GRAVITATION

1. The figure shows elliptical orbit of a planet m about the sun S. The shaded
area SCD is twice the shaded area SAB. If t1 is time for the planet to move from
C to D and t2 is the time to move from A to B then

(a) t1  4t 2 (b) t1  2t 2
(c)t1  t 2 (d ) t1  t 2

2. The radii of circular orbits of two satellites A and B of the earth, are 4R and
R, respectively. If the speed of satellite A is 3V , then the speed of satellite B
will be

3V
(a) (b) 6V
4
3V
(c)12V (d )
2

3. A particle of mass M is situated at the center of a spherical shell of same

a
mass and radius a. The gravitational potential at a point situated at distance
2
from the centre, will be

3GM 2GM
(a)  (b) 
a a
GM 4GM
(c )  (d ) 
a a

4. A man of 50 kg mass is standing in a gravity free space at a height of 10 m

above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2
m/s. When the stone reaches he floor. The distance of the man above the floor
will be
(a) 9.9 m (b)10.1 m
(c)10 m (d ) 20 m

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5. The additional kinetic energy to be provided to a satellite of mass m
revolving around a planet of mass M, to transfer it from a circular orbit of
radius R1 to another of radius R2 ( R2  R1 )is

 1 1   1 1 
(a) GmM  2  2  (b) GmM   
 R1 R2   R1 R 2 
 1 1  1  1 1 
(c) 2GmM    (d ) GmM   
 R1 R2  2  R1 R2 

6. The dependence of acceleration due to gravity g on the distance r from the

centre of the earth, assumed to be a sphere R of uniform density is as shown in
figures below

The correct figure is

(a) 4 (b)1
(c ) 2 (d ) 2

7. (1) Centre of gravity (C.G) of a body is the point at which the weight of the
body acts.

(2) Centre of mass coincides with the centre of gravity if the earth is assumed
to have infinitely large radius .

(3) To evaluate the gravitational field intensity due to any body at an external
point, the entire mass of the body can be considered to be concentrated at its
C.G.

(4) The radius of gyration of any body rotating about an axis is the length of the
perpendicular dropped from the C.G. of the body to the axis.

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Which one of the following pairs of statements is correct ?
(a) (4) and (1) (b) (1) and (2)
(c) (2) and (3) (d ) (3) and (4)

8. A planet moving along an elliptical orbit is closest to the sun at a distance r1

and farthest away at a distance of r2. If v1 and v2 are the linear velocities at
v1
these points respectively, then the ratio is
v2

(a) (r1 / r2 ) 2 (b) r2 / r1

2
(c) (r2 / r1 ) (d ) r1 / r2

9. 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 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

2GM 2GM
(a) (b)
R2 R
2 gM
(c ) (d ) 2 gR 2
R2

10. A particle of mass M is situated at the centre of a spherical shell of same

,mass and radius a. The magnitude of the gravitational potential at a point at
a/2 distance from the centre, will

GM 2GM
(a) (b)
a a
3GM 4GM
(c ) (d ) 
a a
th
1
11. The height at which the weight of a body becomes its weight on the
16
surface of earth (radius R), is
(a) 5R (b) 15R
(c ) 3 R (d ) 4 R

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12. A spherical planet has a mass MP and diameter DP. A particle of mass m
falling near the surface of this planet will experience due to gravity, equal to

4GM P GM P m
(a) (b)
D P2 D P2
GM p 4GM p m
(c ) 2
(d )
D P D P2

13. A geostationary satellite is orbiting the earth at a height of 5R above that

surface of the earth, R being the radius of the earth . The time period of
another satellite in hours at a height of 2R from the surface of the earth is
(a) 5 (b) 10
6
(c ) 6 2 (d )
2

14. If v e is escape velocity and v a is orbital velocity of a satellite for orbit close to
the earth’s surface, then these are related by

( a ) v o  2v e (b) v o  ve
( c ) v e  2v o ( d ) v e  2v o

15. Which one of the following plots the variation of gravitational field on a
particle with distance r due to a thin spherical shell of radius R?( r is measured
from the centre of the spherical shell)

16. Infinite number of bodies, each of mass 2 kg are situated on x-acis at

distance 1 m, 2m, 4m, 8m, ......, respectively, from the origin . The resulting
gravitational potential due to this system at the origin will be

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 4
(a)  G (b)  4G
3
8
(c )  G (d )  G
3

17. A body of mass ‘m’ is taken from the earth’s surface to the height equal to
twice the radius (R) of the earth. The change in potential energy of body will be

1
(a) 3 mgR (b) mgR
3
2
(c) mg 2 R (d ) G mgR
3

18. A black hole is an object whose gravitational field is so strong that even
light cannot escape from it. To what approximate radius would earth (mass =
5.98 10 24 Kg ) have to be compressed to be a black hole ?

(a)10 9 m (b) 10 6 m
(c) 10 2 m (d ) 100 m

19. Dependence of intensity of gravitational field (E) of earth with distance (r)
from centre of earth is correctly represented by

20. Kepler’s third law states that square of period of revolution (T) of a planet
around the sun, is proportional to third powder of average distance r between
sun and planet i.e T 2  Kr 3 here K is constant.

If the masses of sun and planet are M and m respectively then as per Newton’s
law of gravitation force of attraction between them is

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 GMm
F , here G is gravitational constant.
r2

The relation between G and K is described as

1
(a) K  G (b) K 
G
(c) GK  4 2 (d ) GMK  4 2

21. Two spherical bodies of mass M and 5M and radii R and 2R are released in
free space with initial separation between their centres equal to 12R. If they
attract each other due to gravitational force only, then the distance covered by
the smaller body before collision is
(a) 7.5 R (b) 1.5 R
(c) 2.5 R (d ) 4.5 R

22. A remote-sensing satellite of earth revolves in a circular orbit at a height of

0.25  10 6 m above the surface of earth. If earth’s radius is
6.38  10 6 m and g  9.8 ms 2 . then the orbital speed of the satellite is

(a) 9.13 km s 1 (b) 6.67 km s 1

(c) 7.76 km s 1 (d ) 8.56 km s 1

23. A satellite S is moving in an elliptical orbit around the earth. The mass
satellite is very small compared to the mass of the earth. Then,

(a) the linear momentum of S remains constant in magnitude.

(b) the acceleration of S is always directed towards the centre of the earth.

(c) the angular momentum of S about the centre of the earth changes in
direction, but its magnitude remains constant.

(d) the total mechanical energy of S varies periodically with time.

24. At what height from the surface of earth the gravitation potential and the
value of g are  5.4  10 7 J kg-2 and 6.0 ms-2 respectively ? Take the radius of
earth as 6400 km.
(a) 1400 km (b) 2000 km
(c) 2600 km (d )1600 km

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25. 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 earth is

(a) 1 : 4 (b) 1 : 2
(c ) 1 : 2 (d )1 : 2 2

26. Starting from the centre of the earth having radius R, the variation of
g(acceleration due to gravity) is show by

27. A satellite of mass m is orbiting the earth (of radius R ) at a height h from its
surface. The total energy of the satellite in term of g0, the value of acceleration
due to gravity at the earth’s surface, is

mg 0 R 2 mg 0 R 2
(a) (b) 
2( R  h ) 2( R  h )
2mg 0 R 2 2mg 0 R 2
(c ) (d ) 
Rh Rh

28. The acceleration due to gravity at a height 1 km above the earth is the
same as at a depth d below the surface of earth. Then

3
(a) d  1 km (b) d  km
2
1
(c) d  2 km (d ) d  km
2

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29. Two astronauts are floating in gravitational free space after having lost
contact with their spaceship. The two will

(a) move towards each other.

(b) move away from other.

(c) will become stationary

(d) keep floating at the same distance between them.

SOLUTIONS
1. (b) 11. (c) 21. (a)
2. (b) 12. (a) 22. (c)
3. (a) 13. (c) 23. (b)
4. (b) 14. (d) 24. (c)

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5. (d) 15. (b) 25. (d)
6. (a) 16. (b) 26. (b)
7. (a) 17. (d) 27. (b)
8. (b) 18. (c) 28. (c)
9. (b) 19. (a) 29. (a)
10. (c) 20. (d)

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