v 2)2v 3)4v 4)None of these

11) The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of
A. What is the height of jump by the same person on the planet B?
1) 23 m 2) 29 m 3)18 m 4)6 m

12) The dimensions of the gravitational constant G are

1)M −1 L3 T −2 2)M 3 L1 T −2 3)M 1 L3 T −2 4)M −3 L3 T 3

13) Time period T of a satellite revolving in an orbit of radius r is such that

1)T α r 2)T α r2 3)T α √r 4)T 2 α r3

14) Two spheres of masses m and M are suited in air and gravitational force between them is 'F'. The space around the mass is now filled with a liquid of
 specific gravity 3. The gravitational force now will be
1) F9 2)3F 3)F 4) F3

15) If the radius of earth decreases by 10%, the mass remaining unchanged, then the acceleration due to gravity
1)decreases by 19% 2)increases by 19% 3)decreases by more than 19% 4)increases by more than 19%

16) The gravitational force between two bodies is decreased by 36 % when the distance between them is increased by 3m. The initial distance between
them is
1)6 m 2)9 m 3)12 m 4)15 m

17) A body released at infinite distance from the earth starts falling towards it. If R is the radius of the earth, and g the acceleration due to gravity on the
surface of the earth, then the velocity acquired by it before reaching the surface is
1)√2gR 2)√gR 3)√5gR 4)gR

18) The escape velocity of a body of 1 kg mass on a planet is 100 m/s. Gravitational Potential energy of the body at the planet is
1)– 5000 J 2)– 1000 J 3)– 2400 J 4)5000 J

19) If ve is escape velocity and v0 , is orbital velocity of the satellite for orbit close to the Earth's surface, then these are related by
1)v0 = √2ve 2)v0 = ve 3)ve = √2v0 4)ve = √2v0

20) A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The
maximum height attained by the body is
1)R/3 2)R/2 3)R/4 4)R/5

21) ve and vp denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then
1)ve = vp 2)ve = vp /2 3)ve = 2vp 4)ve = vp /4

22) The escape velocity of an object from the earth depends upon the mass of the earth (M), its mean density, its radius (R) and the gravitational constant
(G). Thus the formula for escape velocity is
1)v = R√ 8π
3 Gρ 2)v = M √ 8π
3 GR
3)v = √2GMR 4)v = √ 2GM
R2

23) The escape velocity from earth is ves . A body is projected with velocity 2ves . With what constant velocity will it move in the inter planetary space
1)ves 2)3ves 3)√3ves 4)√5ves

24) A body falls freely towards the earth from a height 2R above the surface of the earth, where initially it was at rest. If R is the radius of the earth, then
its velocity on reaching the surface of the earth is
1)√ 43 gR 2)√ 23 gR 3) 43 √gR 4)2 √gR

25) The ratio of the K.E required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves
in a circular orbit just above Earth's atmosphere is
1)One 2)Two 3)Half 4)Infinity

26) Let the minimum external work done in shifting a particle from centre of the earth to earth's surface be W1 and that from the surface of the earth to
W1
infinity be W2 . Then W2
is equal to

1)1:1 2)1:2 3)2:1 4)1:3

27) Find the escape velocity of particle of mass m which is situated at a radial distance r (from centre of earth) above the earth's surface. M is the mass
earth

1)√ GM
2r 2)√ GM
r
3)√ 2GM
r
4)None of these

28) The Earth is assumed to be a sphere of radius R. A plat form is arranged at a height R from the surface of the earth. The escape velocity of a body
from this platform fve, where ve is its escape velocity from the surface of the earth. The value of f is
1
1)√2 2) √2 3) 13 4) 12
29) A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and
R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not
return back to earth is

1)√ 2GM
R
2)√ 2GM
R2
3)√2gR2 4)√ 4GM
R2

30) The kinetic energy needed to project a body of mass m from the earth's surface to infinity is
1) 14 mgR 2) 12 mgR 3)mgR 4)2 mgR

31) A particle is kept at rest at a distance R (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does
not return is

1)√ GM
4R 2)√ GM
2R 3)√ GM
R
4)√ 2GM
R

32) The ratio of escape velocity at earth (ve ) to the escape velocity at a planet (vp ) whose radius and mean density are twice as that of the earth is
1)1 : √2 2)1 :2 3)1 : 2√2 4)1 : 4

33) With what velocity should a particle be projected so that its height becomes equal to the radius of earth?
1/2 1/2 1/2 1/2
1)( GM
R
) 2)( GM
2R ) 3)( 2GM
R
) 4)( 4GM
R
)

34) A satellite revolves around the earth in a circular orbit with a speed equal to half the escape velocity of an object from the surface of earth. If R is the
radius of earth, the height of the orbit above the surface of earth is:
1)R 2)3R/2 3)2R 4)R/2

35) A satellite revolves round the Earth in a circular orbit with a speed that is half of the escape velocity from Earth. If the satellite is suddenly stopped in
the orbit, then it falls and hits the surface of Earth with a speed of (g is acceleration due to gravity near the surface of Earth and R is the radius of
Earth)

1)√ 2)√ 3)√

4gR 2gR gR
4)√gR
3 3 2

36) The gravitational potential energy of a body of mass 2 kg resting on the surface of a hypothetical planet X is -64 MJ. The escape velocity of a body
from the surface of the planet is:
1)4√2 km/s 2)8 km/s 3)8√2 km/s 4)4 km/s

37) The mass of earth is 81 times that of the moon and radius of the earth is 4 times that of the moon. If ‘v’ is escape velocity for an object from the earth,
the escape velocity for an object from the moon is
1)v/18 2)2v/9 3)9v/2 4)18 v

38) A particle is projected from the mid-point of the line joining two fixed particles each of mass m. If the distance of separation between the fixed
particles is l, the minimum velocity of projection of the particle so as to escape is equal to
1)√ Gm
l
2)√ Gm
2l
3)√ 2Gm
l
4)2√ 2Gm
l

39) A planet of radius R has an acceleration due to gravity of gs on its surface. A deep smooth tunnel is dug on this planet, radially inward, to reach
a point P located at a distance of R/2 from the centre of the planet. Assume that the planet has uniform density. The kinetic energy required to be
given to a small body of mass m, projected radially outward from P, so that it gains a maximum altitude equal to thrice the radius of the planet
from its surface, is equal to:
1) 63
16
mgs R 2) 38 mgs R 3) 98 mgs R 4) 21
16
mgs R

40) An artificial satellite is moving in a circular orbit around the earth. The height of the satellite above the surface of the earth is R. Suppose the satellite
is stopped suddenly in its orbit and allowed to fall freely, on reaching the earth its speed will be:
1)√gR 2)2√gR 3)3√gR 4)5√gR

41) If R=radius of the earth and g=acceleration due to gravity on the surface of the earth, the acceleration due to gravity at a distance r (r>R) from the
centre of the earth is proportional to
1)r 2)r2 3)r−2 4)r−1
42) Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If Re is
the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection?
1)0.2 Re 2)2 Re 3)0.5Re 4)5 Re

43) Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the
centre of earth to the points far away from the surface of earth

1) 2) 3) 4)None of
these

44) The change in potential energy when a body of mass m is raised to a height nR from the earth's surface is (R = radius of earth)
n 2 n
1)mgR n−1 2)nmgR 3)mgR n2n+1 4)mgR n+1

45) Mass M is uniformly distributed only on the curved surface of a thin hemispherical shell. A, B and C are three points on the circular base
of the hemisphere, such that A is the centre. Let the gravitational potential at points A, B and C be VA , VB , VC respectively. Then
1)VA > VB > VC 2)VC > VB > VA 3)VB > VA and VB > VC 4)VA = VB = VC

46) The gravitational potential at centre of earth is

1) −2GM
R
2) −3GM
2R
3) 3GM
2R
4) −GM
2R

47) If three particles each of mass m are placed at the three corners of an equilateral triangle of side 𝑙, the work done to increase the side of that triangle 2l
is
2 2 2 2
1) 3Gm
l
2) 3Gm
2l
3) Gm
2l
4) Gm
l

48) A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The velocity of the body when it passes
through the centre of the planet, through its diametrical chute is (assume m coming from ∞)
1)√ 2GM
R
2)√ GM
R
3)√ 35 GM
R
4)√ 25 GM
R

49) A body is falling under gravity. When it loses a gravitational potential energy U , its speed is v. The mass of the body is
1) 2U
v
U
2) 2v 3) 2U2 4) 2vU2
v

50) How much work per kilogram need to be done to shift a 1 kg mass from the surface of the earth to infinity? (Take acceleration do gravity =g and
radius of the earth=R)
1)g/R 2)R/g 3)gR 4)g/R2