LEVEL-1

MCQs Having One Correct Answer Only

shell of mass M. The point A is
8. Fig. 3.58 shows a spherical
1. In planetary motion from the centre of the shell. If a
not at the centre but away
(a) the angular speed remains constant then
particle of mass m is placed A,
at

(b) the total angular momentum remains constant

(c) the linear speed remains constant M
(d) neither the angular momentum nor angular speed remains A
constant
2. A planet revolves in an elliptical orbit around the sun. Then
out of the following physical quantities, the one which remains
constant is
FIGURE 3.58
(a) velocity (b) kinetic energy
(a) it remains at rest
(c) momentum d)angular momentum
3. If the earth is at one fourth of its present distance from the (b) it experiences a net force towards the centre
sun, then the duration of the year will be (c) it experiences a net force away from the centre
(a) half the present year (d) none of the above
(b) one-eighth the present year 9. Assuming that the earth is a sphere of radius R, gravitational
acceleration on its surface is g and mass of the earth is M,
(c) one fourth the present year
then its mean density is
d)one sixth the present year
4. A satellite is launched into a circular orbit of radius R around 4TGR
the earth. A second satellite is launched into an orbit of radius (a) 38 (b)
4 TtGR 3g
101 R. The time period of the second satellite is larger than
that of the first one by approximately 4T G (d) 3g GR
(a) 0-5% (b) 1-5%
(d) 3-0%
(c)3R8 4T
(c) 19% 10. If the radius of earth were to shrink by one percent, its mass
5. A satellite revolves around the earth in an elliptical orbit. Its remaining the same, the acceleration due to gravity on the
speed is earth's surface would
(a) same at all points on the orbit (a) decrease by 1% (b) increase by 1%
(b) greatest when it is farthest from the earth (c) increase by 2% (d) decrease by 2%
(c) greatest when it is closest to the earth 11. Two planets of radii r and r2 are made from the same material.
(d) greatest neither when it is closest nor when it is farthest ratio of the acceleration due to gravity 81/82 at the surtace
from the earth, but at some other point of the two planets is
6. A planet moves around the sun. At a point P, it is closest from (a) (rylr) (6) (r/r)
the sun at a distance d and has a speed v. At another point
Q, when it is farthest from the sun at a distance d2, its speed (c) r (d) rr2
will be 12. The two planets with radii Ri, R2 have densities P. P2 and
atmospheric pressures P and p2, respectively. The ratio of
(a) dy/d (b) davld masses of their atmospheres, neglecting variation of g and
within the limits of atmosphere, is
(c) dv,ld (d) d / d
7. A satellite goes along an elliptical path around earth. The rate (a) R p PRP2
of change of arc length swept by the satellite is proportional
to
P2RP2 6)pRP
(a)r (b) PRPL
(c) / 2 (d)r (C)pRP2 P22P
3/32
13. Rate of change of weight near the earth's surface varies with
height h as (a)
(a)h (b) h 9D
4D
(c)hl
14. The acceleration due
(d) 1/2
(c)5 in air and the
to gravity
the surface of moon is only
at
22. Two of masses m and M are situated
spheres
one-sixth of that of the earth. If the earth and moon are assumed around the
them is F. The space
to have same gravitational force between 3. The
density, then ratio of the radius of the moon to masses is now filled
with a liquid of specific gravity
radius of the earth is
gravitational force will now be
b) F/'3
(a) (a) F
(b) (d) 3 F
(6)/3 (c) F/9
6400 km and that of Mars is
1 23. The radius of the earth is about
(c) about 10 times the
36 about 3200 km. The mass of the earth is
(62/3 mass of Mars. An object weighs
200 N on the surface of the
15. Given that the acceleration due would be
to gravity at a height h is same earth. Its weight on the surface of Mars
as that at a depth d below the surface of the earth. If both h b) 20 N
(a) 6N
and d are small as compared to the radius of the earth, then (c) 40 N (d) 80 N
which of the following relations is correct?
due to gravity
(a) 2 h=d (b) h = d 24. At the surface of a certain planet, acceleration
is one quarter of that on earth. Ifa brass ball
is transported on
(c)h=2 d (d) h d this planet, then which one of the following statements
is NOT
16. The value of g at a depth d is two third the value of that on the correct?
earth's surface. The value of d in terms of radius of earth R is ball has the same mass on the other planet as on
(a) the brass
(a) 2 R/3 (6) R/3 earth
(c)R/6 d) R/2 (b) the of the brass ball on this
mass planet is a quarter of its
17. The value of g on the earth's surface is 980 cm/s". Its value at mass as measured on earth
a height of 64 km from the earth's surface is (Radius of earth (c) the weight of the brass ball on this planet is a quarter of
is 6400 km) the weight as measured on earth
(a) 96040 cm/s (b) 984.90 cm/s (d) the brass ball has the same volume on the other planet as

(c) 982.45 cm/s2 (4) 977.55 cm/s2 on earth

25. If the earth stops about its axis, the acceleration due
rotating
a distancefrom the centre of
18. A Point mass mo is placed at
3
to gravity will remain unchanged at
(b) Latitude 45°
a uniform spherical shell of mass M and radius R. The (a) Equator
(c) Latitude 60 (d) Poles
gravitational force on the point mass mo is
man at the equator would
26. If a weigh (3/5)th of his weight, the
GM m
(a) 9GM m (b)
R2
angular speed of the earth is
R2
4 GM mo
(a) 2&
(c) Zero
)R around
V5R
19. Two satellites A and B of the same mass are revolving 2 R
the earth in the concentric circular orbits such

of satellite B from the centre of the earth is

that the distance
thrice as compared
(d58
27. The rotation of the Earth having radius R about its axis speeds
satellite A from the centre of the earth.
to the distance of the upto a value such that a man at latitude 60" feels weightless.
The ratio of the centripetal force acting
on B as compared to
The duration of the day in such case will be?
that on A is

(a) 1/3 (b) 3

(6) 8
(c) 1/9 () 1//3
the earth and
20. If the mass of a planet is 10% less than that of
that of the earth, the acceleration
the radius 20% greater than (d) 4
on the planet will be
due to gravity
5/8 times that on the surface of the earth 28. A cavity of radius R/2 is made inside a solid sphere of radius
(a)
3/4 times that on the surface of the earth R. The centre of the cavity is located at a distance R/2 from
(b)
of the earth the centre of the sphere. The gravitational field at a point P
(c)1/2 times that on the surface
the earth that is at a distance R/2 from the centre of the sphere and
(d)9/10 times that on the surface of
lying on the opposite side of cavity on the line joining both
the centres of Earth and Moon is D
21. If the distance between the centres of sphere and cavity is. [Here g =GM/R-, where
that of Moon, at what distance
and mass of Earth is 81 times M is the mass of the sphere]
field will be zero?
fromthe centre of Earth gravitational
 35. The gravitational potential energy of a body of mass m is
U = ax + by. The magnitude of acceleration of the body will
be

ab
(a)
m
RI2
a2 +b2 (d)
a2+b2
FIGURE 3.59 (c)
m m

(a) 36. The approximate percentage change in the acceleration of the

earth from the situation of total eclipse of the sun to the
(c) (d) None of these situation where the moon is on the other side of earth directly
16
opposite to the sun is (Given, r average distance between
29. If earth rotates x times faster than its
present speed about its the sun and earth, r2 average distance between the moon
axis in order that bodies lying on its
equator just fly off into and the earth, M M, M, are masses of moon, sun and earth
space, then x is nearly given by
respectively)
(a) x= 1 (b) *= 2
2
(c) x = 17
()r=289 (M 100
30. The rotation of the earth
having radius R about its axis speeds
upto a value such that a man on equator feels weightless. The
duration of the day in such case will be
Mx 100 ) 2 Mmx 100
) m
R 2M,
37. A rocket is fired from the earth's surface to the moon's surface.
The distance between the centres of earth and the moon is r
and the mass of the earth is 81 times the mass of the moon.
()8 4 R The gravitational force on the rocket will be zero, when its
Vs V8
31. Three particles each of mass m are placed at the vertices of an distance from the moon is
(a) r/20 (b) 15
equilateral triangle of side a. The gravitational field intensity
at the centroid of the triangle is (c) 710 (d) 15
38. Two particles each of mass 1
Gm kg placed at P and Q such
are
(a) Zero that PO = 0Q = L. The
a
gravitational force experienced by
another 1 kg mass placed at R, where OR =L is
(c)2Gm2 (d Cm2 R
2 a
32. If three uniform spheres, each having mass M and radius r,
are kept in such a way that each touches the other two, the
magnitude of the gravitational force on any sphere due to the
other two is
L

(a)
GM (b) 2GM2 FIGURE 3.60
42
G
(a)
2GM2 3 GM2
(C)A (d)42 (d) Zero
33. Two astronauts have deserted their
spaceship in a region of
space far from the gravitational attraction of any other body. 39. Given that mass of the earth is M and its radius is R.
A bodyis
Each has a mass of 100 kg and they are 100 m dropped from a height equal to the radius of the earth above
apart. They are
initially at rest relative to one another. How long will it take the surface of earth. When it reaches the
will be
ground its velocity
for the gravitional attraction to bring them closer by 1 cm
(a) 2-52 days (b) 1.41 days
(a) GM GM /2
(c) 0-70 days
34. The
(d) 141 s
gravitational field in a region is given by
R
R
& (5i+ 12j) N/kg. The magnitude of the gravitational
20M
(c2GM2

force acting on a particle of mass 2 kg placed at the origin,

will be
R
40. The gravitational
potential energy of a
body at a distance r
(a) Zero (b) 13 N from the centre of
earth
the centre of earth is
is U. Its weight at a distance 2r from
(c) 26 N (d) 75 N
 -U
(b)
U
GMmo (b)
GMm
2r
(a)2R R

GMm 11
4r (c)
41. A particle of mass 10 kg is kept on the surface of a uniform possible of find the required work as the nature
(d) It is not
sphere of mass 100 kg and radius 10 cm. Find the work to be of distribution of mass is not known.
done against the gravitational force the
between them to take the M and 2 M, respectively, having
particle far away from the sphere. (G 6-67 x 10-1 Nm/kg) 47. Two rings having masses
3.62.
=
same radius R are placed coaxially as shown in the fig.
(a) 6-67 x 109J (b) 6-67 x 10-7J
(c) 13-34 x 10-10 J (d)3.33 x 10-10 J 3R
42. A person brings
a mass of 2
kg from A to B. The increase in P
kinetic energy of the mass is 4 J and the work done
by person
on the mass is 10 J. The gravitational
potential difference
-

between B and A (i.e., VB - Va) is

M 2M
(a) 4 J/kg (b) 7 J/kg
FIGURE 3.62
(c)-3 Jkg (d)-7 J/kg
If the mass distribution on both the rings is non-uniform, then
43. The potential at the surface of a planet of mass M and radius
the gravitational potential at point P is
R is assumed to be zero. Choose the most appropriate option

(a) The potential at infinity is

GM (a) +
R
(c) zero
GM
(b) The potential at centre of planet is B information
2R (d) cannot be determined from the given
distance of 3 R from
48. A point mass m is released from rest at a
(c) Both (a) and (6) are correct of radius R and mass
the centre of a thin-walled hollow sphere
a)Both (a) and (b) are wrong M as shown. The hollow sphere is fixed in position and the
attractionof
44. The change in potential energy when a body of mass m is only force on the point mass is the gravitational
hollow
raised to a height n R from earth's surface is (R radius of the
=
the hollow sphere. There is a very small hole in the
falls shown. The
earth) sphere through which the point mass as
P
velocity of a point mass when passes through point
it at a

(b) mg R distance RI2 from the centre of the sphere is

(a) mg R

(c) mgR (mg R|?+1

distribution is given by
45. The gravitational field due to a mass 3R
Klx in x-direction. Taking the gravitational potential to
8
distance x is
be zero at infinity, its value at
K
R
ER2
3K
FIGURE 3.63
()- (d)212
non-uniform distribution of mass M and 2 GM S GM
46. Consider a ring having
radius R. A point mass my
is taken slowly from point A to point
by the external
(a 3R (b)3R
so, work done
B away from the ring. In doing 4 GM
force against the gravitational
force exerted by ring is 25 GM (d) 3R
C 24 R
M
49. A man starts falling towards a planet of mass M and radius R.
As he reaches near to the surface, he realizes that he will pass

4 through a small hole in the planet. As he enters the hole, he

sees that the planet is really made of two pieces a spherical
shell of negligible thickness of mass 2 M/3 and a point mass
M/3 at the centre. The change in the acceleration due to gravity
experienced by the man is
FIGURE 3.61
 55. A tunnel is dug across the diameter of earth. A ball is released
(b) 0 from the surface of earth into the tunnel. The velocity of ball
when it is at a distance R/2 from centre of earth is
GM 4 GM (where R = radius of earth and M = mass of earth)

R R 3 GM 2 GM
50. A particle of mass mo is placed at the centre of a fixed, uniform
semicircular ring of radius R and mass m as shown in the fig.
3.64. The work required to displace the particle from centre
(a)
4R 6)3R
of the ring to infinity is GM (
2 GM
R
(c)2R
56. A small body of super dense material, whose mass is twice
the mass of the Earth but whose size is very small compared
to the size of the Earth, starts from rest at a height H << R
mo above the Earth's surface. If it reaches the Earth's surface in
time , then t is equal to?

(a) 2H/gs (b) H/g

(c)2H/38 (d) 4H/3s
FIGURE 3.64
57. A thin hollow spherical shell is compressed to half its radius.
Gm o Gm The gravitational potential at the centre
2R
(6)
(a) increases (b) decreases
Gm mo (c) remains same
(h
(d) 2Gmmo
(c)2R R
(4) during the compression increases then returns at the
previous value
51. A rocket of mass m is launched vertically from the surface of
58. There is a concentric hole of radius R in a solid sphere of
the earth with an initial speed v. Assuming the radius of the
radius 2 R. Mass of the remaining portion is M. What is the
earth to be R and negligible air resistance, the maximum height
gravitational potential at centre?
attained by the rocket above the surface of the earth is

(a)

R
c)
R
52. A particle is projected vertically upward with velocity
FIGURE 3.65
2 GM from the surface of earth. The height attained by it
3 R (a) G M 7 GM
is (G, M and R have usual meanings) 7R
(6)
14R
(a) 3 R (b) R/2
3 GM 9 GM
(c) 2 R (d) R/3
53. Given that the gravitational potential on earth surface is Vo
7R d)
14R
59. A small ball of mass m is released at a height R above the
The potential at a point distant half the radius of earth from
Earth surface, as shown in the fig. 3.66. The maximum depth
the centre will be
of the ball to which it goes is RI2 inside the Earth through a
narrow groove before coming to rest
momentarily. If the groove
(b2 contains 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)
(c) 2 Vo ()
54. If the gravitational acceleration at surface of Earth is g, then
increase in potential energy in lifting an object of mass m to a
m www.
RM
height equal to the radius R of Earth will be
K
mgR (b) 2 mgR
(a)
gR FIGURE 3.66
(c) mgR (4
 (a) GMm
aR (b) GMm

9GMm
(c)
(d)
7GMm
R3 R3 FIGURE 3.68
60. A particle of mass m is
transferred from the centre of the base (a) increases continuously
of a uniform solid
hemisphere of mass M and radius R to (b) decreases continuously
infinity. The work performed in the process by the
force exerted on the gravitational (c) first decreases, then
increases
particle by
the hemisphere is
decreases
3 GMm d) first increases, then
3 GMm and M are placed at distance d apart.
(a)2 R (b) 4 R 66. Two bodies of masses m
The gravitational potential
V at the position where the
field due to them is zero is
gravitational
(c) GMm 3 GMm
R objects
61. Two of masses
(d)- 4

and 2
R (a) V=(m +M) (b) V=-
m m are at rest at infinite
separation. They move towards each other under mutual
gravitational attraction. At the instant, when the separation
(c) V-
GM
d
V--m+
d M2
between them is r, which of the following is true? It has a uniform
67. Asphere of radius R has its centre at the origin.
(a) The total energy of the system is zero mass density Po except that there is a spherical
hole of radius
(b) The force between them is not zero r= RI2 whose centre is at x = RI2 as shown in the fig. 3.69.
The magnitude of gravitational field at a point distant x on the
(c) The centre of mass of the system is at rest
X-axis, where x > R is
d) All are true
62. Two spherical bodies having masses M and 3 M, and radii r YA
and 4 r respectively are released in free space from rest such
that the initial separation between their centres is 13 r. If only
force is gravitational attraction, the distance covered by the
smaller body just before collision is
(a) 6r (b) 2 r

39
FIGURE 3.69
63. Two spherical bodies of masses M and 5 M and radii R and12 4 GTR'PO
R, respectively, are released in free space with initial separation (a)
between their centres equal to 12 R. If they attract each other 8(x-R/2)J
due to gravitational force only, then the distance covered by
the smaller body just before collision is () 4GrR'P 2 -
(b)
(a) 25 R (b) 4-5 R 8 (r R/2)|
(d) 15R
(c) 75 R
(c)
(c)
2GTRPo1
64. Find the distance between centre of gravity and centre of mass 3
of a two particle system. Each particle has same mass.
8(x-R/2)3 J

oRRPOs-R/2*
other paticle is at
One particle is on the surface of earth, the
the centre of earth and R is the radius
of Earth (d) 3

68. The gravitational field in a region is given by

g (4i+j)Nkg-, Work done by this field is zero when a
particle is moved along a line. Choose the correct equation of
the line.
(a) y +4 x= 2 b) 4y+x=6
(c) x+ y = 5 (d) none of these
FIGURE 3.67
(b) RI2 69. A missile is launched with a velocity less than the escape
(a) R
(d) R/4 velocity. The sum of its kinetic and potential energy is
(c) zero
kept at some distance (a) positive (b) negative
65. Two identical symmetric objects
are as

from the surface of one sphere (c) zero

shown. A point mass m is taken
this process, the potential (d) may be positive or negative depending upon its initial
to the surface of other sphere. During
energy of system velocity
 70. When escape velocity is from the surface of the earth
given to a
particle on surface of earth, 78. A projectile is fired straight up
its total energy is air resistance, the ratio of radius R
with velocity v. Neglecting
(a) zero maximum distance from centre of earth to
(b) greater than zero of the earth to the
which the projectile rises is
(c) less than zero GM m
(d)
2R 2 (b)
71. If (a) 1- 2 gR 2 gR
a
particle is projected
from earth's surface in
vertically
upward direction, its escape velocity is u. When it is projected
at an angle 60° with
vertical, the escape velocity will be 2
(c) 1 - (d)
(a) u (6) 2 u gR gR
79. The orbital velocity of a satellite at a height R above the surface
(c)u/2 (d)uv3/2 of the earth is v. What will be the value of the escape velocity
72. The escape velocity from the earth's from the same location?
surface is 11 km/sec.A
certain planet has a radius twice that of the
earth but its mean (b)
density is the same as that of the earth. The value of the escape (a) 2v v

velocity from this planet would be: (d) v/2

(c)v/2
(a) 22 km/sec (b) 11 km/sec 80. If vo be the orbital velocity of an artificial satellite orbiting
(c) 5-5 km/sec () 16-5 km/sec just above the earth's surface, then the orbital velocity of the
73. The ratio of the escape same satellite orbiting at an altitude equal to earth's radius is
velocity from the earth's surface to
that from moon's surface is
3
& = 6 8m Dia, = 4 Dia,)

(a) V12:1
(a) Vo3
6)o2
(b)24:1
Vo
(c)1:12 (d) 1:24 (c) v2
74. Two planets of masses M and
M, are situated r distance apart. 81. Velocity of a point on the equator of a rotating spherical planet
With what minimum velocity should a mass m be
from the mid point of the two
projected is v. The angular velocity of the planet is such that, the value
planets so that it escapes away of g at the equator is half of g at the pole. Determine the
from the gravitational pull of both?
escape velocity for a polar particle on the planet as a function
of v.
(a) G(M+M2) G(M+M,)
()2 (a) 6 v
(c) 4 v
(b) 2 v
(d) 3 v
(c) GM-M
N (d 2GM-M 82. Two satellites A and B go around the earth in circular
orbits at
heights RA and Rg respectively, from the surface of earth.
75. The escape velocity from the earth is Assume the earth to be a uniform sphere of radius
ve A body is projected RE. The
with velocity v> v With what constant ratio of the magnitudes of the velocity, v^hvg of the
velocity will it move satellite is
in the interplanetary
space?
(a) v- Ve (b) v+e (a) RB
RA
76. A particle is thrown
vertically upwards from the surface of
Rg+RE
earth and it reaches to a maximum height
of earth. The ratio of the velocity of
equal to the radius
projection to the escape
RA+R
83. The orbital velocity of an
(dRA Rg
velocity on the surface of earth is artificial satellite in a circular orbit
just above the earth's surface is v. For a satellite
altitude of half of the earth's radius, the orbiting at an
( ()
(a) 3 v/2
orbital velocity is
(b) 3/2v
(c) c)2/3v d) 2 v/3
84. Select the correct alternative
77. A projectile is fired from the surface of earth of radius R with
a velocity kv, (where v, is the escape velocity from surface of (a) The gravitational field inside a
spherical planet must be non-zerospherical cavity, within a
earth and k< 1). Neglecting air resistance, the maximum height and uniform
of rise from the centre of earth is (b) When a body is projected
horizontally at an appreciable
height above the Earth, with a velocity less than for a large
orbit,
it will fall to the circular
(b)R Earth along a
(c) A body of zero total parabolic path
mechanical energy placed
in a
(d) k R
gravitational field will escape the field
(d) Earth's satellite must be in
equatorial plane
85. Two satellites A and B
go around a
planet P in circular orbit
having radii 4 R and R
respectively. If the speed of the satellite (d)R
A is 3 V, the speed of the
satellite B will be
(c)R 2 that the force of attraction
be such
(a) 12 V 93. If the law of gravitation of their
b) 6 V between two particles vary inversely as the 5/2th power
(c) (4/3) V orbital velocity vo plotted against
(d) (3/2) V separation, then the graph of
86. If an artificial satellite is from the earth's center on a log-log
moving in a circular orbit around the the distance r of a satellite
earth with a speed equal to half is
the magnitude of the escape scale is shown. The slope of graph
velocity from the surface of earth, the height of the satellite In Vo
above the surface of the earth is
(Radius of earth is R)
(a) 2 R
(b) R/2
(c)R
(d)R/4
87. Let G be the universal gravitational constant and p be the Inr
uniform density of a
spherical planet. Then shortest possible FIGURE 3.70
period of rotation around a planet can be
(b) - 5/2
(a) - 5/4

(a) TTG (b)

3 TG (c) 3/4
(d) - 1

V2p 94. If the time of revolution of a satellite is T, then its kinetic

to
energy is proportional
() 37T (a) T-3 b)T-3
VGp (c) T-1 (d) T-2
88. An artificial satellite is moving in a circular orbit around the
in a year. If thee
earth with a speed equal to half the magnitude of escape 95. The moon revolves around the earth 13 times
ratio of the distance of the earth from the sun to the distance
velocity from the surface of earth. The height of the satellite
is 392, then ratio of mass of the
above the surface of earth's surface will be (Radius of earth, of the moon from the earth
sun to the mass of the earth is
R 6400 km)
(a) 6000 km (b) 5800 km (392 S/2
3923
(c) 7500 km () 6400 km (a)
132 (615
89. Geostationary satellite orbits around the earth in a circular
orbit at a height of 36000 km from the earth's surface. Then, 392 133
(c)
the time period of a spy satellite orbiting at a height of 1600 133 3922

km above the earth's surface (Rearth = 6400 km) will approxi- 96. A satellite is launched in the equatorial plane in such a way
mately be that it can transmit signals upto 60° latitude on the earth. The
(b) 1 hr angular velocity of the satellite is
(a) 1/2 hr
(c) 2 hr (d) 4 hr GM GM
90. A projectile after deviating from its path, starts moving round
the Earth in a circular path of radius equal to nine times the
@2R
radius of Earth R. Its time period will be GM 33 GM
R (b) 27x 2m,
4R 8R3
(a) 21 97. The radius of a planet is R. A satellite revolves around it in a
circular orbit of radius r with angular speed o. The acceleration

(c) R (d) 0-8x3n due to gravity on planet's surface will be

around earth in an orbit (a)

91. A satellite is in a geostationary orbit
velocity of earth about its axis R2 R
of radius r. If the angular
be in a geostationary orbit around
doubles, the satellite can now
earth of radius (c) (d) ro
R2
98. A geostationary satellite orbits around the earth in a circular
(a)
orbit of radius 36000 km. Then, the time period of a spy
satellite orbiting a few 100 km above the earth's surface
73 (Rearth6400 km) will approximately be
92. the gravitational force varies inversely as the nth (a) 1/2 h (b) 1h
Suppose
power of distance.
Then, the time period a planet in circular
of
(c) 2h (d) 4h
orbit of radius R around the sun will be proportional to
99. An instrument is released from an artificial earth-satellite by
n+l
simply detaching it from the outer wall of the satellite. The
(b) R 2
(a) R" package
 (a) will shoot forward in the same orbit with double the 108. A sateilite is seen after each 8 h over the equator at a plane on
velocity of the satellite the earth when its sense of rotation is opposite to the earth.
(6) will go to the outer space and will get lost The time interval after which it can be seen at the same place
when the sense of rotation of the earth and the satellite is the
(c)will fall to the earth below
same will be
(d) will continue moving along with the satellite into the same
(a) 8 h (b) 12 h
orbit and with the same velocity
(c) 24 h (d) 6 h.
100. A particle is projected upwards from the surface of earth
(radius = R) with a speed equal to the orbital speed of a satellite 109. A satellite is revolving around the earth with orbital speed vo
near the earth's surface, The height to which it would rise is If it stops suddenly, the speed with which it will strike the
surface of earth would be
(a) 2R (b) R/V2 velocity of a particle on earth's surface)
(c)R
(v =
escape
(d) 2R
101. In a gravitational field, a body at a given position has
(a) (b) o
(a) binding energy which increases as its speed increases Vo
(b) binding energy which is independent of its speed
(c) zero binding energy when it is at rest - (d) - 2
(d) maximum binding energy when it is at rest 110. A satellite is in a circular orbit very close to the surface of a
planet. At some point it is given an impulse along its direction
102. An artificial satellite moving in circular orbit around the earth
of motion, causing its velocity to increase n times. It now goes
has a total (kinetic + potential) energy Eo. Its PE. is
into an elliptical orbit. The maximum possible value of n for
(a)-Eo (b) 1.5 Eo this to occur is
(c) 2 Eo (d) E
103. The kinetic energy of a satcllite in its orbit around the earth is
) 2 (b) 2
E. What should be the minimum kinetic energy of the satellite
(c) 2+1
so as to enable it escape from the gravitational pull of the
earth? -1
111. Two satellites of same mass m are launched in the same orbit
(a) 4 E (b) 2 E r around the earth of mass M so as to rotate opposite to each
(c) V2E other. If they collide inelastically and stick together as
(d) E wreckage, the total energy of the system just after collision is
104. Two satellites of earth, S and S2 are moving in the same orbit.
The mass of S is four times the mass of S2. Which one of the (a) 2 G I M m (b)GMm
following statements is true? r
(a) The potential energies of earth and satellite in the two GM m
cases are equal (c) (d) GM m
2r 4r
(6) S1 and S2 are moving with the same speed
112. A satellite of mass m revolving in circular orbit of radiusr
(c) The kinetic energies of the two satellites are equal
around the earth of mass M has binding energy E. The angular
(d)The time period of S, is four times that of S momentum of the satellite will be
105. By what percent, the magnitude of energy of a satellite has to
be increased to shift it from an orbit of radius r to 3 r/2? (a) 2Emr (6) 2Emr
(a) 66-7% (b) 33-3%
(c) Emr (d) E mr
(c) 15% (d) 20-3%
113. A satellite S is moving in an elliptical orbit around the earth.
106. The energy required to launch a satellite of mass m from the The mass of the satellite is very small compared to the mass
surface of earth of radius R in a circular orbit at an altitude of the earth. Then,
2R is (mass of earth is M)
(a) the acceleration of S is always directed towards the centre
(a) m M (b) G m M of the earth
6R 3R (b) the angular momentum of S about the centre of the earth
changes in direction but its magnitude remains constant
(c)
Gm M
(d) GmM (c) the total mechanical energy of S varies periodically with
2R 3R
time
107. A satellite of mass m is moving around the earth in a circular (d) the linear momentum of S remains constant in magnitude
orbit of radius r. If the mass of the earth is M, then the energy
114. When a body is projected at an angle with the horizontal in
required to take the satellite to an orbit of radius 3 r is the uniform gravitational field of the earth, the angular
GM m momentum of the body about the centre of earth as it proceeds
(a) M mn
(b)2r along its path

GM m (a) remains constant

GM m (d)
(c)3r 6r 6) increases
 (c) decreases are separated
119. Two massive particles of mass M and m (M> m) under
(d) initially decreases and then rotate with equal angular velocity
increases after reaching its by a distance d. They
highest point. their gravitational attraction. The linear speed of the particle
115. In reference frame fixed to sun,
a of mass m is
(a) power associated with the
gravitational force for a
planet GM m GM
revolving around the sun in (b) M+ m) d
(b) work done by the sun on the
an
elliptical
planet is
orbit is
always zero
zero
(a)M+m) d
(c) work done by the sun on the Gm2
planet is zero for complete GM
revolution of its path
(d) the gravitational force
acting on the planet is equal to
dM+m)d
120. Three identical particles each of mass M move along
a common

centripetal force m where v is speed of planet and r circular path of radius R under the mutual interaction of each
other. The velocity of each particle is
is distance between sun
and planet
116. A point P is on the axis of a fixed GM
ring of mass M and radius R,
at a distance 2 R from the
from P and reaches O under the
centre O. A small
particle starts
() R
b)3R
Its speed at O will be gravitational attraction only.

(a) zero 2 GM
() 3R
3 R
121. Four particles of equal mass M move along a circle of radius
R
R under the action of their mutual gravitational attraction. The

(c) 2GM
R (5-1)
- (d
speed of each particle is

117. A system of binary stars of masses ( R 2 2.GM

circular orbits of radii ra and
m and mg are moving in
rg respectively. If TA and Tg are
R
the time periods of masses
m and mg respectively, then
GM2+1
3/2 2-1)
(b) TA TB (ifrA> ) 122. A straight smooth tunnel is dug through a spherical planet whose
mass Po constant. The tunnel passes through the centre
density is
(c)TA Tp if m> m) ()TA TB of the planet and is perpendicular to the planet's axis of rotation.
118. Two particles of equal mass m go around a circle of radius R which is fixed in space. The planet rotates with the angular
under the action of their mutual gravitational attraction. The velocity @ so that objects in the tunnel have no acceleration
speed of each particle with respect to their centre of mass is relative to the tunnel. Find the value of o.

Gm Gm
R b4R
Gm Gm
c)3R (2R () GPo ) 2GPo
 ASSIGNMENT-1

MCOs Having One Correct Answer Only

1. (b) 2. (d) 3. (b) 4. (b) 6. (c) 7. (d) 8. (a) 9. (a) 10. (c)
5. (c)
11. (d) 12. (d) 13. (b) 14. (a) 15. (a) 16. (b) 17. (a) 18. (c) 19. (c) 20. (a)
21. (d) 22. (a) 23. (d) 24. (b) 25. (d) 26. (a) 27. (c) 28. (b) 29. (c) 30. (a)
31. (b) 32. (d) 33. (b) 34. (c) 35. (c) 36. (d) 37. (c) 38. (a) 39. (b) 40. (c)
41. (b) 42. (d) 43. (c) 44. (c) 45. (b) 46. b) 47. (a) 48. (d) 49. (a) 50. (b)
51. (c) 52. (b) 53. (d) 54. (a) 55. (a) 56. (c) 57. 6) 58. (d) 59. (d) 60. (a)
61. (d) 62. (a) 63. (c) 64. (b) 65. (d) 66. (d) 67. (a) 68. (a) 69. (b) 70. ()
71. (a) 72. (a) 73. (b) 74. (b) 75. (d) 76. (a) 77. (c) 78. (a) 79. (a) 80. (d)
81. (b) 82. (d) 83. (c) 84. (c) 85. (b) 86. (c) 87. (d) 88. (d) 89. (c) 90. (b)
91. (c) 92. (b) 93. (c) 94. (b) 95. (a) 96. (b) 97. (c) 98. (c) 99. (d) 100. (c)
101. (d) 102. (c) 103. (b) 104. (b) 105. (b) 106. (a) 107. (c) 108. (c) 109. (d) 110. (b)
111. (a) 112. (b) 113. (a) 114. (a) 115. (c) 116. (d) 117. () 118. (b) 119. (b) 120. (b)
121. (c) 122. (a)