GRAVITATION

EXERCISE # 1
Q.1 Two satellites S1 and S2 revolve round a planet in the same direction in circular orbits. Their period of revolution
are 1 hour and 8 hour respectively. The radius of S 1 is 104 km. The velocity of S2 with respect to S1 will be
[1]  × 104 km/hr [2] /3 × 104 km/hr [3] 2 × 104 km/hr [4] /2 × 104 km/hr
Q.2 In the above example the angular speed of S2 as actually observed by an astronaut in S1 is
[1] /3 rad/hr [2] /3 rad/sec [3] /6 rad/hr [4] 2/7 rad/hr
Q.3 A mass M splits into two parts m and (M – m), which are then separated by a certain distance. What ratio
(m/M) maximies the gravitational force between the parts ?

2 3 1 1
[1] [2] [3] [4]
3 4 2 3

1
Q.4 If an object having mass 3 kg in moving with a velocity that is the velocity of light then inertial mass will
2
be

[1] 2 kg [2] 1 kg [3] 3 kg [4] 0 kg

Q.5 What would be the angular speed of earth, so that bodies lying on equator may appear weightless ?
(g = 10m/s2 and radius of earth = 6400 km)
[1] 1.25 × 10–3 rad/sec [2] 1.25 × 10–2 rad/sec [3] 1.25 × 10–4 rad/sec [4] 1.25 × 10–1 rad/sec
Q.6 The speed with which the earth have to rotate on its axis so that a person on the equator would weight
(3/5)th as much as present will be (Take the equatorial radius as 6400 km.)
[1] 3.28 × 10–4 rad/sec [2] 7.826 × 10–4 rad/sec [3] 3.28 × 10–3 rad/sec [4] 7.28 × 10–3 rad/sec
Q.7 On a planet (whose size is the same as that of earth and mass 4 times to the earth) the energy needed to
lift a 2kg mass vertically upwards through 2m distance on the planet is (g = 10m/sec 2 on surface of earth)
[1] 16 J [2] 32 J [3] 160 J [4] 320 J
Q.8 Two bodies of mass 100 kg and 104 kg are lying one meter apart. At what distance from 100 kg body will
the intensity of gravitational field be zero

1 1 1 10
[1] m [2] m [3] m [4] m
9 10 11 11

Q.9 Two bodies of mass 102 kg and 103 kg are lying 1m apart. The gravitational potential at the mid-point of the
line joining them is
[1] 0 [2] –1.47 Joule/kg [3] 1.47 Joule/kg [4] –147 × 10–7 joule/kg
Q.10 If g is the acceleration due to gravity on the earth’s surface, the gain in P.E. of an object of mass m raised
from the surface of the earth to a height of the radius R of the earth is

1 1
[1] mgR [2] 2mgR [3] mgR [4] mgR
2 4

Q.11 The mass and radius of earth and moon are M1, R1 and M2, R2 respectively. Their centres are d distance apart.
With what velocity should a particle of mass m be projected from the mid point of their centres so that it may
escape out to infinity.

G(M1  M2 ) 2G(M1  M2 ) 4G(M1  M2 ) GM1M2

[1] [2] [3] [4]
d d d d

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Q.12 A satellite has to revolve round the earth in a circular orbit of radius 8 × 10 3 km. The velocity of projection
of the satellite in this orbit will be
[1] 16 km/sec [2] 8 km/sec [3] 3 km/sec [4] 7.08 km/sec
Q.13 The moon revolves round the earth 13 times in one year. If the ratio of sun-earth distance to earth-moon distance
is 392, then the ratio of masses of sun and earth will be
[1] 365 [2] 356 [3] 3.56 × 105 [4] 1

OA
Q.14 The earth is revolving round the sun in an elliptical orbit. If  x, the ratio of speeds of earth at B and A
OB
will be

[1] x [2] x [3] x2 [4] x x

Q.15 A satellite of mass m is revolving in a circular orbit of radius r. the relation between the angular momentum J of
satellite and mass m of earth will be

mr
[1] J  G .Mm 2r [2] J  GMm [3] J  GMmr [4] J 
M

Q.16 A space ship is launched into a circular orbit close to earth’s surface. What additional velocity has now to
be imparted to the space ship in the orbit to overcome the gravitational pull ? (radius of earth = 6400 km,
g = 9.8 m/sec2)
[1] 3.285 km/sec [2] 32.85 m/sec2 [3] 11.32 km/sec [4] 7.32 m/sec
Q.17 The radio of the radius of the earth to that of the moon is 10. The ratio of g an earth to the moon is 6. The
ratio of the escape velocity from the earth’s surface to that from the moon is approximately
[1] 10 [2] 8 [3] 4 [4] 2
Q.18 Acceleration due to gravity on a planet is 10 times the value on the earth. Escape velocity for the planet and
the earth are Vp and Ve respectively Assuming that the radii of the planet and the earth are the same, then

Ve
[1] VP = 10 Ve [2] VP = 10 Ve [3] VP  [4] V  Ve
P
10 10

Q.19 A satellite is moving round the earth. In order to make it move to infinity, its velocity must be increased by
[1] 20% [2] it is impossible to do so
[3] 82.8% [4] 41.4%
Q.20 A space shuttle is launched in a circular orbit near the earth's surface. The additional velocity be given to the
space-shuttle to get free from the influence of gravitational force, will be
[1] 1.52 km/s [2] 2.75 km/s [3] 3.28 km/s [4] 5.18 km/s
Q.21 If the radius of earth is to decrease by 4% and its density remains same, then its escape velocity will
[1] remain same [2] increase by 4% [3] decrease by 4% [4] increase by 2%
Q.22 A body of mass m is situated at a 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

mgR e mgR e
[1] mgRe [2] 2mgRe [3] [4]
5 16

Q.23 The potential energy of a body of mass 3kg on the surface of a planet is 54 joule. The escape velocity will be
[1] 18m/s [2] 162 m/s [3] 36 m/s [4] 6 m/s

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Q.24 The escape velocity from a planet is v0. The escape velocity from a planet having twice the radius but same density
will be
[1] 0.5 v0 [2] v0 [3] 2v0 [4] 4v0
Q.25 If the kinetic energy of a satellite orbiting around the ear:th is doubled then
[1] the satellite will escape into the space. [2] the satellite will fall down on the earth
[3] radius of its orbit will be doubled [4] radius of its orbit will become half
Q.26 The escape velocity from the earth does not depend upon
[1] mass of earth [2] mass of the body [3] radius of earth [4] acceleration due to gravity
Q.27 The relation between the escape velocity from the earth and the velocity of a satellite orbiting near the earth's
surface is

[1] ve = v [2] ve = V 2 [3] ve = 2v [4] ve = v / 2

Q.28 There is no atmosphere on moon because

[1] it is near the earth [2] it is orbiting around the earth
[3] there was no gas at all
[4] the escape velocity of gas molecules is less than their root-mean square velocity
Q.29 A missile is launched with a velocity less than the escape velocity. The sum of kinetic energy and potential energy
will be
[1] positive [2] negative [3] negative or positive, uncertain [4] zero
Q.30 The escape velocity is

[1] 2gR [2] gR [3] gR [4] 2gR

Q.31 An earth satellite is moved from one stable circular orbit to another higher stable circular orbit. Which one of the
following quantities increases for the satellite as a result of this change
[1] gravitational force [2] gravitational potential energy [3] centripetal acceleration [4] Linear orbital speed
Q.32 The relay satellite transmits the television programme continuously from one part of the world to another because
its
[1] period is greater than the period of rotation of the earth
[2] period is less than the period of rotation of the earth about its axis
[3] period has no relation with the period of the earth about its axis
[4] period is equal to the period of rotation of the earth about its axis
Q.33 A satellite appears to be at rest when seen from the equator. Its height from the earth's surface is nearly
[1] 35800km [2] 358000 km [3] 6400km [4] such a satellite cannot exist
Q.34 A body is dropped by a satellite in its geo-stationary orbit
[1] it will burn on entering into the atmosphere [2] it will remain in the same place with respect to the earth
[3] it will reach the earth in 24 hours [4] it will perform uncertain motion
Q.35 A satellite of earth can move only in those orbits whose plane coincides with
[1] the plane of great circle of earth [2] the plane passing through the poles of earth
[3] the plane of a circle at any latitude of earth [4] none of these
Q.36 If the universal constant of gravitation were decreasing uniformly with time, then a satellite in orbit would still
maintain its
[1] radius [2] tangential speed [3] angular momentum [4] period of revolution

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Q.37 A planet is moving in an elliptic orbit. If T, V, E, L stand respectivley for its kinetic energy, gravitational potential
energy, total energy and magnitude of angular momentum about the centre of force, which of the following state-
ments is correct
[1] T is conserved
[2] V is always positive
[3] E is always negative

[4] L is conserved but the direction of vector L changes continuously

Q.38 A satellite launching station should be

[1] near the equatorial region [2] near the polar region
[3] on the polar axis [4] all locations are equally good
Q.39 The INSAT 1-B satellite was launched -
[1] from SHAR in Karnataka [2] aboard U.S. space Shuttle challenger
[3] aboard the Soviet spaceship SOYUZ-7 [4] from France
Q.40 The minimum number of satelites needed to be placed at the surface of earth for world-wide communication
between any two locations is -
[1] 6 [2] 4 [3] 3 [4] 5
Q.41 Which of the following Indian sateelites has the maximum period of revolution -
[1] Aryabhatta [2] Bhaskara [3] Rohini [4] INSAT-1B
Q.42 Consider a satellite going round the earth in a circular orbit. Which of the following statements is wrong
[1] it is a freely falling body
[2] it is acted upon by a force directed away from the centre of the earth which counter balances the gravitational pull
[3] it is moving with a constant speed
[4] its angular momentum remains constant
Q.43 The ratio of distances of satellites A and 8 above the earth's surface is 1.4 : 1, then the ratio of energies of
satellites 8 and A will be
[1] 1.4 : 1 [2] 2 : 1 [3] 1 : 3 [4] 4 : 1
Q.44 If mass of earth is 5.98 x 1024 kg and earth moon distance is 3.8 x 105 km, the orbital period of moon, in days is
[1] 27 days [2] 2.7 days [3] 81 days [4] 8.1 days
Q.45 With what velocity a satellite is to be projected to establish it at a height 6R above the earth's surface-
(g = 9.8m/s2 and R = 6400 km)
[1] 11.2 km/s [2] 10.4 km/s [3] 8.6 km/s [4] 7.9 km/s
Q.46 The period of revolutions of two satellites are 3 hours and 24 hours. The ratio of their velocities will be
[1] 1 : 8 [2] 1 : 2 [3] 2 : 1 [4] 4 : 1
Q.47 The average radii of orbits of mercury and earth around the sun are 6 x 107 km and 1.5 x 108 km respectively, The
ratio of their orbital speeds will be

[1] 5: 2 [2] 2: 5 [3] 2.5 : 1 [4] 1 : 25

Q.48 A satellite is projected with a velocity 1.5 times the orbital velocity just above the surface of earth. Initial velocity
of the satellite is parallel to the surface of earth. The maximum distance of the satellite from earth will be
[1] 2Re [2] 8Re [3] 4Re [4] 3Re

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Q.49 The ratio of kinetic and potential energies of a satellite is

[1] 1 : 4 [2] 4 : 1 [3] 1 : 2 [4] 2 : 1
Q.50 The ratio of kinetic energy of a body orbiting near the earth's surface and the kinetic energy of the same body
escaping the earth's gravitational field is

[1] 1 [2] 2 [3] 2 [4] 0.5

Q.51 A satellite of earth is moving in its orbit with a constant speed v. If the gravity of earth suddenly vanishes, then this
satellite will
[1] continue to move in the orbit with velocity v.
[2] start moving with velocity v in a direction tangential to the orbit
[3] fall down with increased velocity
[4] be lost in outer space.
Q.52 A satellite is moving in a circular orbit around earth with a speed v. If its mass is m, then its total energy will be
3 1 1
[1] mv 2 [2] mv2 [3] mv 2 [4]  mv 2
4 2 2

Q.53 Two artificial satellites A and B are at a distances rA and rB above the earth's surface. If the radius of earth is R, then
the ratio of their speeds will be

1/ 2 2 2 1/ 2
 rB  R   rB  R   rB   rB 
[1]   [2]   [3]   [4]  
 rA  R   rA  R   rA   rA 

Q.54 Orbital velocity of INSAT 1-B is nearly

[1] 11.2 km/s [2] 7.9 km/s [3] 2.6 km/s [4] 1.8 km/s
Q.55 An astronaut feels weightlessness because
[1] gravity is zero there
[2] atmosphere is not there
[3] energy is zero in the chamber of a rocket.
[4] the fictitious force in rotating frame of reference cancels the effect of weight.
Q.56 Binding energy of moon and earth is

GMeMm GMeMm GMeMm GMeMm

[1] rem [2] 2rem [3]  rem [4]  2rem

Q.57 The formula of period of revolution of a satellite is

R R2 GM R3
[1] T  2 [2] T  2 [3] T  2 [4] T  2
GM GM R3 GM

Q.58 The period of revolution of a communication satellite of earth is

[1] zero [2] 4.8 hours [3] 36 hours [4] 24 hours
Q.59 If a satellite is orbiting very near to the earth's surface than its orbital velocity depends upon
[1] mass of the satellite [2] mass of earth only [3] radius of earth only [4] mass and radius of earth
Q.60 In an artificial satellite a person will have
[1] zero mass [2] zero weight [3] some weight [4] infinite weight

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Q.61 Following quantity is conserved in the motion of a satellite -

[1] angular velocity [2] linear velocity [3] some weight [4] linear momentum
Q.62 A satellite moves in a path of radius r with a velocity v, the mass of earth will be

vr v 2r Gr G
[1] [2] [3] 2 [4]
G G v vr 2
Q.63 A satellite of mass m is revolving around the earth of mass M in a path of radius r, the angular velocity of the
satellite will be

GM G GM
[1] M Gr [2] [3] M [4]
r r r3
Q.64 The velocity of a satellite orbiting near the earth's surface is

GM
[1] GR [2] gR [3] [4] 2gR
R2
Q.65 For a satellite revolving with time period T at a distance r from the centre of earth, the following remains constant

T T2 T3
[1] [2] T2r3 [3] [4]
R R3 R2
Q.66 Kinetic energy of a satellite will be

GmM GmM GmM GmM

[1] 2 [2] 2r [3] 2 [4]
2r r r
Q.67 The velocity of a satellite at a height h above the earth's surface is

GM GM GM GM
[1] [2] 2 [3] [4]
R R h Rh
Q.68 A particle falls on earth: (i) from infinity (ii) from a height 10 times the radius of earth. The ratio of the velocities
gained on reaching at the earth's surface is

[1] 11 : 10 [2] 10 : 11 [3] 10 : 11 [4] 11 : 10

Q.69 The intensity of gravitational field at a point situated at a distance of 8000 km from the centre of the earth is 6N/kg.
The gravitational potential at that point is - (in joule/kg)
[1] 8 x 106 [2] 2.4 x 103 [3] 4.8 x 107 [4] 6.4 x 1014
Q.70 The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

[1] [2] [3] [4]

Q.71 By which curve will the variation of gravitational potential of a hollow sphere of radius R with distance be depicted ?

[1] [2] [3] [4]

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Q.72 The potential energy due to gravitational field of earth will be maximum at
[1] infinite distance. [2] the poles of earth [3] the centre of earth [4] the equator of earth
Q.73 A body is in a state of rest at infinite distance. If it is made a satellite of earth, which of the following physical
quantities will be reduced
[1] gravitational force [2] kinetic energy [3] potential energy [4] mass
Q.74 If g denotes the value of acceleration due to gravity at a point distant r from the centre of earth of radius R. Then if
r < R, then

1 1
[1] g  2 [2] g  [3] g  r [4] g  r 0
r r

Q.75 In above question if r > R then

1 1
[1] g  2 [2] g  [3] g  r [4] g  r 0
r r

Q.76 There is a body lying on the surface of the earth and suppose the earth suddenly loses its power of attraction then
[1] the mass of the body will be reduced to zero [2] the weight of the body will be reduced to zero
[3] both will be reduced to zero [4] it becomes infinity
Q.77 A body of mass m is taken to the bottom of a deep mine. Then
[1] its mass increases [2] its mass decreases [3] its weight increases [4] its weight decreases
Q.78 Weightlessness experienced while orbiting the earth, in space-ships, is the result of
[1] inertia [2] acceleration [3] zero gravity [4] centre of gravity
Q.79 There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the
smaller body, the intensity of gravitational field will be zero ?

1 1 1 10
[1] m [2] m [3] m [4] m
9 10 11 11

Q.80 Two boys of masses 50kg and 60kg are 1m apart. The gravitational force of attraction between them
(G=6.67 x 10–11 N x m2/kg2) is
[1] 2 x 10–10 N [2] 2 x 10–7 N [3] 2 x 10–4 N [4] 2 x 10–1 N
Q.81 ge and gv denote the acceleration due to gravity on the surface of the earth and another planet whose mass and
radius are twice that of the earth. Then

ge
[1] gv = ge [2] gv = ge/2 [3] gv = 2ge [4] g v 
2

Q.82 If 'R' is the radius of earth and 'g' the acceleration due to gravity then mass of earth will be :

gR 2 g 2R Rg GR 2
[1] [2] [3] [4]
G G G g

Q.83 A body suspended from a spring balance is placed in a satellite. Reading in balance is W 1 when the satellite
moves in an orbit of radius R. Reading in balance is W 2 when the satellite moves in an orbit of radius 2R. Then
[1] W1 = W2 [2] W1 > W2 [3] W1 < W2 [4] W1 = 2W2
Q.84 The acceleration due to gravity of that planet whose mass and radius are half those of earth, will be (g is accelera-
tion due to gravity at earth's surface)
[1] 2g [2] g [3] g/2 [4] g/4

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Q.85 Atmospheric pressure shown by a barometer placed in a moving lift will be

[1] greater if lift descends with acceleration. [2] less if lift descends with retardation

[3] greater if lift descends with retardation [4] less if lift ascends with constant velocity

Q.86 The weight of a body is half of the weight at the surface of earth when the height above the earth's surface is nearly-

[1] 2000km [2] 2600km [3] 3200km [4] 6.5 km

Q.87 If the distance between the centres of earth and moon is D and mass of earth is 81 times that of moon. At what
distance from the centre of earth the gravitational field will be zero

[1] D/2 [2] 2D/3 [3] 4D/5 [4] 9D/10

Q.88 The value of g on the surface of earth is 9.8 m/s2 and the radius of earth is 6400km. The average density of earth
in kg/m3 will be

[1] 5.29 x 103 [2] 2.64 x 103 [3] 7.60 x 103 [4] 1.46 x 103

Q.89 If acceleration due to gravity at any point is g/2, then the intensity of gravitational field at that point will be

[1] g/2 [2] 2g [3] g [4] zero

Q.90 If a person can jump on the earth's surface upto a height of 2m, his jump on a satellite where acceleration due to
gravity is 1.96 m/s2, will be

[1] 5m [2] 10m [3] 20m [4] 2m

1
Q.91 The mass of moon is 1/81 of the mass of earth and the acceleration due to gravity is th of acceleration due to
6
gravity on earth. The ratio of radii of moon and earth is

[1] 6/81 [2] 4/729 [3] 2 / 27 [4] 2 / 48

Q.92 If the diameter of the earth becomes twice its present value but its mass remains unchanged, then the weight of
an object on the surface of earth will be

[1] two times [2] four times [3] one-fourth [4] eight times

Q.93 The curve depicting the dependence of intensity of gravitational field on the distance r from the centre of the earth is

[1] [2] [3] [4]

Q.94 On increasing the angular velocity of the earth, the value of g in India

[1] will decrease [2] will increase [3] will remain unchanged [4] can increase or decrease.

Q.95 If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density d and
the distance r from the centre of earth will be

[1] d  r [2] d  r1/2 [3] d  1/r [4] d  1/r2

Q.96 The acceleration due to gravity

[1] is constant [2] increases on going below the earth's surface

[3] is maximum at equator [4] is zero at the centre of earth

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Q.97 If keeping the radius constant earth is assumed to be made of iron whose density is 7.5 gm/cm3, then the value of g
[1] remains unchanged because its radius is not changed.
[2] decreases
[3] increases
[4] becomes infinite because iron is ferro-magnetic.
Q.98 Newton's law of gravitation is called universal law because
[1] force is always attractive
[2] it is applicable to lighter and heavier bodies
[3] it is applicable at all times
[4] it is applicable at all places of universe for all distances between all particles.
Q.99 If the density of a planet is constant, then the curve between the g on its surface and its radius r will be

[1] [2] [3] [4]

Q.100 The acceleration due to gravity will be maximum

[1] at the earth's surface [2] at the centre of the earth
[3] in the aeroplane flying at a height of 5 km [4] at a depth 5 km below the earth's surface
Q.101 The acceleration due to gravity will be minimum
[1] at north pole [2] at south pole
[3] at equator [4] at mid point between the equator and the pole
Q.102 Which of the following statement is wrong for acceleration due to gravity
[1] g deaeases on going above the surface of earth [2] g increases on going below the surface of earth
[3] g is maximum at poles [4] g increases on going from equator to poles
Q.103 Acceleration due to gravity at the centre of the earth is
[1] 9 [2] g/2 [3] zero [4] infinite
Q.104 A bomb explodes on the moon. On the earth
[1] we will hear the sound after,1 0 minutes [2] we will hear the sound after 2 hours 18 minutes
[3] we will hear the sound after 37 minutes [4] we can not hear the sound of explosion
Q.105 The relation between acceleration due to gravity g and gravitational constant G is

G GR 2 GM
[1] g  2 [2] g  [3] g  [4] g = GMR2
MR M R2

Q.106 Which of the following formula is correct- (d is the density of earth)

4 4 4 dG 4 dG
[1] g  Gd [2] g  RGd [3] g  [4] g 
3 3 3 R 3 R2

Q.107 The weight of a body at the centre of the earth will

[1] be greater than that at earth's surface [2] be equal to zero
[3] be less than that at earth's surface. [4] become infinite.

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Q.108 The orbital speed of Jupiter is

[1] greater than the orbital speed of earth [2] less than the orbital speed of earth
[3] equal to orbital speed of earth [4] zero
Q.109 Venus looks brighter than other stars because
[1] It is heavier than other stars [2] It has higher density than other stars
[3] It is closer to the earth than other stars [4] It has no atmosphere
Q.110 Orbit traced out by a planet around the sun is in general
[1] circular [2] elliptical [3] parabolic [4] none of the above
Q.111 The gravitational force between two bodies is
[1] repulsive at short distances [2] attractive at large distances
[3] repulsive at large distances [4] attractive at all distances
Q.112 The first successful determination of G in the laboratory was carried out by
[1] Sir Airy [2] Maskylene [3] Cavendish [4] Faraday
Q.113 Newton's law of gravitation
[1] can be inferred only from the behaviour of the planets
[2] can be directly verified in a laboratory
[3] accounts for the speed of rotation of planets about their axes
[4] is valid only in the solar system
Q.114 If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect ?
[1] viscous force [2] Archimedes uplift [3] electrostatic force [4] magnetic force
Q.115 The ratio of the inertial mass to gravitational mass is equal to
[1] 1/2 [2] 1 [3] 2 [4] no fixed number
Q.116 Newton's law of gravitation is true for
[1] only uncharged particles [2] only for planets
[3] only for heavenly bodies [4] all the bodies
Q.117 Gravitational force Fg and electric force Fe are acting between two electrons which are at a distance of 10cm from
Fg
each other. The order of the ratio will be
Fe

[1] 1036 [2] 10 [3] 10–36 [4] 10–43

Q.118 On doubling the distance between two masses the gravitational force between them will
[1] remain unchanged [2] become one-fourth [3] become half [4] become double
Q.119 Two metallic spheres of same radius R and same material are in contact with each other, the force of attraction
between them will be

1 1
[1] F  R2 [2] F  R4 [3] F  2 [4] F 
R R4

1
Q.120 Consider a particle moving in a circular orbit under the action of an attractive central force F  . Its orbital period
r
T will depend on r as.

1
[1] T  r3/2 [2] T  r [3] T  r2/3 [4] T 
r
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Q.121 Newton's law of gravitation

[1] is not applicable outside the solar system.

[2] is used to govern the motion of satellites only

[3] controls the rotational motion of satellites and planets

[4] controls the rotational motion of electrons in atoms

Q.122 The periods of revolution of two artificial satellites X and Y moving around earth are Tx and Ty respectively. The ratio
of their distances from the centre of earth is
1/ 2 2/3 3/2
Tx  Tx   Tx   Tx 
[1] T [2]   [3]   [4]  
y  Ty   Ty   Ty 

Q.123 Upto which distance the gravitational law is applicable

[1] 108m [2] 1 m [3] 10–10m [4] at all distances

Q.124 Approximate mass of earth in kg is

[1] 1040 [2] 1025 [3] 1000 [4] 1010

Q.125 The paths of planets moving around the sun are

[1] circular [2] elliptical [3] parabolic [4] hyperbolic

ANSWER KEY EXERCISE # 1

Que . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A ns . 1 1 3 1 1 2 3 3 4 3 3 4 3 1 1
Que . 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A ns . 1 2 2 4 3 3 3 4 3 1 2 2 4 2 4
Que . 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
A ns . 2 4 1 2 1 3 3 1 2 3 2 2 1 1 2
Que . 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A ns . 3 1 4 3 4 2 4 1 2 4 2 4 4 4 2
Que . 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
A ns . 3 2 4 2 3 2 4 1 3 3 3 1 3 1 3
Que . 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
A ns . 2 4 2 3 2 2 1 1 1 2 2 4 1 1 2
Que . 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
A ns . 3 3 1 1 3 4 3 4 1 1 3 2 3 4 3
Que . 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
A ns . 2 2 2 4 2 4 3 2 2 2 4 4 2 2 2
Que . 121 122 123 124 125
A ns . 3 3 4 2 2

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EXERCISE # 2
Q.1 The radii of paths of two planets moving around the sun are R 1 and R 2 and their periods are T 1 and T2
respectively, T 1/T2 will be

3/2 3/2 1/ 2 1/ 2
 R2   R1   R2   R1 
[1]   [2]   [3]   [4]  
 R1   R2   R1   R2 

Q.2 The dimensions of G are

[1] ML3T–2 [2] M–1LT–2 [3] M–1L3T–2 [4] M–1L4T–2

Q.3 The Jupiter’s period of revolution round the sun is 12 times that of the earth. Assuming the planetary orbits to
circular, how many times the distance between the Jupiter and sun exceeds that between the earth and the sun.
[1] 5.242 [2] 4.242 [3] 3.242 [1] 2.242
Q.4 The mean distance of mars from sun is 1.524 times the distance of the earth from sun. The period of revolution of
mars around sun will be
[1] 2.88 earth year [2] 1.88 earth year [3] 3.88 earth year [4] 4.88 earth year
Q.5 The semi-major axes of the orbits of Mercury and Mars are respectively 0.387 and 1.524 in astronomical units. If
the period of Mercury is 0.241 year, what is the period of Mars.
[1] 1.2 years [2] 3.2 years [3] 3.9 years [4] 1.9 years
Q.6 If a graph is plotted between T2 and r3 for a planet then its slope will be

4 2 GM
[1] [2] [3] 4 GM [4] 0
GM 4 2

Q.7 Four particles, each of mass m, are placed at the corners of square and moving along a circle of radius r under the
influence of mutual gravitational attraction. The speed of each particle will be

GM Gm Gm  2 2  1  2 2 Gm
[1] (2 2  1) [2] [3] [4]
r r r  4  r

Q.8 Three particles of equal mass m are situated at the vertices of an equilateral triangle of side . What should be the
velocity of each particle, so that they move on a circular path without changing .

GM GM 2GM GM
[1] [2] [3] [4] 3
2  
Q.9 What will be the acceleration due to gravity on the surface of the moon if its radius is 1/4 th the radius of the earth
and its mass is 1/80 th the mass of the earth.
[1] g/6 [2] g/5 [3] g/7 [4] g/8
Q.10 The speed with which the earth would have to rotate on its axis so that a person on the equator would weight
3/5 th as much as at present, will be (Take the equatorial radius as 6400 km.)
[1] 7.8 x 10-3 radian/sec [2] 7.8 x 10-4 radian/sec [3] 7.8 x 10-5 radian/sec [4] 7.8 x 10-2 radian/sec
Q.11 At what height above the earth’s surface the acceleration due to gravity will be 1/9 th of its value at the earth’s
surface? Radius of earth is 6400 km.
[1] 12800km [2] 1280km [3] 128000km [4] 128km
Q.12 If the radius af the earth were to shrink by one percent, its mass remaining the same, the acceleration due to
gravity on the earth's surface would
[1] decrease [2] remain unchanged [3] increase [4] none of these

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Q.13 At what height above the Earth's surface does the force of gravity decrease by 10%. Assume radius of earth to be
6370 km.
[1] 350km [2] 250km [3] 150km [4] 300km
Q.14 A particle is suspended from a spring and it stetches the spring by 1 cm on the surface of earth. The same particle
will stretches the same spring at a place 800 km above earth surface by
[1] 0.79 cm [2] 0.1 cm [3] /6 rad/hr [4] 2/7 rad/hr
Q.15 The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar
eclipse to the position on the other side of earth in line with sun is - (mass of moon = 7.36 x 10 22 kg, the orbital
radius of moon 3.8 x 108m)
[1] 6.73 x 10–2 m/s2 [2] 6.73 x 10–3 m/s2 [3] 6.73 x 10–4 m/s2 [4] 6.73 x 10–5 m/s2
Q.16 With what velocity must a body be thrown upward form the surface of the earth so that it reaches a height of
10 Re ? Earth's mass Me = 6 x 1024 kg, radius Re = 6.4 x 106 m and G = 6.67 x 10–11 N-m2/kg2.
[1] 10.7 x 104m/s [2] 10.7 × 103 m/s [3] 10.7 x 105m/s [4] 1.07 × 104 m/s
Q.17 The radius of the earth is Re and the acceleration due to gravity at its surface is g. The work required in raising a
body of mass m to a height h from the surface of the earth will be

mgh mgh mgh mg

[1] [2] [3] [4]
 h   h 
2
 h    h
1   1  1   1 
  R R
 Re   R e 
 e    e

Q.18 If the satellite is stopped suddenly in its orbit which is at a distance equal radius of earth from earth's surface and
allowed to fall freely into the earth, the speed with which it hits the surface of earth will be
[1] 7.919 m/sec [2] 7.919 km/sec [3] 11 .2 m/sec [4] 11.2 km/sec
Q.19 A projectile is fired vertically upward from the surface of earth with a velocity K ve where ve is the escape velocity
and K < 1. Neglecting air resistance, the maximum height to which it will rise measured from the centre of the
earth is - (where R = radius of earth)

R R 1 K 2 K2
[1] 2 [2] 2 [3] [4]
1 K K R R
Q.20 A satellite is revolving in an orbit close to the earth's surface. Taking the radius of the earth as 6.4 x 106 meter, the
value of the orbital speed and the period of revolution of the satellite will respectively be. (g = 9.8 meter/sec 2)
[1] 7.2 km/sec., 84.6 minutes [2] 2.7 km/sec., 8.6 minutes
[3] .72 km/sec., 84.6 minutes [4] 7.2 km/sec., 8.6 minutes
Q.21 If the period of revolution of an artificial satellite just above the earth be T and the density of earth be , then

2 3
[1] T2 = 3 × G [2]  T2 varies with time [3]  T  [4] none
G
Q.22 A body of mass 100 kg falls on the earth from infinity. What will be its energy on reaching the earth ? Radius of the
earth is 6400 km and g = 9.8 m/s2. Air friction is negligible.
[1] 6.27 x 109J [2] 6.27 x 1010J [3] 6.27 x 1010J [4] 6.27x107J
Q.23 An artificial satellite of the earth is to be established in the equatorial plane of the earth and to an observer at the
equator it is required that the satellite will move eastward, completing one round trip per day. The distance of the
satellite from the centre of the earth will be- (The mass of the earth is 6.00 x 10 24 kg and its
(angular velocity = 7.30 x 10–5 rad/sec)
[1] 2.66 x 103m [2] 2.66 x 105m [3] 2.66 x 106m [4] 2.66 x 107m
Q.24 Two satellites P and Q of same mass are revolving near the earth surface in the equitorial plane. The satellite P
moves in the direction of rotation of earth whereas Q moves in the apposite direction. The ratio of their kinetic
energies with respect to a frame attached to earth will be.
2 2
 8363   7437   8363   7437 
[1]   [2]   [3]   [4]  
 7437   8363   7437   8363 
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Q.25 The mass of the sun if the mean radius of earth's orbit is 1.5 × 10 8 km and G = 6.67 x 10-11 Nm2 /kg2 will be
[1] 2 × 1010 kg [2] 3 × 1010 kg [3] 2 × 1030 kg [4] 3 × 1030 kg
Q.26 The masses and the radius of the earth and the moon are M 1, M2 and R1, R2 respectively their centres are at
distance d apart. The minimum speed with which a particle of mass m should be projected form a point midway
between the two centres so as to escape to infinity will be

G G G G M1
[1] 2 (M1  M2 ) [2] (M1  M2 ) [3] (M1  M2 ) [4] 2 d M
d d 2d 2

Q.27 The diameter of a planet is four times that of the earth. The time period of a pendulum on the planet, if it is a second
pendulum on the earth will be- (Take the mean density of the planet equal to that of the earth).
[1] 1s [2] 2s [3] 3s [4] 4s
Q.28 A geostationary satellite is revolving at a height 6R above the earth's surface, where R is the radius of earth. The
period of revolution of a satellite orbiting at a height 2.5R above the earth's surface will be

[1] 24 hours [2] 12 hours [3] 6 hours [4] 6 2 hours

Q.29 Two artificial satellites whose masses are m1 and m2 are moving in circular orbits of radii r1 and r2 respectively if
r1 > r2 then which of the following statements is true about the speeds v 1 and v2 of the satellites

v1 v 2
[1] v1 = v2 [2] v1 > v2 [3] v1 < v2 [4] r  r
1 2

Q.30 The value of g at any place is 9.8m/s2. If the size of the earth suddenly shrinks to half but the density remains
unchanged, then the value of g at that place will be
[1] 4.9 m/s2 [2] 9.8 m/s2 [3] 3.1 m/s2 [4] 19.6 m/s2
Q.31 In the figure, motion of a planet around the sun in elliptical path is shown with sun at one of its foci. Two shaded
areas shown in figure are equal. If the times taken by the planet to move from A to B and from C to D are t 1 and t2
respectively, then

[1] t1 < t2 [2] t1 > t2 [3] t1 = t2 [4] there is no relation between t1 and t2.
Q.32 The escape velocity of a body at earth is 11.2 km/s, the escape velocity of the body thrown at an angle 45° with the
horizontal will be

11.2
[1] 11.2 km/s [2] 22.4 km/s [3] km/s [4] 11.2 2 km/s
2

Q.33 Mass of a planet is 5 x 1024 kg and radius is 6.1 x 106m. The energy needed to send a 2 kg body into space from
its surface, would be
[1] 9 joule [2] 18 joule [3] 2.2 x 108 joule [4] 1.1 x 108 joule
Q.34 The gravitational potential difference between a planet's surface and a point at a height 20m from the surface is
2 joule/kg. If the gravitational field is uniform, then the work done in carrying a body of mass 5kg to a height 4m
above the surface is
[1] 2 joule [2] 20 joule [3] 40 joule [4] 10 joule
1
Q.35 The acceleration due to gravity at the surface of earth is 10 m/s 2. The mass of planet mars is th and radius is
10
1
as compared to earth. The acceleration due to gravity at the surface of Mars will be
2
[1] 8m/s2 [2] 16m/s2 [3] 24m/s2 [4] 4 m/s2

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 GRAVITATION
Q.36 How much energy will be needed for a body of mass 100kg to escape from the earth
(g = 10m/s2 and radius of earth = 6.4 x 106m)
[1] 6.4 x 109 joule [2] 8 x 106 joule [3] 4 x 1016 joule [4] zero
Q.37 The acceleration due to gravity on the surface of earth is 10m/s 2 and the radius of earth is 6400km. With what
minimum velocity must a body be thrown from the surface ofthe earth so that it reaches a height of 6400km ?
[1] 8 km/s [2] 64km/s [3] 1 km/s [4] 32 krn/s

1 1
Q.38 The mass of planet mars is th of the mass of earth and radius is of the radius of earth. If the escape velocity
10 2
at the earth is 11.2km/s, then the escape velocity at Mars will be
[1] 10km/s [2] 5 km/s [3] 20 km/s [4] 40 krn/s
Q.39 If the radius of earth is 6400km and the acceleration due to gravity g is 10 rn/s , the angular velocity of earth for
2

which the weight of a body would become zero at equator, will be

1 1 1
[1] rad/s [2] rad/s [3] rad/s [4] impossible
400 800 1600
Q.40 The speed of a satellite of mass 500kg at a height 103 km above the earth's surface is 7.36 x 103 rn/ s. If the orbit
of satellite is circular then the gravitational force due to earth on satellite is (in N)
[1] 4 x 102 [2] 3.66 x 103 [3] 3.75 x 104 [4] 4.5 x 102
Q.41 The percentage increase in the weight of a body taken from equator to poles on the earth's surface, will be
(g = 9.8m/s2, R = 6400 km)
[1] 4.5 [2] 1.2 [3] 0.43 [4] 0.04
Q.42 A second's pendulum is taken from earth to a mountain of height 8 km, the change in its period will be
[1] 0.25s [2] 0.025s [3] 0.0025s [4] negligible
Q.43 The loss in weight of a body taken from earth's surface to a height h is 1%. The change in weight taken into a mine
of depth h will be
[1] 1 % loss [2] 1 % gain [3] 0.5% gain [4] 0.5% loss
Q.44 Angular momentum of a planet of mass m orbiting around sun is J, areal velocity of its radius vector will be

1 J m 1
[1] mJ [2] [3] 2 J [4] 2 mJ
2 2m
Q.45 A satellite is set in a circular orbit of radius R. Another satellite is set in a circular orbit of radius 1.01 R. The
percentage difference of the period of the second satellite with respect to first satellite will be
[1] 1 % increased [2] 1 % decreased [3] 1.5% increased [4] 1.5% decreased
Q.46 The potential energy of a body of mass m is U = ax + by the magnitude of acceleration of the body will be

ab ab a2  b2 a2  b2
[1] [2]   [3] [4]
m  m  m m
Q.47 Clock A based on spring oscillations and a clock B based on oscillations of simple pendulum are synchronised on
earth. Both are taken to mars whose mass is 0.1 times the mass of earth and, radius is half that of earth. Which
of the following statement is correct
[1] Both will show same time
[2] Time measured in clock A will be greater than that in clock B
[3] Time measured in clock B will be greater than that in clock A
[4] Clock A will stop and clock B will show time as it shows on earth
Q.48 Which of the following statements is not correct for a second's pendulum synchronised at equator. The period of
seconds pendulum
[1] at poles is less than 2s [2] in INSAT-IB will be infinite.
[3] at the centre of earth will be zero [4] on moon will be greater than 2s.

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 GRAVITATION
Q.49 If the length of the day is T, the height of that TV satellite above the earth's surface which always appears
stationary from earth, will be

1/ 3 1/ 3 1/ 3 1/ 3
 4 2GM   4 2GM   GMT 2   GMT 2 
[1] h   2

 [2] h   2


 R [3] h  
 4 2 
 R [4] h   
2 
R
 T   T     4  

Q.50 The weight of a man is equivalent to 50kg-wt. If keeping the density of earth constant the radius of the earth is
doubled, then the weight of the man will become
[1] 100kg wt [2] same [3] half [4] zero
Q.51 If two bodies of mass M and m are revolving around the centre of mass of the system in circular' orbits of radii R
and r respectively due to mutual interaction. Which of the following formula is applicable

GMm GMm GMm GMm

[1]  m 2r [2]  m  2r [3]  m 2R [4]  m  2r
(R  r )2 R 2
r 2 2
R r 2

Q.52 A mass of 10kg is balanced on a sensitive physical balance. A 1000 kg mass is placed below 10kg mass at a
distance of 1m. How much additional mass will be required for balancing the physical balance
[1] 66 x 10–15kg [2] 6.7 x 10–8 kg [3] 66 x 10–12kg [4] 6.7 x 10–6kg
Q.53 A number of particles each of mass 0.75kg are placed at distances 1m, 2m, 4m, 8m etc. from origin along positive
X-axis. the intensity of gravitational field at the origin will be

3 1
[1] G [2] G [3] G [4] zero
4 2
Q.54 Two satellites A and B (each of mass m) of earth are put in circular orbits around the centre of earth. The height of
satellite A above the earth's surface is equal to the radius R of earth and that of satellite B is 3R. The ratio of
potential energies of satellites A and B is
[1] 1 : 2 [2] 2 : 1 [3] 3 : 1 [4] 1 : 3
Q.55 If the angular speed of earth is increased so much that the objects start flying from the equator, then the length of
the day will be nearly

1
[1] 1 hours [2] 8 hours [3] 18 hours [4] 24 hours
2
Q.56 Imagine the acceleration due to gravity on earth is 10m/s 2 and on mars is 4 m/s2. A traveller of mass 60kg goes
from earth to mars by a rocket moving with constant velocity. If effect of other planets is assumed to be negligible,
which one of the following graphs shown the variation of weight of traveller with time

[1] A [2] B [3] C [4] D

Q.57 Two satellites of same mass m are revolving round the earth E(mass M) in the same orbit of radius r. Rotational
directions of the two are opposite therefore, they can collide. Total mechanical energy of the system (both satel-
lites and earths) is - (m < < M)

GMm 2GMm GMm

[1]  [2]  [3]  2r [4] zero
r r

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Q.58 A missile which missed its target, went into orbit around the earth. The radius of the orbit is four times the radius
of the parking orbit of a satellite. The period of the missile as satellite is
[1] 2 days [2] 4 days [3] 8 days [4] 16 days
Q.59 What should be the angular velocity of earth about its own axis so that the weight of the body at the equator would

become 3 th of its present value. (Radius of earth at equator = R e)

5
5 g 2 g 3 g 5 g
[1] 2 Re [2] 5 Re [3] 5 Re [4] 3 Re

Q.60 Two particles of masses m and M are initially at infinity and at rest. Both particles move towards each other due
to mutual interaction. When the distance between them is d, the relative velocity of approach will be
1/ 2 1/ 2
 2Gd   2G(M  m)  Mm 2 Gd
[1]   [2]   [3] 2 G   [4]
M  n   d   d  (M  m)

Q.61 The radius of earth is 6.4 x 106 m and acceleration due to gravity at earth's surface is 9.8 m/s2. The temperature required
by the Oxygen molecules to escape from the earth's surface is (universal gas constant R = 8.3 joule/mole - K)
[1] 1.59 x 105 K [2] 15.9 x 105 K [2] 159 x 105 K [4] 0.159 x 104 K
Q.62 A satellite whose mass is m is orbiting around the earth at a height R above the earth's surface. If the intensity of
gravitational field at the earth's surface is g and radius of earth is R, then the kinetic energy of the satellite will be
[1] mgR/4 [2] mgR/2 [3] mgR [4] 2 mgR
Q.63 The masses of moon and earth are 7.36 x 10 kg and 5.98 x 10 kg respectively and their mean separation is
22 24

3.82 x 105 km. The energy required to break the earth-moon system is
[1] 12.4 x 1032 J [2] 7.68 x 1028J [3] 5.36 x 1024J [4] 2.96 x 1020 J
Q.64 Three identical point masses, each of mass 1 kg lie in the x-y plane at points (0, 0) (0, 0.2m) and (0.2m, 0). The
gravitational force on the mass at tbe origin is

[1]1.67 x 10–19 ( î  ĵ ) N [2] 3.34 x 10–10 ( î  ĵ ) N [3] 1.67 x 10–9 ( î  ĵ ) N [4] 3.34 x 10–10 ( î  ĵ ) N
Q.65 The value of g at any point is 9.8m/s2. If earth is reduced to half of its present size by shrinking without loss of
mass but the point remains at the same position, then the value of g at that point will be
[1] 4.9 m/s2 [2] 3.1 m/s2 [3] 9.8m/s2 [4] 19.6 m/s2
Q.66 The acceleration due to gravity on the moon is one-sixth that on earth. If the average density of moon is three-fifth
that of earth, the moon's radius in terms of earth's radius R e is
[1] 0.16Re [2] 0.27Re [3] 0.32Re [4] 0.36Re
Q.67 The ratio of radii of two satellites is p and the ratio of their accelerations due to gravity is q. The ratio of their escape
velocities will be
1/ 2 1/ 2
q p
[1]   [2]   [3] pq [4] pq
p q
Q.68 The acceleration due to gravity of that planet whose mass and radius are half those of earth, will be (g is accelera-
tion due to gravity at earth's surface)
[1] 2g [2] g [3] g/2 [4] g/4
Q.69 A satellite is revolving around earth in a circular orbit. The radius of orbit is half of the radius of the orbit of moon.
Satellite will complete one revolution in
[1] 2–3/2 lunar month [2] 2–2/3 lunar month [3] 23/2 lunar month [4] 22/3 lunar month
Q.70 Assuming earth as a sphere of radius R, the weight of mass 1 kg at a distance 2R from the centre of earth is 2.5N.
The weight of same mass at a distance 3R will be
[1] 4.75N [2] 3.75N [3] 2.5N [4] 1.1 N
Q.71 One planet is orbiting around the sun, At a point P it is at minimum distance d1 from the sun and at that time speed
is v1. If at a another point Q it is at maximum distance d2 from the sun then at this point the speed of planet will be
[1] d12 v1/d22 [2] d2 v1 /d1 [3] d1v1/d2 [4] d22v1/d12

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Q.72 Two metallic balls of mass m are suspended by two strings of length L. The distance between upper ends is . The
angle at which the string will be inclined with vertical due to attraction, is

GM GM GM
1 1 GM
[1] tan 1 [2] tan 1 [3] tan [4] tan
g 2
gL 2 g  gL
Q.73 The radius of a planet is 74 x 10 km. A satellite of this planet completes one revolution in 16.7 days. If the radius
3

of the orbit of satellite is 27 times the radius of planet, then the mass of planet is
[1] 2.3 x 1027kg [2] 2.3 x 1030kg [3] 2.3 x 1032kg [4] 2.3 x 1042kg
Q.74 If Me is the mass of earth and Mm is the mass of moon (Me = 81 Mm). The potential energy of an object of mass m
situated at a distance R from the centre of earth and r from the centre of moon, will be
R  1  81 1   81 1 
[1]  GmM m   r  2 [2]  GmM e   
81 1
[3]  GmM m    [4] GmM m   
 81  R  r R   R r  R r
Q.75 Two satellites S1 and S2 are moving in the same direction and in same plane around a certain planet and their
periods are 1 hour and 8 hours respectively, the radius of the orbit of satellite S1 is 104 km. The angular velocity of
satellite S2 measured by an astronaut sitting in satellite S1 will be

  2 2
[1] rad / hr [2] rad / hr [3] rad / hr [4] rad / hr
2 3 3 5
Q.76 The sun's mass is 3.2 x 105 times the earth's mass and the sun is about 400 times as far from the earth as the
moon is. Assuming sun-moon distance to be equal to sun-earth distance, the ratio of magnitude of pull of the sun
on the moon to the pull of earth on the moon is
[1] 2 [2] 4 [3] 0.5 [4] 0.25
Q.77 A body of mass M is divided into two parts of masses m and (M - m). If they are kept at a constant distance, then
the relation between m and M for maximum force of attraction between them, will be

M 2 M M
[1] m  [2] m  M [3] m  [4] m 
4 3 3 2
Q.78 The maximum and minimum distances of earth from the sun are r 1 and r2 respectively. When the earth is on the
perpendicular drawn at the major axis of the orbit its distance from the sun will be
2r1r2  r1  r2  (r  r ) (r1  r2 )
[1] (r  r ) [2]  r  r  [3] 1 2 [4]
1 2  1 2 4 3
Q.79 A planet of mass m is moving in an elliptical orbit about the sun (mass of sun = M). The maximum and minimum
distances of the planet from the sun are r 1 and r2 respectively. The period of revolution of the planet will be
proportional to
[1] r13/2 [2] r23/2 [3] (r1 – r2)3/2 [4] (r1 + r2)3/2
Q.80 A body placed at a distance R0 from the centre of earth, starts moving from rest. The velocity of the body on
reaching at the earth's surface will be
(Re = radius of earth and Me = mass of earth)

 1 1   1 1  1 1  1 1 
[1] GMe    [2] 2GMe    [3] GMe  [4] 2GMe  R  R 
R  R   e 0 
 e R0   e Re  Re R0
Q.81 The masses and the radii of earth and moon are respectively M e, Re and Mm, Rm,. The distance between the
centres is r. At what minimum velocity a particle of mass m be projected from the mid point of the distance
between their centres so that it may escape into space ?

4G 4G 2G 2G
[1] (Me  Mm ) [2] (Me  Mm ) [3] (Me  Mm ) [4] (Me  Mm )
r r r r
Q.82 A planet of mass m is moving in an elliptical path about the sun. Its maximum and minimum distances from the
sun are r1 and r2 respectively. If Ms is the mass of sun then the angular momentum of this planet about the centre
of sun will be

2GMS r1 r2 2GMsr1 r2 2GMsm(r1  r2 )

[1] (r1  r2 ) [2] 2GMsm (r  r ) [3] m (r1  r2 ) [4] r1 r2
1 2

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Q.83 If a body is taken up to a height of 1600km from the earth's surface, then the percentage loss of gravitational force
acting on that body will be- (Radius of earth Re = 6400 km)
[1] 50% [2] 36% [3] 25% [4] 10%
Q.84 Three particles each of mass 100gm are brought from a very large distance to the vertices of an equilateral triangle
whose side is 20cm in length. The work done will be
[1] 0.33 x 10–11 joule [2] –0.33 x 10–11 joule [3] 1.0 x 10–11 joule [4] –1.00 x 10–11 joule
Q.85 A tunnel is dug along the diameter of the earth. If a particle of mass m is situated in the tunnel at a distance x from
the centre of earth then gravitational force acting on it, will be

GM em GMem GMem GMem

[1] x [2] [3] [4]
R 3e R 2e x 2 (R e  x)2

Q.86 Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The
magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be

24m 2G 6 m 2G 4 2 Gm 2
[1] [2] [3] [4] zero
a2 a2 a2
Q.87 A particle of mass 0.67kg is at a distance of 0.23m from one end of a uniform rod of length 3.0m and mass 5.0kg.
The magnitude of gravitational force due to rod on the particle is
[1] 5.4 x 10–9N [2] 9.2 x 10–10N [3] 3.0 x 10–10N [4] 5.4 x 10–11N
Q.88 Two concentric shells of uniform density have masses M1 and M2 and their radii are R1 and R2 respectively. A particle
of mass m is placed at a distance d from the centre, such that R2 > d > R1. The net force on the particle is

GM1m G(M1  M2 )m G(M1  M2 )m

[1] 2 [2] 2 [3] (d  R )(R  d) [4] zero
d d 1 2

Q.89 The escape speed for a projectile in the case of earth is 11.2 km/sec. A body is projected from the surface of the
earth with a velocity which is equal to twice the escape speed. The velocity of the body when at infinite distance
from the centre of the earth is :

[1] 11.2 km/sec [2] 22.4 km/sec [3] 11.2 3 km/sec [4] 11.2 2 km/sec

Q.90 S stands for Sun, E for Earth and M for Moon. If distance ES is 400 times the distance EM and the gravitational
pull of S on E is 170 times the gravitational pull of M on E, then S has x times the mass of M where x is roughly.
[1] 6.8 x 104 [2] 7.4 x 105 [3] 2.7 x 107 [4] 4.6 x 109
Q.91 A planet revolves in an elliptical orbit around the sun. The semimajor and semiminor axes are a and b, then the
time period T is given by

3 3
2 ab 2 ab
[1] T    [2] T  b
2 3 [3] T  a
2 3 [4] T   
 2   2 

Q.92 F1 and F2 are two pins fixed on a board. A thread of length F1P + PF2 > F1F2 is tied at F1 and F2. The path traced
by the point P is
[1] a circle [2] a parabola [3] an ellipse [4] none of these
Q.93 Two identical satellites are moving in the same circular orbit around the earth but in opposite senses of rotation,
Assuming an inelastic collision to take place, so that the wreckage remains as one piece of tangled material, the
wreckage
[1] will be moving in a circular orbit of half the radius [2] will be moving in a circular orbit on one fourth the radius
[3] will spin with no translatory motion [4] falls directly down
Q.94 If a planet of given density were made larger its force of attraction for an object on its surface would increase
because of planet's greater mass but would decrease because of the greater distance from the object to the centre
of the planet. Which effect predominates ?
[1] increase in mass [2] increase in radius [3] both affect the attraction equally [4] none of the above

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Q.95 Consider the earth to be a homogeneous sphere. Scientist A goes deep down in a mine and scientist B goes high
up in a balloon. The gravitational field measured by
[1] A goes on decreasing and that by B goes on increasing
[2] B goes on decreasing and that by A goes on increasing
[3] each remains unchanged [4] each goes on decreasing
Q.96 The mass and diameter of a planet have twice the value of the corresponding parameters of earth. Acceleration
due to gravity on the surface of the planet is
[1] 9.8 m/sec2 [2] 4.9 m/sec2 [3] 980 m/sec2 [4] 19.6 m/sec2
Q.97 An iron ball and a wooden ball of the same radius are released from a height h in vacuum. The times taken by both
of these to reach the ground are
[1] unequal [2] exactly equal [3] roughly equal [4] zero
Q.98 If the change in the value of g at a height h above the surface of the earth is the same as at a depth x below it.
When both x and h are much smaller than the radius of the earth. Then
[1] x = h [2] x = 2h [3] x = h/2 [4] x = h2
Q.99 An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. If R is the radius
of the earth and g is the acceleration due to gravity at the surface of the earth, the velocity of the satellite in the
orbit is given by

gR 2 gR gR 2
[1] [2] gR [3] [4]
Rh Rh Rh
Q.100 A satellite is going around the earth, Which of the following statements is not correct ?
[1] It is a freely falling body [2] It experiences no acceleration
[3] It is moving with constant speed [4] Its angular momentum is constant
Q.101 At a certain instant of time the mass of a rocket going up vertically is 100kg. If it is ejecting 5 kg of gas per second
at a speed of 400 m/s. The acceleration of the rocket would be (taking g = 10 m/s 2)
[1] 20 m/s2 [2] 10 m/s2 [3] 30 m/s2 [4] 1 m/s2
Q.102 Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed.
The pressure exerted on the rails will
[1] same due to both [2] zero due to both
[3] more for the train which is moving in the direction of motion of the earth
[4] more for the second train which is moving in the direction opposite to the direction of rotation of the earth

ANSWER KEY EXERCISE # 2

Que . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A ns . 2 3 1 2 4 1 3 2 2 2 1 3 1 1 4
Que . 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A ns . 4 3 2 1 1 3 1 4 1 3 1 1 4 3 1
Que . 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
A ns . 3 1 4 1 4 1 1 2 2 2 3 3 4 2 3
Que . 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A ns . 3 2 3 3 1 1 2 1 2 1 3 1 3 2 2
Que . 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
A ns . 1 1 2 1 3 2 4 1 1 4 3 1 1 3 2
Que . 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
A ns . 1 4 1 4 4 1 3 2 4 1 3 3 1 3 3
Que . 91 92 93 94 95 96 97 98 99 100 101 102
A ns . 3 3 4 2 4 2 2 2 4 2 2 4

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 GRAVITATION

EXERCISE # 3
Q.1 If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity
on the earth’s surface would - [MP PET-99]
[1] Decreased by 2% [2] Remain unchanged [3] Increase by 2% [4] Increase by 1%
Q.2 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 a planet having the same density as earth but twice the radius -
[1] S will run faster than P [2] P will run faster than S [NCERT-80]
[3] they will both run at the same rate as on the earth [4] None of these
Q.3 The distance of neptune and saturn from sun are nearly 10 13 and 1012 meters respectively. Assuming that
they move in circular orbits, their periodic times will be in the ratio - [MP PET-2001]

[1] 10 [2] 100 [3] 10 10 [4] 1 10

Q.4 If the change in the value of ‘g’ at a height h above the surface of the earth is the same as at a depth x
below it, then (both x and h being much smaller than the radius of the earth) - [BHU-2002]

h
[1] x = h [2] x = 2h [3] x  [4] x = h 2
2

Q.5 Time period of revolution of a satellite around a planet of radius R is T. Period of revolution around another
planet, whose radius is 3R but having same density is - [CPMT-2000]

[1] T [2] 3T [3] 9T [4] 3 3 T

1 1
Q.6 The mass of the moon is of the earth but the gravitational pull is of the earth. It is due to the fact that -
81 6

81 9
[1] The radius of the moon is of the earth [2] The radius of the earth is of the moon
6 6

[3] Moon is the satellite of the earth [4] None of the above [CPMT-1985]
Q.7 The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded
areas A and B are also shown in the figure which can be assumed to be equal. If t 1 and t2 represent the
time for the planet to move from a to b and d to c respectively, then - [PMT-86,88]
b
a
A
S
B

d
c
[1] t1 < t2 [2] t1 > t2 [3] t1 = t2 [4] t1  t2
Q.8 The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit
of radius 4R is - [CBSE-2002]
[1] 4T [2] T/4 [3] 8T [4] T/8
Q.9 If Ve and Vo represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit
of radius R, then - [AIIMS-2002]

1
[1] Ve = Vo [2] 2 V0  Ve [3] Ve  Vo [4] Ve and Vo are not related
2

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 GRAVITATION

Q.10 If r represents the radius of the orbit of a satellite of mass m moving around a planet of mass M, the velocity
of the satellite is given by - [RPMT-95]

2 M 2 GMm GM 2 GM
[1] v  g [2] v  [3] v  [4] v 
r r r r

Q.11 The ratio of the radius of the earth to that of the moon is 10. The ratio of acceleration due to gravity on
the earth and on the moon is 6. The ratio of the escape velocity from the earth’s surface to that from the
moon is - [NCERT-98]
[1] 10 [2] 6 [3] Nearly 8 [4] 1.66
Q.12 If a body describes a circular motion under inverse square field, the time taken to complete one revolution
T is related to the radius of the circular orbit as - [RPMT-2000]
[1] T  r [2] T  r2 [3] T2  r3 [4] T  r4
Q.13 ve and vp denotes the escape velocity from the earth and another planet having twice the radius and the
same mean density as the earth. Then - [MP PMT-94]
[1] ve = vp [2] ve = vp / 2 [3] ve = 2vp [4] ve = vp / 4
Q.14 The escape velocity of a sphere of mass m from earth having mass M and radius R is given by -

2GM GM 2GMm GM
[1] [2] 2 [3] [4] [CBSE-95]
R R R R

Q.15 An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is
the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the
satellite in the orbit is given by - [NCERT-88]

gR 2 gR gR 2
[1] [2] gR [3] [4]
Rh Rh Rh

Q.16 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 would be (g on earth = 9.8 m/sec 2) - [NCERT-82]
[1] 4.9 m/sec2 [2] 8.9 m/sec2 [3] 19.6 m/sec2 [4] 29.4 m/sec2
Q.17 The escape velocity for a rocket from earth is 11.2 km/sec. Its value on a planet where acceleration due
to gravity is double that on the earth and diameter of the planet is twice that of earth will be in km/sec-
[1] 11.2 [2] 5.6 [3] 22.4 [4] 53.6 [MP PMT-2000]
Q.18 The escape velocity from the earth is about 11 km/second. The escape velocity from a planet having twice
the radius and the same mean density as the earth is - [MP PET-2001]
[1] 22km/sec [2] 11 km/sec [3] 5.5 km/sec [4] 15.5 km/sec
Q.19 A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre
of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is -

Reg
[1] 4.8 hours [2] 48 2 hours [3] [4] Infinite[MP PET-2001]
2

Q.20 Two planets have the same average density but their radii are R 1 and R2. If acceleration due to gravity on
these planets be g1 and g2 repectively, then - [MP PET-1994]

3
g1 R1 g1 R 2 g1 R1
2 g1 R1

[1] g  R [2] g  R [3] g  2 [4] g2 R 3
2 2 2 1 2 R2 2

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 GRAVITATION

Q.21 An iron ball and a wooden ball of the same radius are released from a height ‘h’ in vacuum. The time taken
by both of them to reach the ground is - [AFMC-1998]
[1] Unequal [2] Exactly equal [3] Roughly equal [4] Zero
Q.22 The correct answer to above question is based on - [AFMC-1998]
[1] Acceleration due to gravity in vaccum is same irrespective of size and mass of the body
[2] Acceleration due to gravity in vaccum depends on the mass of the body
[3] There is no acceleration due to gravity in vaccum
[4] In vacuum there is resistance offered to the motion of the body and this resistance depends on the mass
of the body
Q.23 At a given place where acceleration due to gravity is ‘g’ m/sec 2, a sphere of lead of density ‘d’ kg/m 3 is
gently released in a column of liquid of density ‘’ kg/m3. If d >  , the sphere will - [NCERT-1998]
[1] Fall vertically with an acceleration ‘g’ m/sec 2 [2] Fall vertically with no acceleration

d– 
[3] Fall vertically with an acceleration g   [4] Fall vertically with an acceleration g  
 d  d

Q.24 ge and gp denote the acceleration due to gravity on the surface of the earth and another planet whose mass
and radius are twice as that of earth. Then - [NCERT-1998]

[1] gp = ge [2] gp = ge/2 [3] gp = 2ge [4] gp = ge / 2

Q.25 When a body is taken from the equator to the poles, its weight - [EAMCET-1995]
[1] Remains constant [2] Increases
[3] Decreases [4] Increases at N–pole and decreases at S–pole
Q.26 A missile is launched with a velocity less than the escape velocity. the sum of its kinetic and potential energy
is - [MP PET-1995]
[1] Positive [2] Negative
[3] Zero
[4] May be positive or negative depending upon its initial velocity
Q.27 The ratio of the K.E. required to be given to the satellite to escape earth’s gravitational field to the K.E.
required to be given so that the satellite moves in a circular orbit just above earth atmosphere is -
[1] One [2] Two [3] Half [4] Infinity [NCERT-1975]
Q.28 An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon
out of space-ship. The spoon will - [NCERT-1975]
[1] Fall vertically down to the earth [2] Move towards the moon
[3] Will move along with space-ship [4] Will move in an irregular way then fall down to earth
Q.29 If a satellite is orbiting the earth very close to its surface, then the orbital velocity mainly depends on-
[1] The mass of the satellite only [2] The radius of the earth only [NCERT-1982]
[3] The orbital radius only [4] The mass of the earth only
Q.30 A satellite of a the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly
disappears, the statellite will [AIEEE-2002]
[1] Continue to move with velocity v along the original orbit
[2] Move with a vleocity v, tangentially to the original orbit
[3] Fall down with increasing velocity
[4] Ultimately come to rest somewhere on the original orbit

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 GRAVITATION

Q.31 Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of
revolution T. If the gravitational force of attraction between planet and star is proportional to R –5/2 then T2
is proportional to [RPMT-1997]
[1] R3 [2] R7/2 [3] R5/2 [4] R3/2
Q.32 A spherical planet far out in space has a mass M0 and diameter D0. A particle will experience an acceleration
due to gravity which is equal to [Delhi PMT-2002]
[1] GM0/D02 [2] 2mGM0/D02 [3] 4GM0/D02 [4] GmM0/D02
Q.33 Two planets move around the sun. The periodic time and the mean radill of the orbits are T 1, T2 and r1,
r2 respectively. The ratio T1/T2 is equal to [CPMT-1978]
[1] (r1/r2)1/2 [2] r1/r2 [3] (r1/r2)2 [4] (r1/r2) 3/2
Q.34 Two satellites A and B go round a planet P in circular orbits having radill 4R and R respectivley. If the speed
of the satellite A is 3V, the speed of the satellite B will be [UPSEAT-2000]
[1] 12 V [2] 6 V [3] 4/3 V [4] 3/2 V
Q.35 In a gravitationla field, at a point where the gravitational potential is zero [CPMT-1990]
[1] The gravitational field is necessarily zero [2] The gravitational field is not necessarly zero
[3] Nothing can be said definitely about the gravitational field
[4] None of these
Q.36 A geostationay satellie [CPMT-1990]
[1] Revolves about the polar axis
[2] Has a time period less than that of the near earth satellite
[3] Moves faster than a near earth satellite [4] Is stationary in the space
Q.37 The acceleration due to gravity about the earth’s surface would be half of its value on the surface of the
earth at an altitude of (R = 4000 mile) [CPMT-1975]
[1] 1200 mile [2] 2000 mile [3] 1600 mile [4] 4000 mile
Q.38 A satellie revolves around the earth in an elliptical orbit. Its speed [MP PET-2001]
[1] Is the same at all point in the orbit [2] Is greatest when it is closest to the earth
[3] Is greatest when it is farthest from the earth
[4] Goes on increasing or decreasing continuously depending upon the mass of the satellite
Q.39 The largest and the shortest distance of the earth from the sun are r 1 and r2, its distance from the sun
when it is at the perpendicular to the major axis of the orbit drawn from the sun [CBSE-1991]

r1  r2 r1 r2 2 r1 r2 r1  r2
[1] [2] r  r [3] r  r [4]
4 1 2 1 2 3
Q.40 The magnitudes of the gravitational field at distance r 1 and r2 from the centre of a uniform sphere of radius
R and mass M are F1 and F2 respectively. Then [IIT-1994]

F1 r1 F1 r22
[1] F  r if r1 < R and r2 < R [2]  if r > R and r > R
2 2 F2 r12 1 2

F1 r1
[3] F  r if r1 > R and r2 > R [4] none
2 2

Q.41 The radii of two planets are respectively R 1 and R2 and their densities are respectively 1 and 2. The ratio
of the accelerations due to gravity at their surfaces is [MP PET-1994]
 
[1] g1 : g2 = 1 : 2 [2] g1 : g2 = R1R2 : 12 [3] g1 : g2 = R12 : R21 [4] g1 : g2 = R11 : R22
R12 R 22

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 GRAVITATION

Q.42 For the moon to cease to remain the earth’s satellite its orbital velocity has to increase by a factor of

[1] 2 [2] 2 [3] 1/ 2 [4] 3 [MP PET-1994]

Q.43 The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period
of another earth satellite in an orbit at a distance of three earth radii from its surface will be [MP PET-1994]

[1] 83 minutes [2] 83 × 8 minutes [3] 664 minutes [4] 249 minutes

Q.44 In a satellite if the time of revolution is T, then K.E. is proportional to [BHU-1995]

[1] 1/T [2] 1/T2 [3] 1/T3 [4] T–2/3
Q.45 A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into
an orbit of radius (1.01) R. The period of the second satellite is large than that of the first one by apporximately
[1] 0.5 % [2] 1.0 % [3] 1.5 % [4] 3.0 % [IIT-1995]
Q.46 If the distance between the earth and the sun becomes half its present value, the number of days in a year
would have been [IIT-1996]
[1] 64.5 [2] 129 [3] 182.5 [4] 730
Q.47 The change in potential energy, when a body of mass m is raised to a height nR from the earth’s surface
is (R = Radius of earth) [MP PMT-1996]

n n2 n
[1] mgR [2] nmgR [3] mgR [4] mgR
n 1 2
n 1 n 1

Q.48 A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit
is R0 and mass of the earth M, the angular momentum about the centre of the earth is [RPMT-2000]

GM GM
[1] m GMR 0 [2] M GmR 0 [3] m R [4] M R
0 0

Q.49 Escape velocity on a planet is v e. If radius of the planet remains same and mass becomes 4 times, the
escape velocity becomes [MP PMT-1996]
[1] 4ve [2] 2ve [3] ve [4] 1/2 ve
Q.50 The masses and radii of the earth and moon are M 1, R1 and M2, R2 respecitvely. Their centres are distance
d apart. The minimum velocity with which a particle of mass m should be projected from a point midway
between their centres so that it escapes to infinity is [MP PET-1997]

G 2G Gm Gm (M1  M2 )
[1] 2 (M1  M2 ) [2] 2 (M1  M2 ) [3] 2 (M1  M2 ) [4] 2 d (R1  R 2 )
d d d

Q.51 The moon’s radius is 1/4 that of the earth and its mass is 1/80 time that of the earth. If g represents the
acceleration due to gravity on the surface of the earth, that on the surface of the moon is
[1] g/4 [2] g/5 [3] g/6 [4] g/8 [MP PET-2001]
Q.52 The mass of the earth is 81 times that of the moon and the radius of the earth is 3.5 times that of the
moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be
[1] 0.2 [2] 2.57 [3] 4.81 [4] 0.39 [MP PET-1998]
Q.53 The escape velocity from the surface of earth is V e. The escape velocity from the surface of a planet whose
mass and radiu are 3 times those of the earth will be
[1] Ve [2] 3Ve [3] 9Ve [4] 27Ve [MP PET-1998]
Q.54 R is the radius of the earth and  is its angular velocity and g p is the value of g at the poles. The effective
value of g at the latitude  = 60º will be equal to [MP PMT-1994]
[1] gp – 1/4 R2 [2] gp – 3/4 R2 [3] gp – R2 [4] gp + 1/4 R2

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 GRAVITATION

Q.55 The depth d at which the value of acceleration due to gravity becomes 1/n times the value at the surface,
is [R = radius of the earth] [MP PMT-1994]
 n  1  n 
[1] R/n [2] R  [3] R/n2 [4] R 
 n   n  1
Q.56 At what altitude in meter will the acceleration due to gravity be 25% of that at the earth’s surface (Radius
of earth = R meter) [MP PMT-1994]
[1] 1/4 R [2] R [3] 3/8 R [4] R/2
Q.57 If orbital velocity of planet is given by v = G aMbRc, then [EAMCET-1994]
[1] a = 1/3, b = 1/3, c = –1/3 [2] a = 1/2, b = 1/2, c = –1/2
[3] a = 1/2, b = –1/2, c = 1/2 [4] a = 1/2, b = –1/2, c = –1/2
Q.58 Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will
depend on which of the following factors [SCRA-1994]
I. Mass of the planet II. Mass of the particle escaping
III Temperature of the planet IV. Radius of the planet
Select the correct anwer form the codes given below
[1] I and II [2] II and IV [3] I and IV [4] I, III and IV
Q.59 The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’
below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one
of the following is correct - [AIEEE-2005]
h 3h
[1] d = 2h [2] d = h [3] d = [4] d =
2 2
Q.60 A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100kg and radius 10 cm. Find
the work to be done against the gravitational force between them to take the particle far away from the sphere
(you may take G = 6.67 × 10–11 Nm2/kg2)- [AIEEE-2005]
[1] 6.67 × 10–9 J [2] 6.67 × 10–10 J [3] 13.34 × 10–10 J [4] 3.33 × 10–10 J
Q.61 Average density of the earth - [AIEEE-2005]
[1] is directly proportional to g [2] is inversely proportional to g
[3] does not depend on g [4] is a complex function of g
Q.62 Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size.
If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is
g’, then - [CPMT-2005]
[1] g’ = 3g [2] g’ = 9g [3] g’ = 27g [4] g’ = g/9
Q.63 The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of
the Earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface
of the Earth. The value of is - [CPMT-2006]
1 1 1
[1] [2] [3] [4] 2
2 3 2
Q.64 Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of
S2. Which one of the following statements is true [CPMT-2007]
[1] The kinetic energies of the two satellites are equal
[2] The time period of S1, is four times that of S2
[3] The potential energies of earth and satellite in the two cases are equal
[4] S1 and S2, are moving with the same speed

ANSWER KEY EXERCISE # 3

Que . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A ns . 3 2 3 2 1 2 3 3 2 4 3 3 2 1 4
Que . 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A ns . 3 3 1 2 1 2 1 3 2 2 2 2 3 2 2
Que . 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
A ns . 2 3 4 2 1 1 3 2 3 1 4 2 3 4 3
Que . 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A ns . 2 4 1 2 1 2 3 1 1 2 2 2 4 1 2
Que . 61 62 63 64
A ns . 3 1 1 4

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