Gravitation (Home Work) [1]

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HOME WORK
GRAVITATION
1. The force of gravitation is [AIIMS 2002] F1 on a particle placed at A, distance 2R from the
(a) Repulsive (b) Electrostatic centre of the sphere. A spherical cavity of radius
(c) Conservative (d) Non - conservative R/2 is now made in the sphere as shown in the
2. If the distance between two masses is doubled, figure. The sphere with cavity now applies a
the gravitational attraction between them gravitational force F2 on the same particle placed
[CPMT 1973; AMU (Med.) 2000] at A. The ratio F2 / F1 will be[CBSE PMT 1993]
(a) Is doubled (b) Becomes four times
(c) Is reduced to half (d) Is reduced to a quarter
3. A mass M is split into two parts, m and M – m, A
R R
which are then separated by a certain distance.
What ratio of m/M maximizes the gravitational
force between the two parts [AMU 2000]
(a) 1/3 (b) ½ (a) 1/2 (b) 3
(c) 1/4 (d) 1/5 (c) 7 (d) 7/9
4. Three particles each of mass m are placed at the 7. Three uniform spheres of mass M and radius R
three corners of an equilateral triangle. The centre each are kept in such a way that each touches the
of the triangle is at a distance x from either other two. The magnitude of the gravitational
corner. If a mass M be placed at the centre, what force on any of the spheres due to the other two is
will be the net gravitational force on it 3 GM 2 3 GM 2
(a) (b)
(a) Zero (b) 3GMm / x 2 4 R2 2 R2

(c) 2GMm / x 2 (d) GMm / x 2 3 GM 2 3 GM 2

(c) (d)
5. Two identical spheres are placed in contact R2 2 R2
with each other. The force of gravitation 8. A mass of 10kg is balanced on a sensitive
between the spheres will be proportional to (R physical balance. A 1000 kg mass is placed below
= radius of each sphere) 10 kg mass at a distance of 1m. How much
(a) R (b) R2 additional mass will be required for balancing the
(c) R4 (d) None of these physical balance
6. A solid sphere of uniform density and radius R (a) 66  10 15 kg (b) 6.7  10 8 kg
applies a gravitational force of attraction equal to
(c) 66  10 12 kg (d) 6.7  10 6 kg

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Gravitation (Home Work) [2]

9. If R is the radius of the earth and g the radius is half that of earth. Which of the following
acceleration due to gravity on the earth's surface, statement is correct
the mean density of the earth is (a) Both will show same time
[CPMT 1990; CBSE 1995; BHU 1998; MH CET (b) Time measured in clock A will be greater
(Med.) 1999; Kerala PMT 2002] than that in clock B
(a) 4G / 3gR (b) 3R / 4 gG (c) Time measured in clock B will be greater
(c) 3g / 4RG (d) Rg / 12G than that in clock A
10. A mass 'm' is taken to a planet whose mass is (d) Clock A will stop and clock B will show time
equal to half that of earth and radius is four times as it shows on earth
that of earth. The mass of the body on this planet 15. A body weight W Newton at the surface of the
will be [RPMT 1989, 97] earth. Its weight at a height equal to half the
(a) m / 2 (b) m / 8 radius of the earth will be [UPSEAT 2002]
(c) m / 4 (d) m W 2W
(a) (b)
2 3
11. The diameters of two planets are in the ratio 4 : 1
4W 8W
and their mean densities in the ratio 1: 2. The (c) (d)
9 27
acceleration due to gravity on the planets will be
in ratio [ISM Dhanbad 1994] 16. The value of g on the earth's surface is 980
cm/sec2. Its value at a height of 64 km from the
(a) 1 : 2 (b) 2 : 3
earth's surface is
(c) 2 : 1 (d) 4 : 1
(Radius of the earth R = 6400 Kilometers)
12. The acceleration due to gravity on the moon is
[MP PMT 1995]
only one sixth that of earth. If the earth and moon
2
are assumed to have the same density, the ratio of (a) 960 .40 cm / sec (b) 984.90 cm / sec 2
the radii of moon and earth will be (c) 982 .45 cm / sec 2 (d) 977 .55 cm / sec 2
1 1 17. The decrease in the value of g at height h from
(a) (b)
6 (6)1 / 3 earth's surface is
1 1 2h 2h
(c) (d) (a) (b) g
36 (6)2. / 3 R R
13. Let g be the acceleration due to gravity at earth's h R
(c) g (d)
surface and K be the rotational kinetic energy of R 2hg
the earth. Suppose the earth's radius decreases by 18. A simple pendulum has a time period T1 when on
2% keeping all other quantities same, then earth's surface and T2 when taken to a height R
[BHU 1994; JIPMER 2000] above the earth's surface, where R is the radius of
(a) g decreases by 2% and K decreases by 4% earth. The value of T2 / T1 is
(b) g decreases by 4% and K increases by 2% [IIT-JEE (Screening) 2001]
(c) g increases by 4% and K decreases by 4% (a) 1 (b) 2
(d) g decreases by 4% and K increase by 4% (c) 4 (d) 2
14. Clock A based on spring oscillations and a clock 19. A pendulum clock is set to give correct time at
B based on oscillations of simple pendulum are the sea level. This clock is moved to hill station at
synchronised on earth. Both are taken to mars an altitude of 2500m above the sea level. In order
whose mass is 0.1 times the mass of earth and to keep correct time of the hill station, the length
of the pendulum [SCRA 1994]

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Gravitation (Home Work) [3]

(a) Has to be reduced centre. If gravity were to remain constant this

(b) Has to be increased t
time would be t'. The ratio of will be
t'
(c) Needs no adjustment
 
(d) Needs no adjustment but its mass has to be (a) (b)
2 2 2
increased
2 
20. Two blocks of masses m each are hung from a (c) (d)
3 3
balance. The scale pan A is at height H 1 whereas
25. Suppose a vertical tunnel is dug along the
scale pan B is at height H 2 . The error in weighing
diameter of earth assumed to be a sphere of
when H 1  H 2 and R being the radius of earth is uniform mass having density . If a body of
mass m is thrown in this tunnel, its acceleration at
a distance y from the centre is given by
A
m B
m
m
H1
H2
y

 1  2H 1   H1 H2 
(a) mg   (b) 2mg   
 R   R R 
 H 2 H1  H 2 H1 4 3
(c) 2mg    (d) 2mg (a) Gym (b) Gy
 R R  H1  H 2 3 4
21. If the value of 'g' acceleration due to gravity, at 4 4
(c) y (d) Gy
earth surface is 10m / s 2 , its value in m / s 2 at the 3 3
centre of the earth, which is assumed to be a 26. A tunnel is dug along the diameter of the earth. If
sphere of radius 'R' metre and uniform mass a particle of mass m is situated in the tunnel at a
density is [AIIMS 2002] distance x from the centre of earth then
(a) 5 (b) 10/R gravitational force acting on it, will be
(c) 10/2R (d) Zero GM e m GM em
(a) x (b)
Re3 Re2
22. The loss in weight of a body taken from earth's
surface to a height h is 1%. The change in weight GMe m GM e m
(c) (d)
x2 (R e  x) 2
taken into a mine of depth h will be
(a) 1% loss (b) 1% gain 27. The acceleration due to gravity at pole and
(c) 0.5% gain (d) 0.5% loss equator can be related as [DPMT 2002]
23. The weight of body at earth's surface is W. At a (a) g p  g e (b) g p  ge  g
depth half way to the centre of the earth, it will be (c) g p  ge  g (d) g p  g e
(assuming uniform density in earth)
28. Weight of a body is maximum at [AFMC 2001]
(a) W (b) W/2
(a) Moon (b) Poles of earth
(c) W/4 (d) W/8
(c) Equator of earth (d) Centre of earth
24. A particle would take a time t to move down a
straight tunnel from the surface of earth 29. The value of 'g' at a particular point is 9.8m/s2.
(supposed to be a homogeneous sphere) to its Suppose the earth suddenly shrinks uniformly to
half its present size without losing any mass. The
value of 'g' at the same point (assuming that the

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Gravitation (Home Work) [4]

distance of the point from the centre of earth does I I

not shrink) will now be r=R
O O
[NCERT 1984; DPMT 1999] (a) r
(b) r=R r
2 2
(a) 4.9m / sec (b) 3.1m / sec
(c) 9.8m / sec 2 (d) 19 .6m / sec 2
30. The acceleration due to gravity increases by 0.5% I
I
when we go from the equator to the poles. What
will be the time period of the pendulum at the O O
(c) r=R r (d) r=R r
equator which beats seconds at the poles
(a) 1.950 s (b) 1.995 s
(c) 2.050 s (d) 2.005 s 34. A thin spherical shell of mass M and radius R has
a small hole. A particle of mass m is released at
31. There are two bodies of masses 100 kg and 10000
the mouth of the hole. Then
kg separated by a distance 1m. At what distance
from the smaller body, the intensity of m
gravitational field will be zero [BHU 1997]
1 1 R
(a) m (b) m M
9 10
1 10
(c) m (d) m
11 11
32. Which one of the following graphs represents (a) The particle will execute simple harmonic
correctly the variation of the gravitational field motion inside the shell
(F) with the distance (r) from the centre of a (b) The particle will oscillate inside the small,
spherical shell of mass M and radius a but the oscillations are not simple harmonic
(c) The particle will not oscillate, but the speed
of the particle will go on increasing
(d) None of these
35. A solid sphere of uniform density and radius 4
(a) (b) units is located with its centre at the origin O of
coordinates. Two spheres of equal radii 1 unit
with their centres at A(– 2, 0, 0) and B(2, 0, 0)
respectively are taken out of the solid leaving
behind spherical cavities as shown in figure
(c) (d) [IIT-JEE 1993]
y

33. The curve depicting the dependence of intensity

of gravitational field on the distance r from the A B
centre of the earth is O x

(a) The gravitational force due to this object at

the origin is zero

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Gravitation (Home Work) [5]

(b) The gravitational force at the point B (2, 0, 0) 38. A sphere of mass M and radius R2 has a
is zero concentric cavity of radius R1 as shown in figure.
(c) The gravitational potential is the same at all The force F exerted by the sphere on a particle of
points of the circle y 2  z 2  36 mass m located at a distance r from the centre of
sphere varies as (0  r  )
(d) The gravitational potential is the same at all
points on the circle y 2  z 2  4
36. Gravitational field at the centre of a semicircle
R1 R2
formed by a thin wire AB of mass m and length l
is

y
l

A O B x
(a) (b)
Gm r
(a) along x axis
l
F
Gm
(b) along y axis
l
2 Gm
(c) (d)
(c) along x axis
l2
r
2 Gm
(d) along y axis
l2
37. Two concentric shells of different masses m1 and 39. A spherical hole is made in a solid sphere of
m2 are having a sliding particle of mass m. The radius R. The mass of the sphere before
forces on the particle at position A, B and C are hollowing was M. The gravitational field at the
m2 centre of the hole due to the remaining mass is
B

r2 C
r3 m1
R
A
r1

Gm1 G(m1  m2 )m
(a) 0, ,
r22 r12 GM
(a) Zero (b)
Gm 2 Gm1 8R 2
(b) , 0,
GM
r22 r12 GM
(c) (d)
2R 2 R2
G(m1  m 2 )m Gm 2
(c) , ,0
40. A point P lies on the axis of a ring of mass M and
r12 r22
radius a, at a distance a from its centre C. A small
G(m1  m 2 )m Gm1
(d) , 2 ,0 particle starts from P and reaches C under
r12 r2
gravitational attraction only. Its speed at C will be

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Gravitation (Home Work) [6]

 GM Gm
2GM 2GM 1  (a)  (b) 
(a) (b) 1 


 R r
a a  2
  M m  M  m
2GM
(c)  G   (d)  G  
(c) ( 2  1) (d) Zero  R r   R r 
a
45. A person brings a mass of 1 kg from infinity to a
41. If V is the gravitational potential on the surface of point A. Initially the mass was at rest but it moves
the earth, then what is its value at the centre of with a speed of 2 m/s as it reaches A. The work
the earth done by the person on the mass is – 3 J. The
(a) 2V (b) 3V potential of A is
3 2
(c) V (d) V (a) – 3 J/kg (b) – 2 J/kg
2 3
(c) – 5 J/kg (d) – 7 J/kg
42. The diagram showing the variation of
gravitational potential of earth with distance from 46. A thin rod of length L is bent to form a
the centre of earth is semicircle. The mass of the rod is M. What will
be the gravitational potential at the centre of the
circle
GM GM
(a) (b) (a)  (b) 
L 2L
GM GM
(c)  (d) 
2L L
V
47. The escape velocity of a planet having mass 6
r=R times and radius 2 times as that of earth is
O
(c) r (d)
[CPMT 1999; MP PET 2003]
(a) 3 Ve (b) 3Ve
43. By which curve will the variation of gravitational (c) 2 Ve (d) 2Ve
potential of a hollow sphere of radius R with 48. The escape velocity of a particle of mass m
distance be depicted varies as
V V
V [CPMT 1978; RPMT 1999; AIEEE 2002]
(a) m 2 (b) m
O r=R
O 0
r=R
(a) r=R r (b) r (c) m (d) Om1 r
49. How many times is escape velocity (ve ) , of orbital
velocity (v 0 ) for a satellite revolving near earth
V
V [RPMT 2000]
r=R (a) 2 times (b) 2 times
O r= R
(c) (d) O
r r (c) 3 times (d) 4 times
50. The orbital velocity of a satellite at a height h
above the surface of earth is v. The value of
44. Two concentric shells have mass M and m and
escape velocity from the same location is given
their radii are R and r respectively, where R  r .
by [J&K CET 2000]
What is the gravitational potential at their
common centre (a) 2v (b) v

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Gravitation (Home Work) [7]

v v (c) E (d) E/2

(c) (d)
2 2
57. A ball of mass m is fired vertically upwards from
51. How much energy will be necessary for making a the surface of the earth with velocity nv e , where
body of 500 kg escape from the earth v e is the escape velocity and n < 1. Neglecting
[g  9.8 m / s 2 , radius of earth  6.4  10 6 m]
air resistance, to what height will the ball rise?
[MP PET 1999] (Take radius of the earth as R )
(a) About 9.8  10 J (b) About 6.4  10 8 J
6 (a) R / n 2 (b) R /(1  n 2 )
(c) About 3.1  1010 J (d) About 27.4  10 12 J (c) Rn 2 /(1  n 2 ) (d) Rn 2
52. The escape velocity of a body on the surface of 58. The masses and radii of the earth and moon are
M 1 , R1 and M 2 , R 2 respectively. Their centres are
the earth is 11.2 km / s . If the earth’s mass
distance d apart. The minimum velocity with
increases to twice its present value and the radius
which a particle of mass m should be projected
of the earth becomes half, the escape velocity
from a point midway between their centres so that
would become [CBSE PMT 1997]
it escape to infinity is [MP PET 1997]
(a) 5.6 km / s
G 2G
(b) 11 .2 km / s (remain unchanged) (a) 2 (M 1  M 2 ) (b) 2 (M 1  M 2 )
d d
(c) 22.4 km / s Gm Gm(M 1  M 2 )
(c) 2 (M 1  M 2 ) (d) 2
(d) 44.8 km / s d d(R1  R 2 )

53. A rocket is launched with velocity 10 km/s. If 59. A body is projected with a velocity 2ve, where ve
radius of earth is R, then maximum height is the escape velocity. Its velocity when it escapes
attained by it will be [RPET 1997] the gravitational field of the earth is
(a) 2R (b) 3R (a) 7ve (b) 5v e
(c) 4R (d) 5R (c) 3v e (d) v e
54. A missile is launched with a velocity less then the 60. Escape velocity of a body of 1 kg mass on a
escape velocity. The sum of its kinetic and planet is 100 m/sec. Gravitational potential
potential energy is [MP PET 1995] energy of the body at the planet is
(a) Positive [MP PMT 2002]
(b) Negative (a) – 5000 J (b) – 1000 J
(c) Zero (c) – 2400 J (d) 5000 J
(d) May be positive or negative depending upon R
61. A body of mass m rises to a height h  from
its initial velocity 5

55. v e and v p denotes the escape velocity from the

the earth’s surface where R is earth’s radius. If g
is acceleration due to gravity at the earth’s
earth and another planet having twice the radius surface, the increase in potential energy is
and the same mean density as the earth. Then [CPMT 1989]
[NCERT 1974; MP PMT 1994] 4
(a) mgh (b) mgh
(a) v e  v p (b) ve  vp / 2 5
5 6
(c) ve  2v p (d) ve  vp / 4 (c) mgh (d) mgh
6 7
56. The magnitude of the potential energy per unit 62. The work done is bringing three particles each of
mass of the object at the surface of earth is E. mass 10 g from large distances to the vertices of
Then the escape velocity of the object is an equilateral triangle of side 10 cm.
(a) 2E (b) 4 E 2

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(a) 1  10 13 J (b) 2  10 13 J 68. For the moon to cease to remain the earth’s
satellite its orbital velocity has to increase by a
(c) 4  10 11 J (d) 1  10 11 J
factor of [MP PET 1994]
63. The potential energy due to gravitational field of
(a) 2 (b) 2
earth will be maximum at
(c) 1 / 2 (d) 3
(a) Infinite distance
69. Two artificial satellites A and B are at a distances
(b) The poles of earth
r A and rB above the earth’s surface. If the radius
(c) The centre of earth
of earth is R, then the ratio of their speeds will be
(d) The equator of earth 1/ 2 2

r R  
r R 
64. The radius and mass of earth are increased by (a)  B 
 (b)  B 

 rA  R   rA  R 
0.5%. Which of the following statement is false at
2 1/ 2
the surface of the earth [Roorkee 2000]  rB   rB 
(c)  
r  (d) 
r


(a) g will increase  A  A 
(b) g will decrease 70. When a satellite going round earth in a circular
(c) Escape velocity will remain unchanged orbit of radius r and speed v, losses some of its
(d) Potential energy will remain unchanged energy. Then r and v change as
65. Two identical thin rings each of radius R are [EAMCET (Med.) 2000]
coaxially placed at a distance R. If the rings have (a) r and v both will increase
a uniform mass distribution and each has mass (b) r and v both will decrease
m1 and m2 respectively, then the work done in (c) r will decrease and v will increase
moving a mass m from centre of one ring to that (d) r will increase and v will decrease
of the other is 71. A satellite is revolving around a planet of mass M
Gm(m1  m2 )( 2  1) in an elliptical orbit of semi-major axis a. The
(a) Zero (b) orbital velocity of the satellite at a distance r from
2R
the focus will be
Gm 2 (m1  m 2 ) Gm1 m 2 ( 2  1)
(c) (d)  2 1 
1/ 2
 1 2 
1/2
R m2 R (a) GM     (b) GM   
  r a    r a 
66. The orbital velocity of an artificial satellite in a
1/ 2 1/2
circular orbit just above the earth’s surface is v.  2 1   1 2 
(c) GM    (d) GM   
For a satellite orbiting at an altitude of half of the  r2 a 2    r2 a 2 
earth’s radius, the orbital velocity is 72. A geo-stationary satellite is orbiting the earth at a
[Kerala (Engg.) 2001] height of 6 R above the surface of earth, R being
3 3 the radius of earth. The time period of another
(a) V (b) V
satellite at a height of 2.5 R from the surface of
2 2
earth is
2 2
(c) V (d) V [UPSEAT 2002; AMU (Med.) 2002]
3 3
67. The speed of a satellite is v while revolving in an (a) 10 hr (b) (6 / 2 ) hr
elliptical orbit and is at nearest distance ‘a’ from (c) 6 hr (d) 6 2 hr
earth. The speed of satellite at farthest distance
73. Time period of revolution of a satellite around a
‘b’ will be [RPMT 1995]
planet of radius R is T. Period of revolution
(a) (b / a) v (b) (a / b) v around another planet. Whose radius is 3R but
(c) ( a / b ) v (d) ( b / a ) v having same density is [CPMT 1981]

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Gravitation (Home Work) [9]

(a) T (b) 3T (a) 0.5% (b) 1.0%

(c) 9T (d) 3 3 T (c) 1.5% (d) 3.0%
80. A satellite moves eastwards very near the surface
74. A satellite is orbiting around the earth with a
period T. If the earth suddenly shrinks to half its of the earth in the equatorial plane of the earth
radius without change in mass, the period of with speed v0 . Another satellite moves at the
revolution of the satellite will be same height with the same speed in the equatorial
(a) T / 2 (b) T / 2 plane but westwards. If R = radius of the earth
(c) T (d) 2T about its own axis, then the difference in the two
75. A satellite is orbiting around the earth in the time period as observed on the earth will be
equitorial plane rotating from west to east as the approximately equal to
earth does. If  e be the angular speed of the earth 4Rv 0 4Rv 0
(a) (b)
and  s be that of satellite, then the satellite will R 2 4  v 02 R 2  2  v 02
repeatedly appear at the some location after a 4Rv 0 2Rv 0
time t = (c) (d)
R 2 2  v 02 R 2  2  v 02
2 2
(a) (b) 81. A “double star” is a composite system of two
s  c  s  c
stars rotating about their centre of mass under
 
(c) (d) their mutual gravitational attraction. Let us
s  c s  c
consider such a “double star” which has two stars
76. Suppose the gravitational force varies inversely as
the nth power of distance. Then, the time period of masses m and 2m at separation l. If T is the
of a planet in circular orbit of radius R around the time period of rotation about their centre of mass
sun will be proportional to then,
n 1
(a) R n (b) R 2 l3 l3
(a) T  2 (b) T  2
n1 mG 2mG
(c) R 2 (d) R n
l3 l3
77. A geostationary satellite orbits around the earth in (c) T  2 (d) T  2
3mG 4mG
a circular orbit of radius 36000 km. Then, the
time period of a satellite orbiting a few hundred 82. A space probe projected from the earth moves
kilometres above the earth’s surface round the moon in a circular orbit at a distance
(R Earth  6400 km) will approximately be R
equal to its radius Rmoon  where R = radius of
4
[IIT-JEE (Screening) 2002]
the earth. Its rocket launcher moves in circular
(a) 1/2 h (b) 1 h
orbit around the earth at a distance equal to R
(c) 2 h (d) 4 h
from its surface. The ratio of the times taken for
78. If the distance between the earth and the sun
becomes half its present value, the number of one revolution by the probe and the rocket
M
days in a year would have been launcher is  M moon  , where M  mass of the earth 
 80 
[IIT-JEE 1996; RPET 1996]
(a) 64.5 (b) 129 (a) 3:2 (b) 5 :2
(c) 182.5 (d) 730 (c) 1 : 1 (d) 2 : 3
79. A satellite is launched into a circular orbit of 83. The distance of a geo-stationary satellite from the
radius R around the earth. A second satellite is
centre of the earth (Radius R = 6400 km) is
launched into an orbit of radius (1.01) R. The
period of the second satellite is larger than that of nearest to [AFMC 2001]
the first one by approximately [IIT-JEE 1995] (a) 5 R (b) 7 R

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(c) 10 R (d) 18 R 1 1   1 1 
(a) GM e    (b) 2GM e   

84. An artificial satellite is moving in a circular orbit  R e R0   Re R0 
around the earth with a speed equal to half the 1 1  1 
1
escape speed from the earth. If R is the radius of (c) GM e  (d) 2GM e   

R e R0  Re R0 
the earth then the height of the satellite above the
90. If total energy of an earth satellite is zero, it
surface of the earth is
means that
R 2R
(a) (b) (a) The satellite is bound to earth
2 3
(b) The satellite may no longer be bound to
(c) R (d) 2 R
earth’s field
85. If the angular velocity of a planet about its own (c) The satellite moves away from the orbit along a
axis is halved, the distance of geostationary parabolic path
satellite of this planet from the centre of the (d) The satellite escapes in a hyperbolic path
planet will become
91. By what percent the energy of a satellite has to be
(a) (2)1 / 3 times (b) (2) 3 / 2 times increased to shift it from an orbit of radius r to
(c) (2) 2 / 3 times (d) 4 times 3
r
2
86. A satellite moves around the earth in a circular
(a) 66.7% (b) 33.3%
orbit with speed v. If m is the mass of the satellite,
(c) 15% (d) 20.3%
its total energy is [CBSE PMT 1991]
1 1
92. A mass m is raised from the surface of the earth
(a)  mv 2 (b) mv 2 to a point distant R(  1) from the centre of the
2 2
3 1
earth and then put into a circular orbit to make it
(c) mv 2 (d) mv 2 an artificial satellite. The total work done to
2 4
complete this job is
87. The minimum energy required to launch a
satellite of mass m from the surface of earth of (a) mgR(2  1) (b) mgR(2  1)
radius R in a circular orbit at an altitude 2 R is 2  1
(c) mgR(  1) (d) mgR
(mass of earth is M) 2

5GmM 2GmM 93. A satellite of mass m is circulating around the

(a) (b)
6R 3R earth with constant angular velocity. If radius of
GmM GmM the orbit is R 0 and mass of the earth M, the
(c) (d)
2R 3R angular momentum about the centre of the earth
88. The masses of moon and earth are 7.36  10 22 kg is [MP PMT 1996; RPMT 2000]
and 5.98  10 24 kg respectively and their mean (a) m GMR0 (b) M GmR0

separation is 3.82  10 5 km . The energy required (c) m

GM
(d) M
GM
R0 R0
to break the earth-moon system is
(a) 12.4  10 32 J (b) 3.84  1028 J 94. A planet of mass m is moving in an elliptical path
about the sun. Its maximum and minimum
(c) 5.36  10 24 J (d) 2.96  10 20 J distances from the sun are r1 and r2 respectively.
89. A body placed at a distance R0 form the centre of If M s is the mass of sun then the angular
earth, starts moving from rest. The velocity of the momentum of this planet about the center of sun
body on reaching at the earth’s surface will be ( will be
Re  radius of earth and M e  mass of earth) 2GM s r1r2
(a) (b) 2GM sm
(r1  r2 ) (r1  r2 )

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2GMs r1r2 2GMs m(r1  r2 ) (a) The satellite is rotated its axis with
(c) m (d) m
(r1  r2 ) r1r2 compartment of astronaut at the centre of the
satellite
95. Reaction of weightlessness in a satellite is
[RPMT 2000] (b) The satellite is shaped like a wheel
(a) Zero gravity (c) The satellite is rotated around and around till
weightlessness disappears
(b) Centre of mass
(d) The compartment of astronaut is kept on the
(c) Zero reaction force by satellite surface
periphery of rotating wheel like satellite
(d) None of these
100. Which of the following astronomer first proposed
96. A body suspended from a spring balance is placed
that sun is static and earth rounds sun
in a satellite. Reading in balance is W1 when the
[AFMC 2002]
satellite moves in an orbit of radius R. Reading in
balance is W2 when the satellite moves in an orbit (a) Copernicus (b) Kepler
of radius 2R . Then (c) Galilio (d) None
(a) W1  W2 (b) W1  W2
(c) W1  W2 (d) W1  2W2
ANSWER KEY
97. An astronaut feels weightlessness because
(a) Gravity is zero there 1. (c) 2. (d) 3. (b) 4. (a) 5. (c)
(b) Atmosphere is not there 6. (d) 7. (a) 8. (b) 9. (c) 10. (d)
(c) Energy is zero in the chamber of a rocket 11. (c) 12. (a) 13. (c) 14. (b) 15. (c)
16. (a) 17. (b) 18. (d) 19. (a) 20. (b)
(d) The fictitious force in rotating frame of
21. (d) 22. (d) 23. (b) 24. (a) 25. (d)
reference cancels the effect or weight
26. (a) 27. (d) 28. (b) 29. (c) 30. (d)
98. Inside a satellite orbiting very close to the earth’s 31. (c) 32. (d) 33. (b) 34. (d) 35. (a,c,d)
surface, water does not fall out of a glass when it 36. (d) 37. (d) 38. (b) 39. (c) 40. (b)
is inverted. Which of the following is the best 41. (c) 42. (c) 43. (c) 44. (d) 45. (c)
explanation for this 46. (d) 47. (a) 48. (c) 49. (a) 50. (b)
(a) The earth does not exert any force on the 51. (c) 52. (c) 53. (c) 54. (b) 55. (b)
water 56. (a) 57. (c) 58. (a) 59. (c) 60. (a)
(b) The earth’s force of a attraction on the water 61. (c) 62. (b) 63. (a) 64. (a) 65. (b)
is exactly balanced by the force created by 66. (c) 67. (b) 68. (b) 69. (a) 70. (c)
the satellites motion 71. (a) 72. (d) 73. (a) 74. (c) 75. (a)
76. (b) 77. (c) 78. (b) 79. (c) 80. (b)
(c) The water and the glass have the same
81. (c) 82. (b) 83. (b) 84. (c) 85. (c)
acceleration, equal to g, towards the centre of
86. (a) 87. (a) 88. (b) 89. (d) 90. (c)
the earth, and hence there is no relative
91. (b) 92. (d) 93. (a) 94. (c) 95. (c)
motion between them
96. (a) 97. (d) 98. (c) 99. (d) 100. (a)
(d) The gravitational attraction between the glass
and the water balances the earth’s attraction
on the water
99. To overcome the effect of weightlessness in an
artificial satellite

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