442 Gravitation

1. Two identical spheres are placed in contact with each other. The 9. Consider earth to be a homogeneous sphere. Scientist A goes deep
force of gravitation between the spheres will be proportional to ( R = down in a mine and scientist B goes high up in a balloon. The value
radius of each sphere) of g measured by
(a) A goes on decreasing and that by B goes on increasing
(a) R (b) R2 (b) B goes on decreasing and that by A goes on increasing
(c) R 4 (d) None of these (c) Each decreases at the same rate
2. Suppose that the force of earth's gravity suddenly disappears, choose (d) Each decreases at different rates
the correct answer out of the following statements 1
10. The mass of the moon is of the earth but the gravitational pull
(a) The weight of the body will become zero but mass remains the 81
same 1
(b) The mass of the body will become zero but the weight remains is of the earth. It is due to the fact that
6
the same
81
(c) Both the mass and weight will be the same (a) The radius of the moon is of the earth
6
(d) Mass and weight will remain the same
9
3. An earth satellite is moved from one stable circular orbit to a (b) The radius of the earth is of the moon
further stable circular orbit, which one of the following quantities 6
increase (c) Moon is the satellite of the earth
(a) Gravitational force (b) Gravitational P.E. (d) None of the above
(c) Linear orbital speed (d) Centripetal acceleration 11. A weight is suspended from the ceiling of a lift by a spring balance.
When the lift is stationary the spring balance reads W. If the lift
4. Two planets revolve round the sun with frequencies N 1 and N 2 suddenly falls freely under gravity, the reading on the spring balance
revolutions per year. If their average orbital radii be R1 and R 2 will be
(a) W (b) 2 W
respectively, then R1 / R 2 is equal to (c) W/2 (d) 0
(a) ( N 1 / N 2 )3 / 2 (b) ( N 2 / N 1 )3 / 2 12. If a planet consists of a satellite whose mass and radius were both
half that of the earth, the acceleration due to gravity at its surface
(c) ( N 1 / N 2 )2 / 3 (d) ( N 2 / N 1 )2 / 3 would be (g on earth = 9.8 m/sec ) 2

2
5. There is no atmosphere on the moon because (a) 4 . 9 m / sec (b) 8 . 9 m / sec 2
(a) It is closer to the earth (c) 19 . 6 m / sec 2 (d) 29 . 4 m / sec 2
(b) It revolves round the earth
13. At a given place where acceleration due to gravity is ‘g’ m / sec 2 , a
(c) It gets light from the sun
sphere of lead of density ‘d’ kg / m 3 is gently released in a column
(d) The escape velocity of gas molecules is lesser than their root
mean square velocity here of liquid of density ' ' kg / m 3 . If d , the sphere will
6. Two heavenly bodies S 1 and S 2 , not far off from each other are (a) Fall vertically with an acceleration ‘g’ m / sec 2
seen to revolve in orbits (b) Fall vertically with no acceleration
(a) Around their common centre of mass d
(b) Which are arbitrary (c) Fall vertically with an acceleration g
d
(c) With S 1 fixed and S 2 moving round S 1
(d) Fall vertically with an acceleration g
(d) With S 2 fixed and S 1 moving round S 2 d
7. The mass of the moon is about 1.2% of the mass of the earth. 14. g e and g p denote the acceleration due to gravity on the surface of
Compared to the gravitational force the earth exerts on the moon,
the gravitational force the moon exerts on earth the earth and another planet whose mass and radius are twice as
that of earth. Then
(a) Is the same (b) Is smaller
(c) Is greater (d) Varies with its phase (a) gp ge (b) gp ge / 2
8. A clock S is based on oscillation of a spring and a clock P is based
on pendulum motion. Both clocks run at the same rate on earth. On (c) gp 2 ge (d) gp ge / 4
a planet having the same density as earth but twice the radius
(a) S will run faster than P 15. If the value of g at the surface of the earth is 9.8 m / sec 2 , then
(b) P will run faster than S the value of g at a place 480 km above the surface of the earth will
(c) They will both run at the same rate as on the earth be (Radius of the earth is 6400 km)
(d) None of these
 Gravitation 443

(a) 8 . 4 m / sec 2 (b) 9 . 8 m / sec 2 (c) Moon is nearer to the sun

(d) Moon is attracted by other planets
(c) 7 . 2 m / sec 2 (d) 4 .2 m / sec 2 22. The ratio of the radius of a planet ‘A’ to that of planet ‘B’ is ‘r’. The
ratio of acceleration due to gravity on the planets is ‘x’. The ratio of
16. The acceleration due to gravity about the earth's surface would be
the escape velocities from the two planets is
half of its value on the surface of the earth at an altitude of (R =
4000 mile)
r
(a) xr (b)
(a) 1200 mile (b) 2000 mile x
(c) 1600 mile (d) 4000 mile
x
17. A pendulum clock is set to give correct time at the sea level. This (c) rx (d)
r
clock is moved to hill station at an altitude of 2500 m above the sea
level. In order to keep correct time of the hill station, the length of 23. Time period of revolution of a nearest satellite around a planet of
the pendulum radius R is T. Period of revolution around another planet, whose
radius is 3R but having same density is
(a) Has to be reduced
(a) T (b) 3T
(b) Has to be increased
(a) Needs no adjustment (c) 9T (d) 3 3 T
(d) Needs no adjustment but its mass has to be increased 24. The maximum possible velocity of a satellite orbiting round the
earth in a stable orbit is
18. At some point the gravitational potential and also the gravitational
field due to earth is zero. The point is (a) 2 Re g (b) Re g
(a) On earth's surface
Re g
(b) Below earth's surface (c) (d) Infinite
2
(c) At a height Re from earth's surface (Re radius of the
25. A man inside an artificial satellite feels weightlessness because the
earth) force of attraction due to earth is
(d) At infinity (a) Zero at that place
19. A body falls freely under gravity. Its speed is v when it has lost an (b) Is balanced by the force of attraction due to moon
amount U of the gravitational energy. Then its mass is
(c) Equal to the centripetal force
Ug U2 (d) Non-effective due to particular design of the satellite
(a) (b)
v2 g
26. Two identical satellites A and B are circulating round the earth at
2U the height of R and 2R respectively, (where R is radius of the earth).
(c) (d) 2 Ugv 2 The ratio of kinetic energy of A to that of B is
v2
1 2
20. The ratio of the radius of the earth to that of the moon is 10. The (a) (b)
ratio of acceleration due to gravity on the earth and on the moon is 2 3
6. The ratio of the escape velocity from the earth's surface to that 3
from the moon is (c) 2 (d)
2
(a) 10 (b) 6
27. The mean radius of the earth's orbit round the sun is 1 . 5 10 11 .
(c) Nearly 8 (d) 1.66
The mean radius of the orbit of mercury round the sun is
21. Escape velocity from the moon surface is less than that on the earth 6 10 10 m . The mercury will rotate around the sun in
surface, because
(a) A year (b) Nearly 4 years
(a) Moon has no atmosphere while the earth has
(b) Radius of moon is less than that of the earth 1
(c) Nearly year (d) 2.5 years
4

(SET - 8)

2 2. (a) In the absence of gravity weight of the bodies will become zero
4
G R3 6 but mass will not change.
M M 3 R
1. (c) F G F R4
R2 (2 R )2 R2 GMm
3. (b) U . If r increases then U also increases.
r
 444 Gravitation

4. (d) According to Kepler's law T 2 R3 According to problem M p

Me
and R p
Re
2 2
If N is the frequencs then N2 ( R) 3
2
gp Mp Re 1
3/2 2/3 (2) 2 2
N R2 R1 N2 ge Me Rp 2
or 2
N1 R1 R2 N1
gp 2 ge 2 9.8 19 . 6 m /s 2
5. (d)
6. (a) 13. (c) Apparent weight = actual weight – upthrust force

Vdg ' Vdg V g

Gm m m e
7. (a) Force between earth and moon F
r2 d
g' g
This amount of force, both earth and moon will exert on each d
other i.e. they exert same force on each other.
M
14. (b) g . If mass and radius of the planet are twice then g
4 R2
8. (b) g GR . If density is same then g R
3 ge
will be half that of g e i.e. g p
According to problem R p 2Re gp 2 ge 2

1
15. (a) The value of g on the surface of the earth g
l R2
For clock P (based on pendulum motion) T 2
g
1
At height h from the surface of the earth g
Time period decreases on planet so it will run faster because (R h) 2
g p ge
R2 9 . 8 (6400 )2
g g 8 . 4 m /s 2
m (R h)2 (6400 480 )2
For clock S (based on oscillation of spring) T 2
k 2 2 2
g' R 1 R 1 4000
16. (c)
So it does not change. g R h 2 R h 2 4000 h
9. (d) For scientist A which goes down in a mine
By solving we get h 1656 . 85 mile 1600 mile
d
g' g 1
R l
17. (a) T 2 . At the hill g will decrease so to keep the time
g
2h
For scientist B, which goes up in a air g ' g 1 period same the length of pendulum has to be reduced.
R
GM GM
So it is clear that value of g measured by each will decreases 18. (d) V and I
r r2
at different rates.
V 0 and I 0 at r
10. (b) Gravitational pull depends upon the acceleration due to gravity
on that planet. 19. (c) U = Loss in gravitational energy = gain in K.E.

1 1 1 2U
Mm M e , gm ge So, U mv 2 m
81 6 2 v2
1/2 1/2
GM Re Me gm 1 ve ge Re
g = 81 20. (c) = 6 10 60 8 (nearly)
R 2
Rm Mm ge 6 vm g m Rm

9 21. (b)
Re Rm
6
vA gA RA vA
22. (c) ve 2 gR x r rx
11. (d) Reading of spring balance R m (g a) vB gB RB vB

If the lift falls freely then a = g R=0

GM M
12. (c) g g
R2 R2 ***
 Gravitation 445

23. (a) Time period of satellite which is very near to planet

R3 R3 1
T 2 2 T
GM 4 3
G R
3
i.e. time period of nearest satellite does not depends upon the
radius of planet, it only depends upon the density of the planet.
In the problem, density is same so time period will be same.
24. (b) Otherwise centrifugal force exceeds the force of attraction or
we can say that gravitational force won't be able to keep the
satellite in circular motion.
25. (c)
KA rB R hB R 2R 3
26. (d)
KB rA R hA R R 2
3/2 3/2
Tmercury rmercury 6 10 10 1
27. (c) 11
Tearth rearth 1 . 5 10 4
(approx.)
1
Tmercury year
4