LPP - Gravitation FIITJEE

Single Correct
1. If g is the acceleration due to gravity on the earth’s surface, the change in the potential energy of an object of
mass m raised from the surface of the earth to a height equal to the radius R of the earth is
mgR
(A) (B) 2mgR (C) mgR (D)  mgR
2
2. 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 the earth. Its weight on the surface of mars
would be
(A) 6 N (B) 20 N (C) 40 N (D) 80 N

3. A solid sphere of radius R/2 is cut out of a solid sphere of radius R

such that the spherical cavity so formed touches the surface on one
side and the centre of the sphere on the other side, as shown. The m O R/2
initial mass of the solid sphere was M. If a particle of mass m is R O
placed at a distance 2.5R from the centre of the cavity, then what is
the gravitational attraction on the mass m?
2.5R
GMm GMm GMm 23 GMm
(A) (B) (C) (D)
R2 2R2 8R 2 100 R 2
4. If W 1, W 2 and W 3 represent the work done in moving a particle from A B
and 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 m
correct relation between W 1, W2 and W 3. 1 2
(A) W1  W2  W3 (B) W1  W2  W3
(C) W1  W2  W3 (D) W2  W1  W3
3
A

5. 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)
R 3R R 3R
(A) 0, (B) 0, (C) ,0 (D) ,0
4 4 4 4
6. If a man at the equator would weigh (3/5)th of his weight, the angular speed of the earth is
2g g R 2R
(A) (B) (C) (D)
5R R g 5g

7. The masses and radii of the earth and the Moon are M1, R1 and M2, R2, respectively. Their centres are at
distance d apart. The minimum speed with which a particle of mass m should be projected from a point
midway the two centres so as to escape to infinity is
2G  M 1  M 2  4G  M 1  M 2  4GM1 M 2 G  M1  M 2 
(A) (B) (C) (D)
d d d d

8. A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side. The velocity of the
ball when it reaches the centre of the earth is[Given: gravitational potential at the centre of earth =
3 /  2GM / R  ]
(A) R (B) gR (C) 2.5gR (D) 7.1gR

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9. Four particles, each of mass M, move along a circle of radius R under the action of their mutual gravitational
attraction. The speed of each particle is
GM GM GM GM  2 2 1
(A)
R
(B) 2 2
R
(C)
R

2 2 1  (D)
R
 
 4 

10. The mass of the earth is 81 times the mass of the Moon and the distance between the earth and the Moon is
60 times the radius of the earth. If R is the radius of the earth, then the distance between the Moon and the
point on the line joining the Moon and the earth where the gravitational force becomes zero is
(A) 30R (B) 15R (C) 6R (D) 5R

Multi Correct
11. A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth’s centre. The wall of
the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing
force by the particle on the wall, and the acceleration of the particle vary with x(distance of the particle from the
centre) according to

(A) Pressing (B) Pressing

force force

x x
x = R/2 x = R x = R/2 x = R
(C) Acceleration (D) Acceleration

x x
x = R/2 x = R x = R/2 x = R

12. A double star consists of two stars having masses M and 2M. The distance between their centres is equal to r.
They revolve under their mutual gravitational interaction. Then, which of the following statements are not
correct?
(A) Heavier star revolves in orbit of radius 2r/3
(B) Both the stars revolve with the same speed, period of which is equal to 2 / r  3
 2GM 2
/ 3
(C) Kinetic energy of the heavier star is twice that of the other star
(D) None of the above

13. A double star is a system of two stars of masses m and 2m, rotating about their centre of mass only under their
mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation
about their centre of mass will be proportional to
3 1

1/2
(A) r 2 (B) r (C) m (D) m 2

14. 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
(A) mgh, for all values of h (B) mgh , for h  R
1 1
(C) mgR, for h  R (D)  mgR, for h  R
2 2

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15. Which of the following are correct?
(A) Out of electrostatic, electromagnetic, nuclear and gravitational interactions, the gravitational interaction is
the weakest.
(B) If the earth were to rotate faster than its present speed, the weight of an object would decrease at the
equator but remain unchanged at the poles.
(C) The mass of the earth in terms of g, R and G is gR / G .  2

(D) If the earth stops rotating in its orbit around the Sun there will be no variation in the weight of a body on the
surface of earth.

Comprehension – 1

A solid sphere of uniform density and mass M has radius 4m. Its centre is at the Z
origin of the coordinate system. Two spheres of radii 1 m are taken out so that
their centres are at P(0, -2,0) and Q(0,2,0), respectively. This leaves two
spherical cavities.

Y
O Q
P

X
16. What is the gravitational field at the origin of the coordinates axes?
31GM Gm
(A) (B) (C) 31GM (D) Zero
1024 1024
17. What is the gravitational field at the centre of the cavities?
31GM Gm
(A) (B) (C) 31GM (D) GM
1024 1024
2 2
18. What is the gravitational potential at any point on the circle x  z  6 ?
GM GM
(A)  (B) 
6 64 10
GM  1 1  GM  1 1 
(C)   (D)  
2  3 32 10 
 2  3 32 10 


Comprehension – 2

A uniform metal sphere of radius a and mass M is surrounded by a thin uniform

spherical shell of equal mass and radius 4a. The centre of the shell falls on the a
surface of the inner sphere. O
4a
P1
a
P2 a

19. Find the gravitational field intensity at point P1.

GM GM GM GM
(A) (B) (C) (D)
16a 2 8a 2 2a 2 4a 2
20. Find the gravitational field intensity at point P2.
21GM 61GM 61GM 61GM
(A) (B) (C) (D)
900a 2 450a 2 900a 2 1800a 2

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 Integer Type

2
21. A particle of mass m is subjected to an attractive central force of magnitude k / r , k being a constant. If at the
instant when the particle is at an extreme position in its closed orbit, at a distance a from the centre of force, its
speed is (k/2ma), if the distance of other extreme position is b. Find a/b.

22. The earth (mass = 10 kg ) revolves round the sun with an angular velocity 2  107 rad s 1 in a circular orbit
24

8 21
of radius 1.5  10 km. Find the force exerted by the Sun on the earth (in  10 N )

23. The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the
surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R and the radius of
the planet is R’. Then what is the value of R/R’?

24. Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth in size.
If the acceleration due to gravity on the surface of the earth is g and that on the new planet is g’, then what is
the value of g '/ g ?

25. A solid sphere of uniform density and radius R applies a gravitational

force of attraction equal to F1 on a particle placed at a distance 2R from
the centre of the sphere. A spherical cavity of radius R/2 is now made in
the sphere as shown in the figure. The sphere with the cavity now applies
K R
a gravitational force F2 on the same particle. The ratio F1/F2 is . Find
7
the value of K.

FIITJEE Ltd., B – 4, Sec – 16, Noida (U.P), 201301, Ph : 0120 – 4080700. Ph: 9871091470.www.fiitjeenoida.com
FIITJEE Towers, C – 56 A/26 Institutional Area, Sec – 62, Noida (U.P), 201307, 0120-4754800/804/805/811.
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 ANSWER KEY
LPP – 10 – Gravitation
1. A
2. D
3. D
4. B
5. A
6. A
7. B
8. B
9. D
10. C
11. B, C
12. A, C
13. A, D
14. B, C
15. A, B, C, D
16. D
17. A
18. C
19. A
20. C
21. 3
22. 6
23. 2
24. 3
25. 9

FIITJEE Ltd., B – 4, Sec – 16, Noida (U.P), 201301, Ph : 0120 – 4080700. Ph: 9871091470.www.fiitjeenoida.com
FIITJEE Towers, C – 56 A/26 Institutional Area, Sec – 62, Noida (U.P), 201307, 0120-4754800/804/805/811.
FIITJEE Greater Noida, 1st Floor, Wegman's Business Park, Plot no. 3, Sector-KP- III, Greater Noida (U.P), 201308, Ph : 9599773876.