DPP No: 27

Maximum Time TARGET

50 Min JEE-MAINS
SYLLABUS : GRAVITATION

1. Four similar particles of mass m are orbiting in a circle of radius r in the same direction and
same speed because of their mutual gravitational attractive force as shown in the figure.
Speed of a particle is given by

1
 Gm  1  2 2  2
(A)  
r 

4 
(B) 3
Gm
r
(C)
Gm
r

1 2 2  (D) zero
 

2. Three particles P, Q and R are placed as per given figure. Masses of P, Q and R are 3 m,

3 m and m respectively. The gravitational force on a fourth particle ‘S’ of mass m is equal to

3 GM2
(A) in ST direction only
2d2

3 Gm 2 3 Gm 2
(B) 2 in SQ direction and in SU direction
2d 2d2

3 Gm 2
(C) in SQ direction only
2d2

3 Gm 2 3 Gm 2
(D) in SQ direction and in ST direction
2d2 2d2

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3. A stone drop from height 'h' reaches to Earth surface in1 sec. If the same stone taken to Moon
and drop freely then it will reaches from the surface of the Moon in the time (The 'g' of Moon is
1/6 times of Earth):–

(A) second (B) 9 second (C) second (D) 6 second

4. Two bodies of masses m and M are placed at distance d apart. The gravitational potential (V) at
the position where the gravitational field due to them is zero V is :–

(A) (B) (C) (D)

5. Let gravitation field in a space be given as E = – (k/r). If the reference point is at distance
di where potential is Vi then relation for potential is :

1 r
(A) V = k n V + 0 (B) V = k n d + Vi
i i

r r V
(C) V = n d + kVi (D) V = n d + i
i i k

6. A very large number of particles of same mass m are kept at horizontal distances of 1m,
2m, 4m, 8m and so on from (0,0) point. The total gravitational potential at this point (0, 0)
is:

(A) – 8G m (B) – 3G m (C) – 4G m (D) – 2G m

7. Figure show a hemispherical shell having uniform mass density. The direction of gravita-
tional field intensity at point P will be along:

(A) a (B) b (C) c (D) d

8. A body starts from rest at a point, distance R0 from the centre of the earth of mass M,
radius R. The velocity acquired by the body when it reaches the surface of the earth will be

1 1  1 1  1 1  1 1 
(A) GM  R  R  (B) 2 GM  R  R  (C) 2 GM   
 (D) 2GM  R  R 
 0   0   R R0   0 

9. Escape velocity of a body from the surface of Earth is 11.2 km/sec. from the Earth surface. If
the mass of Earth becomes double of its present mass and radius becomes half of its present
radius, then escape velocity will become

(A) 5.6 km/sec (B) 11.2 km/sec (C) 22.4 km/sec (D) 44.8km/sec

10. A body of mass m is situated at distance 4Re above the Earth's surface, where Re is the radius
of Earth how much minimum energy be given to the body so that it may escape :–

(A) mgRe (B) 2mgRe (C) (D)

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11. Periodic-time of satellite revolving around the earth is - ( is density of earth)

1 1
(A) Proportional to (B) Proportional to  (C) Proportional  (D) does not depend on .


12. An orbiting satellite will escape if :

(A) its speed is increased by ( 2  1)100 %

(B) its speed in the orbit is made 1.5 times of its initial value

(C) it stops moving in the orbit

(D) None of these

13. In case of an orbiting satellite if the radius of orbit is decreased :

(A) its Kinetic Energy decreases (B) its Potential Energy decreases

(C) its speed decreases (D) None of these

14. If acceleration due to gravity on the surface of earth is 10 ms–2 and let acceleration due to
gravitational acceleration at surface of another planet of our solar system be 5 ms–2. An
astronaut weighing 50 kg on earth goes to this planet in a spaceship with a constant velocity.
The weight of the astronaut with time of flight is roughly given by

(A) (B) (C) (D)

15. The acceleration due to gravity at a height (1/20)th the radius of the earth above earth’s
surface is 9 m/s2. Find out its approximate value at a point at an equal distance below the
surface of the earth.

12 15
(A) m/s2 = 9.5 m/s2 (B) m/s2 = 5.5 m/s2
2 2

19 17
(C) m/s2 = 9.5 m/s2 (D) m/s2 = 7.5 m/s2
2 2

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16. A small ball of mass 'm' is released at a height 'R' above the Earth surface, as shown in the
figure. If the maximum depth of the ball to which it goes is R/2 inside the Earth through a
narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring
constant K and natural length R, the value of K is (R is radius of Earth and M mass of Earth)

(A) (B) (C) (D)

17. A uniform ring of mass M is lying at a distance 3 R from the

centre of a uniform sphere of mass m just below the sphere as
shown in the figure where R is the radius of the ring as well as
that of the sphere. Then gravitational force exerted by the ring

on the sphere is :

GMm GMm
(A) 2 (B)
8R 3R 2

GMm GMm
(C) 3 (D) 3
R 2
8R 2

18. A projectile is fired from the surface of earth of radius R with a speed k  e in radially outward
direction (where  e is the escape velocity and k < 1). Neglecting air resistance, the maximum
height from centre of earth is

R R
(A) (B) k 2 R (C) (D) kR
k2  1 1 k2

19. Four particles, each of mass M and equidistant from each other, move along a circle of radius
R under the action of their mutual gravitational attration. the speed of each particle is :

(A)
GM
R
(B) 2 2
GM
R
(C)
GM
R

1 2 2  (D)
1 GM
2 R

1 2 2 
20. From a solid sphere of mass M and radius R, a spherical portion
of radius R/2 is removed , as shown in the figure. Taking
gravitational potential V = 0 at r = , the potential at the centre of

the cavity thus formed is :(G = gravitational constant)

GM GM 2GM 2GM

(A) (B) (C) (D)
2R R 3R R

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21. A satellite is moving with a constant speed v in circular orbit around the earth. An object of
mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the
earth. At the time of ejection, the kinetic energy of the object is :

3 1
(A) mv 2 (B) mv 2 (C) 2mv2 (D) mv2
2 2

22. Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R,
TA
and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, T ,
B

is :

1 1
(A) 1 (B) (C) 2 (D)
2 2

23. Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A.
v n
If the escape velocities from the Planets A and B are vA and vB, respectively, then v  4 . The
A

value of n is

(A) 1 (B) 4 (C) 3 (D) 2

24. On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution
Ax
is given by 3 in the x-direction. The magnitude of gravitational potential on the x-axis at
(x 2  a2 ) 2

a distance x, taking its value to be zero at infinity, is

A A
3 1
(A) A(x 2  a2 ) 2 (B) 3 (C) 1 (D) A(x 2  a2 ) 2
(x  a )
2 2 2
(x  a2 )
2 2

25. Two stars of masses m and 2m at a distance d rotate about their common centre of mass in
free space. The period of revolution is :

1 d3 d3 1 3Gm 3Gm
(A) (B) 2 (C) (D) 2
2 3Gm 3Gm 2 d3 d3

ANSWER KEY
1. (A) 2. (C) 3. (A) 4. (D) 5. (B)

6. (D) 7. (C) 8. (C) 9. (C) 10. (C)

11. (B) 12. (A) 13. (B) 14. (A) 15. (C)

16. (D) 17. (D) 18. (C) 19. (D) 20. (B)

21. (D) 22. (A) 23. (B) 24. (C) 25. (B)

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