CHAPTER 8 GRAVITATION

(HOTS + MOTS )
PART A
1. A sphere of mass 40 kg is being attracted by anothersphere of mass 80 kg with a force equal to 1/4 of
amilligram weight when their centres are 30 cmapart. Calculate the value of G.
(Ans. 6.88 × 10−11 Nm2 kg −2 )
2. The centres of two identical spheres are 1.0 m apart. If the gravitational force between the spheres be
1.0 N, then what is the mass of each sphere? (G = 6.67 × 10−11 m3 kg −1 s−2 ). (Ans. 1.225 × 105 kg)

3. Find the gravitational attraction between two H‐ atoms of a hydrogen molecule.Given G = 6.67 ×
10Nm2 kg −2 , mass of the atom= 1.67 × 10−27 kg and distance between two H‐ atoms= 1Ao .(Ans. 1.86 ×
10−44 N)
4. Calculate the force of gravitation between twobodies, each of mass 100 kg and 1 m apart on thesurface
of the earth. Will the force of attraction bedifferent if the same bodies are taken on the moon,their
separation remaining constant?(Ans. 6.67 × 10−7 N, No)
5. An apple of mass 0.25 kg falls from a tree. What isthe acceleration of the apple towards the earth?Also
calculate the acceleration of the earth towardsthe apple. Mass of the earth = 5.983 × 1024 kg,Radius of the
earth = 6.378 × 106 m and G = 6.67 × 10−11 Nm2 kg −2. (Ans. 9.810 ms−2 , 4.099 × 10−25 ms −2 )
6. If the mass of the sun is 2 × 1030 kg, the distance ofthe earth from the sun is 1.5 × 1011 m and period
ofrevolution of the earth around the sun is one year(= 365.3 days), calculate the value of
gravitationalconstant. (Ans. 6.69 × 10−11 Nm2 kg −2 )

7. How far from earth must a body be along a line towards the sun so that the sun’s gravitational pull on it
balances that of the earth. Distance between sun and earth’s centre is 1.5 × 1010 km. Mass of sun is3.24 ×
105 times mass of earth. (Ans. 2.63 × 107 km)

PART B
1. A spherical mass of 20 kg lying on the surface of the earth is attracted by another spherical mass of150
kg with a force equal to the weight of 0.25 mg. The centers of the two masses are 30 cm apart. Calculate
the mass 0ṫ the earth, Radius of the earth= 6 × 106 m. (Ans. 4.8 × 1024 kg)
2. The period of moon around the earth is 27.3 days and radius of the orbit is 3.9 × 105 km. G = 6.67 ×
10−11 Nm−2 kg −2 , find the mass of the earth. (Ans. 6.31 × 1024 kg)
3. Assuming the earth to be a uniform sphere ofradius 6400 km and density 5.5g cm-3, find thevalue of g on
its surface.BGiven G = 6.66 × 10−11 Nm2kg-2. (Ans. 9.82 ms-2)
4. The mass of Jupiter is 314 times that of earth and thediameter of Jupiter is 11.35 times that of earth. If
′g ′has a value of 9.8 ms−2 on the earth,what is itsvalue on Jupiter? (Ans. 23.90 ms -2)
5. The value of ′g ′ on the surface of the earth is9.81 ms -2. Find its value on the surface of the moon.Given
mass of earth = 6.4 × 1024 kg, radius of earth= 6.4 × 106 m, mass of moon = 7.4 × 1022 kg, radiusof moon =
1.7ó × 106 m. (Ans. 1.63 ms-2)
6. An astronaut on the moon measures the acceleration due to gravity to be 1.7 ms -2. He knows that the
radius of the moon is about 0.27 times that of the earth. Find the ratio of mass of the earth to that to the
moon, if the value of g on the earth’s surface is 9.8 ms -2.
7. The acceleration due to gravity on the surface of the earth is 10 ms-2. The mass of the planet Mars as
compared to earth is 1/10 and radius is 1/2. Determine the gravitational acceleration of a body on the
surface of Mars. (Ans. 79)
8. A body weighs 100 kg on earth. Find its weight onMars. The mass and radius of Mars are 1/10 and 1/2
ofthe mass and radius of earth. (Ans. 40 kg wt)
9. The weight of a person on the earth is 80 kg. Whatwill be his weight on the moon?Mass of the moon=
7.34 × 1022 kg, radius 1.75 × 106 m and gravitational constant = 6.67 × 10−11 Nm2 kg-2.
What will be the mass of the person at the moonand acceleration due to gravity there? If this personcan
jump 2 m high on the earth, how much high canhe jump at the moon?
(Ans. 128 N, 80 kg,1.6ms−2 , about 12 m)
10. On a planet whose size is the same and mass 4 timesas that of the earth, find the energy needed to lift
a 2kg mass vertically upwards through 2 m distance injoule. The value of g on the surface of earth is10
ms−2 . (Ans. 160 J)

PART C
1. The radius of the earth is 6000 km. What will be the weight of a 120 kg body if it is taken to a height of
2000 km above the surface of the earth? (Ans. 67.5 kg f)
2.A body of mass m is raised to a height h from the surface of the earth where the acceleration due to
gravity is g. Prove that the loss in weight due to variation in g is approximately 2 mgh/R, where R is the
radius of the earth.
3.The Mount Everest is 8848 m above sea level.Estimate the acceleration due to gravity at this height,
given that mean g on the surface of the earth is 9.8 ms -2 and mean radius of the earth is 6.37 × 10 6 m.
(Ans. 9.772 ms-2)
4.At what height above the surface of the earth willthe acceleration due to gravity be 25% of its valueon the
surface of the earth ? Assume that the radius of the earth is 6400 km. (Ans. 6400 km)
5. Find the value of g at a height of 400 km above the surface of the earth. Given radius of the earth, R =
6400 km and value of g at the surface of the earth = 9.8 ms-2. (Ans. 8.575 ms-2)
6. How far away from the surface of earth does the acceleration due to gravity become 4% of its value on
the surface of earth ? Radius of earth = 6400 km. [Delhi 98] (Ans. 25,600 km)

PART D
1. Find the value of g at a depth of 610 km from the surfaceof the earth. Given radius of the earth, R = 6400
km and the value of g on the surface of the earth is 9.8ms-2.(Central Schools 17] (Ans. 8.82 ms-2)
2. Calculate the depth below the surface of the earthwhere acceleration due to gravity becomes half of its
value at the surface of the earth. Radius of the earth = 6400 km. (Ans. 3200 km)
3. How much below the surface of the earth does theacceleration due to gravity become 70% or its value at
the surface of the earth ? Radius of the earth is 6400 km. (Ans. 1920 km)
4. How much below the surface or the earth does the acceleration due to gravity (i) reduces to 36% (ii)
reduces by 36% of its value on the surface of the earth ? Radius or the earth =6400 km. [Delhi 13]
(Ans. (i) 4096 km (ii) 2304 km]
5. Compare the weights of a body when it is (i) 100 kmabove the surface of the earth and (ii) 100 km below
the surface or the earth. Radius or the earth is 6300 km. (Ans. 0.984)

PART D
1.Calculate the value of acceleration due to gravity ata place of latitude 45°. Radius of the earth = 6.38 ×
103 km. (Ans. 9.783 ms-2)
2. If the earth stops rotating about its axis, then what will be the change in the value of y at a place in the
equatorial plane ? Radius of the earth = 6400 km. (Ans. 3.4 cms-2)
3. Assuming that the whole variation of the weight of a body with its position on the surface of the earth
is due to its rotation, find the difference in the weight of 5 kg as measured at the equator and at the poles.
Radius of the earth = 6.4 × 10 6 m. (Ans. 17.2 gf)
4. How many times faster than its present speed theearth should rotate so that the apparent weight of
anobject at equator becomes zero ? Given radius of theearth = 6.37 × 10-6 m. What would be the duration
ofthe day in that case ? (Ans. 17 times faster, 1.412 h)

PART E
1.The gravitational field intensity at a point 10,000 km from the centre of the earth is 4.8 N kg -1. Calculate
the gravitational potential at that point. (Ans. - 4.8 × 107J kg-1)
2. The distance between the earth and the moon is 3.85 × 10 8 metre. At what point in between the two
will the gravitational field intensity be zero ? Mass of the earth = 6.0 × 10 24 kg, mass of the moon = 7.26 ×
1022 kg. (Ans. 3.47 × 108 m from the centre of the earth)
3. Two bodies of masses 100 kg and 1000 kg are at a distance 1.00 metre apart. Calculate the
gravitational field intensity and the potential at the middle-point of the line joining them.
Take G = 6.67 ×10-7 Nm2kg-2. (Ans. 2.40 × 10-7 Nkg-1, - 1.47 × 10-7J kg-1)
4. The mass of the earth is 6.0 × 10 24 kg. Calculate (i) the potential energy of a body of mass 33.5 kg
and (ii) the gravitational potential, at a distance of 3.35 × 10 10 m from the centre of the earth. Take G = 6.67
× 10-11 Nm2 kg-2. [Ans. (i) - 4.02 × 105 J (ii) - 12 × 103 J kg-1]
5.The radius of the earth is R and the acceleration dueto gravity at its surface is g. Calculate the work
mgh
required in raising a body of mass m to a height h from the surface of the earth. Ans. (− h )
1+
R

6.Find the work done to bring 4 particles each of mass100 gram from large distances to the vertices of a
square of side 20 cm. (Ans. - 1.80 × 10-11 J)

PART F
1.Find the velocity of escape at the moon. Given thatits radius is 1.7 × 10° m and value of 'g' is 1.63 ms -2.
(Ans. 2.354 kms-1)
2.The mass of Jupiter is 1.91 × 10 36 kg and its diameteris 13.1 × 10 7 m. Calculate the escape velocity on
the surface of Jupiter.(Ans. 1.972 × 10 9 ms-1)
3If earth has a mass V rimes and radius twice that of a planet Mars, calculate the minimum velocity
required by a rocket to pull out of gravitational force of Mars. Take the escape velocity on the surface of
earth to be 11.2 kms-1. (Ans. 5.28 kms-1)
4.The escape velocity of a projectile on the surface of the earth is 11.2 kms-1. A body is projected out with
twice this speed. What is the speed of the body far away from the earth i.e. at infinity ? Ignore the presence
ot the sun and other planets, etc. (Ans. 19.4 kms-1)
5.Find the velocity of escape from the sun, if its mass is 1.89 ×1030 kg and its distance from the earth is
1.59 ×108 km. Take G = 6.67×10-11Nm2kg-2. (Ans. 3.98 × 104 ms-1)
6.A body is at a height equal to the radius of the earth from the surface of the earth. With what velocity be it
thrown so that it goes out of the gravitational field of the earth ? Given Me = 6.0 × 1024 kg, Re = 6.4 × 10b m
and G = 6.67 × 10-11 Nm2 kg-2. (Ans. 7.9 kms-1)
7.A body of mass 100 kg falls on the earth from infinity. What will be its velocity on reaching the earth ?
What will be its K.E. ? Radius of the earth is 6400 km and g = 9.8 ms-2. Air friction is negligible.
(Ans. 11.2 kms-1, 6.27 × 109 J)

PART G
1.An artificial satellite circled around the earth at a distance of 3400 km. Calculate its orbital velocity and
period of revolution. Radius of earth = 6400 km and g = 9.8 ms -2. (Ans. 6400 ms-1, 9621s)
2.The orbit of a geostationary satellite is concentric and coplanar with the equator of earth and rotates
along the direction of rotation of earth. Calculate the height and speed. Take mass of earth = 5.98 × 10 27 g
and its radius = 6400 km. Given, π2 = 9.87. (Ans. 35850 km, 3.071 kms-1)
3.A satellite revolves round a planet in an orbit justabove the surface of planet. Taking G = 6.67× 10 -11 Nm2
kg-2 and the mean density of the planet = 8.0 × 103kg m-3, find the period of satellite. (Ans. 4206.7 s)
4.An artificial satellite of mass 100 kg is in a circular orbit of 500 km above the earth's surface. Take radius
of earth as 6.5 × 106 m. (i) Find the acceleration due to gravity at any point along the satellite path, (ii) What
is the centripetal acceleration of the satellite ? Take g = 9.8 ms -2. [Ans. (i) 8.45 ms-2 (ii) 8.45 ms-2]
5.A space-ship is launched into a circular orbit closeto the 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 the earth = 6400
km, g = 9.8 ms-2). [Roorkee 88] (Ans. 3.278 kms-1)
PART H
1.A rocket is launched vertically from the surface of the earth with an initial velocity of 10 kms -1. How far
above surface of the earth would it go ? Radius of earth = 6400 km and g = 9.8 ms -2. (Ans. 2.5 × 104 km)
2.A satellite of mass 250 kg is orbiting the earth at a height of 500 km above the surface of earth. How
much energy must be expended to rocket the satellite out of the gravitational influence of the earth ? Given
mass of the earth = 6.0 × 1024 kg,radius of the earth = 6400 km and G = 6.67×10-11Nm2 kg-2. (Ans. 7.25 ×
109 J)
3.A body is to be projected vertically upwards fromearth's surface to reach a height of 9R, where R is the
radius of earth. What is the velocity required to do so ? Given g = 10 ms -2 and radius of earth = 6.4 × 10 6 m.
(Ans. 1.073 × 104ms-1)
4.Show that the velocity of a body released at a distance r from the centre of the earth, when it strikes the
surface of the earth is given bywhere R and M are the radius and mass of the earth respectively. Also show
that the velocity with which the meteorites strike the surface of the earth is equal to the escape velocity.
5.Calculate the energy required to move an earth satellite of mass 10 3 kg from a circular orbit of radius 2R
to that of radius 3R. Given mass of the earth, M = 5.98 × 10 24 kg and radius of the earth, R = 6.37 × 10 6 m.
[Delhi 141 (Ans. 5.02 × 109 J
PART I
1.The distance of Venus from the sun is 0.72 AU. Find the orbital period of Venus. (Ans. 223 days)
2.If the earth be one half its present distance from the sun, how many days will the present one year on the
surface of earth change ? (Ans. Year decreases by 236 days)
3.The distance of planet Jupiter from the sun is 5.2 times that of the earth. Find the period of revolution of
Jupiter around the sun. (Ans. 11.86 years)
4.The planet Neptune travels around the sun with a period of 165 years. Show that the radius of its orbit is
approximately 30 times that of earth's orbit, both being considered as circular.
5.A geostationary satellite is orbiting the earth at aheight 6R above the surface of earth, where R is the
radius of the earth. Find the time period of another satellite at a height of 2.5R from the surface of earth in
hours.[IIT 87] (Ans. 6√2 h)
6. The radius of earth's orbit is 1.5 × 10' km and that of Mars is 2.5 × 10 11 m. In how many years, does
the Mars complete its one revolution? (Ans. 2.15 years)
7. A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and
minimum distances of the planet from the sun are r1 and r2 respectively. Find the relation for the time period
of the planet in terms of r1 and r2. (Ans. T(r1 + r2)3/2]
 CHAPTER 8 GRAVITATION
(MOTS AND LOTS TYPE)
TYPE A – VERY SHORT ANSWER QUESTIONS ( 1 MARKS EACH)
1. What is difference between gravitation and gravity ?
2. What do you mean by free fall of a body ?
3. State Newton's law of gravitation.
4. Does the force of attraction between two bodies depend upon the presence of other bodies and
properties of intervening medium ?
5. The value of G on the surface of earth is6.67×10-11 Nm2 kg-2. What is its value on the moon ?
6. What is the dimensional formula of gravitational constant?[Delhi 13]
7. Do all the bodies fall with the same constant acceleration in the absence of air resistance ?
8. What are the values of g and G at the centre of the earth ?
9. Give one point of difference between g and G.
10. Which is scalar and which is vector amongst g andG?
11. Name the scientist who first determined the value of G experimentally.
12. Name the apparatus used for the experimental determination of G.
13. Do the gravitational forces obey Newton's third law of motion ?
14. The gravitational force between two bodies is 1 N.If the distance between them is doubled, what will
be the force ?[Himachal 06]
15. Does the acceleration with which a body fallstowards the centre of the earth depend on mass of the
body ?
16. Calculate the force of attraction between two balls each of mass 1 kg when their centres are 10 cm
apart. The value of gravitational constant
G = 6.67 × 10-11 Nm2kg-2. [Delhi 97]
17. The distance of Pluto from the sun is 40 times the distance of earth. If the masses of earth and Pluto
be equal, what will be ratio of gravitational forces of sun on these planets ?
18. Write an expression for the acceleration due to gravity on the earth's surface.
19. Write an equation for the mean density of the earth.
20. The gravitational force acting on a rocket at a height h from the earth's surface is 1/ 3 rd of the force
acting on a body at sea level. What is relation between h and R e (radius of the earth) ?
21. The mass and diameter of a planet are twice those of the earth. What will be acceleration due to gravity
at the planet, if acceleration due to gravity on the earth is g ?
22. What is the mass of a body that weighs 1 N at a place where g = 9.80 ms -2 ?
23. How much is the torque due to gravity on a body about its centre of mass ?
24 Which is greater - the attraction of earth for 1 kg of iron or attraction of 1 kg of iron for the earth ?
Give reason.
25. Has gravity any effect on inertial mass ?
26. Why do different planets have different escape velocities ?
27. On what factors does the value of g depend ?
28 What is the effect of altitude on acceleration due to gravity ?
29. What is the effect of non-sphericity of the earth onthe value of 'g' ? [Delhi 03]
30. If accelerations due to gravity at a height h and at a depth d below the surface of the earth are equal,
how are h and d related ?
31 How does the weight of a body vary enroute from the earth to the moon ? Would its inertial mass
change and gravitational mass change ?
32. What is the time period of a sample pendulum at the centre of the earth ?
33. What will be our weight at the centre of earth, if the earth were a hollow sphere ?
34. A body of mass 5 kg is taken to the centre of the earth. What will be its mass there ?
35 If a man goes from the surface of the earth to a height equal to the radius of the earth, then what
will be his weight relative to that on the earth ? What if he goes equally below the surface of the earth ?
36. The earth is acted upon by the gravitational force of attraction due to the sun. Then why does the
earth not fall towards the sun ?
37 Suppose the earth stops rotating about its axis. What will be the effect on the weight of bodies ?
38 If the earth rotates faster, how does g change at poles ?
39. What is the effect on our weight due to revolution of the earth about the sun ?
40. Write the formula for the gravitational potential energy of mass m at a finite distance r in the
gravitational field of mass M.
41. What is the work done in bringing a body of mass m from infinity to the surface of the earth ?
42. What is the unit of intensity of the gravitational field ?
43. What is the value of gravitational potential energy at infinity ?
44. What is the value of the gravitational intensity at the earth's surface and at the earth's centre ?
45. What is the relation between gravitational intensity and gravitational potential at a point ?
46. Why is gravitational potential energy negative ?
47. The gravitational potential energy of a body at a distance r from the centre of the earth is U. What is
the weight of the body at that point ?
48. From where does a satellite get centripetal force for moving around its planet ?
49. What is escape velocity ? Write down its minimum value on the surface of the earth.
50. Define orbital velocity of a satellite.
51. How does the orbital velocity of a satellite dependon the mass of the satellite ? [Delhi 04]
52. A satellite revolves close to the surface of a planet.How is its orbital velocity related with velocity of
escape from that planet ?[Chandigarh 07]
53. What are the values of the escape velocities for the moon and the sun respectively ?
54. Which has greater value of escape velocity-Mercury or Jupiter ?
55. Does the escape velocity of a body depend upon the density of a planet ?
56. Why does hydrogen escape from the earth's atmosphere more readily than oxygen ?
57. Does the speed of a satellite remain constant in an orbit ?
58. The speed of revolution of an artificial satelliterevolving close to the surface of the earth is 8 kms-1.
What will be the escape velocity for a body on the earth ?[Manipur 99]
59. A satellite revolving around the earth loses height. What happens to its time period ?
60. If the kinetic energy of a satellite revolving in an orbit close to the earth's surface happens to be
doubled, will the satellite escape ?
61. The escape velocity on earth is 11.2 kms-1. What will be its value on a planet having double the radius
and eight times the mass of the earth ?
62. What is Geosynchronous satellite ?[Delhi 95]
63. What is a parking orbit ?
64. What is the use of stationary orbit ?
65. What is (i) period of revolution and (ii) sense of rotation of a geostationary satellite ? [Himachal 06]
66. The centripetal force on a satellite revolving around the earth is F.
(i) What is the gravitational force due to earth on it ?
(ii) What is the net force on it ?
67. What is the angular velocity of a geostationary satellite in radian per hour ?
68. A spring balance is suspended inside an artificial satellite revolving around the earth. If a body of
mass 1 kg is suspended from it, what would be its reading ?
69. The escape velocity from the earth for a body of 20 g is 11 kms -1. What will be its value for a body
of100 g ?
70. A body lying on the surface of planet Venus has gravitational potential energy equal to - 7.5 × 106
J. How much energy will be required for the body to escape from the planet ?
71. Two artificial satellites are revolving around the earth, one closer to its surface and other away from
it. Which has larger speed ?
72. Write two conditions for the existence of atmosphere on a planet.[
73. Write the most important applicationofgeostationarysatellite.
74. What would happen toanartificial satellite if itsorbital velocity is slightly decreased due to some
defects in it ?
75. What is the frequency of oscillation of a simplependulum mounted in a cabin that is freely falling under
gravity ? [Delhi 05]
76. What is the basis ofKepler'slawof areas ofplanetary motion ?
77. What is the basis of Newton's law of gravitation ?
78. A simple pendulum is mounted inside a spacecraft. What should be its time period of vibration ?
79. The gravitational potential energy of a body at a point in a gravitational field of another body
GMm
is− r . What does thenegative sign show ?

80. What is a polar satellite ?[Delhi16]

81. What is full form of geostationary satellite APPLE ?
82. What will be the kinetic energy needed to project abody of mass m from the earth's surface (radius R)
to infinity ?
83. What is gravitational force ?
84. Define universal gravitational constant.
85. What is the weight of a body at the centre of theearth ?
86. Where does the body weigh more - at the surface ofthe earth or in a mine ?
87. If the change in the value of 'g' at a height 7/ abovethe surface of earth is same as that at a depth 'x'
below it (both x and h being much smaller than radius of earth), then how are x and h related to each
other ?
88. How would the value of 'g' change if the earth were to shrink slightly without any change in mass ?
89. If the radius of the earth shrinks by 1 percent, its mass remaining the same by what percentage will the
acceleration due to gravity on its surface change ?
90. The distances of two planets from the sun are 10 11 m and 1010 m respectively. What is the ratio of time
period of these two planets ?
91. Name India's first cosmonaut.
92. What is weightlessness ?
93. Give two uses of geostationary satellites.
94. Give two uses of polar satellites.
95.What are the time period and height of a geostationary satellite above the surface of the earth ?

TYPE B – SHORT ANSWER QUESTIONS ( 2 OR 3 MARKS)

1. State Newton's law of gravitation. Hence define universal gravitational constant. Give the value and
dimensions of G. [Meghalaya 96, 99 ; Himachal 07]
2. State the universal law of gravitation. Establish the relationship M g = gR2 / G, where Me and Re are the
mass and radius of the earth respectively.
3. Define acceleration due to gravity. Deriveexpression for the variation of 'g' with height from the surface of
the earth.
4. Derive an expression for g (acceleration due to gravity) at a depth d from the surface of earth. Consider
the earth as a sphere of uniform mass density. What happens to 'g' at the centre of earth.
5. Define acceleration due to gravity. Show that gravity decreases with depth.
6. Explain the variation of ‘g‘ with (i) shape of earth ; (it) rotation of earth and prove that the weight of body
remains unchanged at the poles of earth.
7. Discuss the variation of ‘g‘ (i) with altitude (ii) with depth (iii) with latitude : Rotation of earth.
8. Show that the acceleration due to gravity at a height h above the surface of the earth has same value as
that at depth d = 2h below the surface of the earth.
9. Explain gravitational potential at a point in gravitational field. Give relation between gravitational field
intensity and gravitational potential. [Delhi 17]
10. Define gravitational potential energy. Give its SIunit. [Delhi 13]
11. Define the term gravitational field. Show that acceleration due to gravity is equal to the intensity of
gravitational field at any point.
12. Define gravitational potential. Give its SI unit.
13. What do you mean by gravitational potential energy of a body ? Obtain an expression for it for a body of
mass m lying at distance r from the centre of the earth. Hence write the expression for gravitational
potential. [Chandigarh 08 ; Delhi 08, 10]
14. (i) What is meant by gravitational field strength ? (ii) Which of the planets of the solar-system hasthe
greatest gravitational field strength ?
(iii) What is the gravitational field strength of a planet where the weight of a 60 kg astronaut is 300 N ?
15. What is the maximum value of potential energythat can be possessed by a heavenly body ? Give the
general expression for potential energy of an object near the surface of earth. [Central Schools
03]
16. Define gravitational P.E. Write the relation between gravitational potential and gravitational P.E.
17. (i) Define escape velocity.
(ii) Derive expression for the escape velocity of an object from the surface of a planet.
(iii) Does it depend on location from where it is projected
18. Derive an expression for the escape velocity of a satellite projected from the surface of the earth.
19. What is escape velocity ? Prove that escape velocity from the surface of earth is 112 kms -1.
20. What happens to a body when it is projectedvertically upwards from the surface of the earth with a
speed of 11200 m/s, and why ? Compare escpae speeds for two planets of masses M and 4M and
radii 2 R and R respectively . [Delhi 2003]
21. A black hole is a body from whose surface nothingmay ever escape. What is the condition for a
uniform spherical mass M to be a black hole ? What should be the radius of such a black hole if its
mass is the same as that of the earth ? [Delhi 03C]
22. Define the term orbital speed. Establish a relationfor orbital speed of a satellite orbiting very close to
the surface of the earth. Find the ratio of this orbital speed and escape speed. [Delhi 05]
23. What are geostationary satellites ? Calculate the height of the orbit above the surface of the earth in
which a satellite, if placed, will appear stationary.
24. Find the expression of total energy of a satellite revolving around the surface of earth. What is the
significance of negative sign in the expression ?
25. What is the binding energy of a satellite. Derive anexpression for it. [Delhi 17]
26. State and explain Kepler's laws of planetary motion. Name the physical quantities which remain
constant during the planetary motion.
27. State and derive Kepler's law of periods (or harmonic law) for circular orbits.
28. (a) According to Kepler's second law, the radiusvector to a planet from the sun sweeps out equal areas
in equal interval of time. The law is consequence of which conservation law ?
29. (a) State Kepler's third law of periods.
(b)Two satellites are at different heights (smaller and larger) from the surface of earth. Which would
have greater velocity ?
(c)What is the formula for escape velocity interms of g and R ?
30. What is a polar satellite ? Explain how does it scan the entire earth in its each revolution ? Give two
important uses of a polar satellite.
31. What do you mean by the term weightlessness ? Explain the state of weightlessness of
(i) a freely falling body
(ii) an astronaut in a satellite orbiting the earth.
32. Distinguish between inertial and gravitational masses, giving an illustration for each. Show that the two
types of masses are equivalent.
33. State the conditions necessary for a satellite toappear stationary.
34. Define orbital velocity. Derive an expression for theorbital velocity of a satellite revolving around a
planet.
35. Two bodies of masses M and m ( M > m) areallowed to fall freely from the same height. If air resistance
for each body is same, which one will reach the ground first.

TYPEC – LONG ANSWER QUESTIONS ( 5 MARKS)

1.. Explain how did Newton discover the universal law of gravitation ?
2. What is meant by acceleration due to gravity ? Obtain an expression for it in terms of mass of the earth
and gravitational constant. Explain how the mass and the density of the earth can be obtained from the
knowledge of G.
3. What do you mean by acceleration due to gravity ?Discuss the variation of g on the surface of the earth
due to axial rotation of the earth. Derive the necessary relation.
4. Obtain an expression for the acceleration due togravity on the surface of the earth in terms of mass of
the earth and its radius. Discuss the variation of acceleration due to gravity with altitude, depth and
rotation of the earth.
5. What is escape velocity ? Obtain an expression for the escape velocity on earth. Why is it that there is
no atmosphere on the moon ? Explain. [Chandigarh 08 ; Delhi 16]
6. (a) Define Orbital velocity and establish anexpression for it.
(b) Calculate the value of orbital velocity for an artificial satellite of earth orbiting at a height of 1000
km.
7. Define orbital velocity and time period of a satellite. Derive expressions for these.
8. State Kepler's laws of planetary motion. Deduce Newton's law of gravitation from Kepler's law.
 CHAPTER 8 GRAVITATION
(HOTS AND MOTS TYPE)
1. The force of gravitation is
(a)repulsion (b) electrostatic (c) conservative (d) non-conservative
2. Which of the following is an evidence to show that there must be a force acting on earth and directed toward
the sun ?
(a) deviation of the falling bodies towards east (b) revolution of the earth round the sun
(c) phenomenon of day and night (d) apparent motion of sun round the earth
3. A man waves his arms, while walking. This is
(a) to keep constant velocity (b) to ease the tension
(c) to increase the velocity (d) to balance the effect of earth's gravity
4. If mass of a body is M on the earth surface, then the mass of the same body on the moon surface is
(a) M/6 (b) zero (c) M (d) none of these
5. Two spheres of same size, one of mass 2 kg and another of mass 4 kg are dropped simultaneously from
the top of Qutab Minar (height = 72 km). When they are 1 m above the ground, the two spheres have the
same
(a) momentum (b) kinetic energy (c) potential energy (d) acceleration [AIIMS 06]
6. Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration of gravity g 1 /
g2 at the surfaces of the planets is
(a) r1 / r2 (b) r2 / r1 (c)(r1/r2)2 (d)(r2/r1)2 (AIIMS 85]
7. If the radius of earth shrinks by one percent and its mass remaining the same, then acceleration due to
gravity on the earth's surface will
(a) decrease (b) increase (c) remain constant (d) either (a) or (c)
8. At what depth below the surface of the earth, is the value of g same as that of a height of 5 km ?
(a) 10 km (b) 7.5 km (c) 5 km (d) 2.5 km [AIIMS 2K]
9 A body weighed 250 N on the surface. Assuming the earth to be a sphere of uniform mass density, how
much would it weigh half way down to the centre of earth ?
(a) 240 N (b) 210 N (c) 195 N (d) 125 N [AIIMS 95]
10. Knowing that mass of moon is M/81 (where M is the mass of earth), find the distance of the point, where
gravitational field due to earth and moon canceleach other. Given that the distance between the earth and
moon is 60 R, where R is the radius of earth.
(a) 2R (b)4R (c) 6 R (d) 8 R
11. If the earth stops moving around its polar axis, then what will be the effect on the weight of a body placed
at the south pole ?
(a) Remain same (b) Increase (c) Decrease but not zero (d) Decrease to zero
12. The value of g at a particular point is 9.8 ms -2. Suppose the earth suddenly shrinks uniformly to half its
 present size without losing any mass. The value of g at the same point (distance of the point from the
centre of the earth does not change) will now be
(a) 9.8 ms-2 (b) 4.9 ms-2 (c) 19.6 ms-2 (d) 39.2 ms-2 [AIIMS 13]
13. A wire of length l and mass m is bent in the form of a semicircle. The gravitational field intensity at the
centre of semicircle is

Gm Gm 2 πGm 2 πGm
(a) πl along x-axis (b) πl
along y-axis (c) l2
along y-axis (d) l2
along x-axis

14. The maximum vertical distance through which a full dressed astronaut can jump on the earth is 0.5 m.
Estimate the maximum vertical distance through which he can jump on the moon, which has a mean density
2/3 rd that of the earth and radius one quarter that of the earth.
(a) 1.5 m (b) 3 m (c) 6 m (d) 7.5 m [AIIMS 2014]
15. The reading of a spring balance corresponds to 100 N while situated at the north pole and a body is kept
on it. The weight recorded on the same scale if it is shifted to the equator (take, g =10m/s 2 and radius of the
earth, R = 6.4 × 103m) is
(a) 99.66 N (b) 110 N (c) 97.66 N (d) 106 N [AIIMS 15]
16. The velocity with which a projectile, must be fired so that it escapes earth's gravitation, does not depend
on
(a) mass of the earth ( b) mass of the projectile
(c) radius of the projectile's orbit (d) gravitational constant [AIIMS 03]
17. The angular velocity of rotation of a star (of mass M and radius R) at which the matter starts to escape
from its equator, is
(a)√2 GM 2 ⁄R (b) √2 GM⁄R3 (c) √2 GM⁄R (d) √2 GR⁄M
18. In what manner, does the escape velocity of a particle depend upon its mass ?
(a)m2 (b) m (c) m0 (d) m-1
19. Escape velocity of a body, when projected from the earth's surface is 11.2 km s-1. If it is projected at an
angle of 60° with the horizontal, then escape velocity will be
(a) 11.2 km s-1 (b) 11.b km s-1 (c) 12.8 km s-1 (d) 16.2 km s-1
20. The mass of moon is 1/81 of earth's mass and its radius ¼ of that of earth. If the escape velocity from the
earth's surface is 11.2 km s-1, its value for the moon is
(a) 0.14 km s-1 (b) 0.76 km s-1 (c) 2.45 km s-1 (d) 5.2b km s-1 [AIIMS 2K]
21. The escape velocity from the earth is 11.2 km s-1. The escape velocity from a planet having twice the
radius and the same mean density as the earth is
(a) 22.4 km s-1 (b) 11.2 km s-1 (c) 5.5 km s-1 (d) 15.5 km s-1
22. There is no atmosphere on the moon, because
(a) it is closer to the earth and also it has the inactive inert gases in it.
(b) it is too far from the sun and has very low pressure in its outer surface.
(c) escape velocity of gas molecules is greater than their root mean square velocity.
 (d) escape velocity of gas molecules is less thantheir root mean square velocity. [AIIMS 94]
23. A missile is launched with a velocity less than escape velocity. The sum of its kinetic and potential
energies is
(a) zero (b) negative (c) positive (d) first (u) then (b)
24. A satellite of the earth is revolving in a circular orbit with a uniform speed r. If the gravitational force
suddenly disappear^, the satellite will
(a) continue to move with velocity v along the original orbit (b) move with a velocity v tangentially to the
original orbit
(c) fall down with increasing velocity (d) ultimately come to rest, somewhere on theoriginal orbit
25. Two satellites of masses m1and m2 (m1 > m2) are going around the earth in orbits of radii r1and r2(r1>r2).
Which statement about their velocities is correct ?
(a) v1 = v2 (b) v1/r1= v2/r2 (c) v1>v2 (d) v1<v2 [AIIMS 94]
26. If v be the orbital velocity of a satellite in a circular orbit close to the earth's surface and v e is the escape
velocity from the earth, then relation between the two is
(a)ve=v (b)ve=√2v (c) v = √3ve (d) ve = 2v [AIIMS 02]
27. A satellite is in an orbit around the earth. If its kinetic energy is doubled, then
(a) it will maintain its path (b) it will fall on the earth
(c) it will rotate with a great speed (d) it will escape out of earth's gravitational field
28. All the known planets move in
(a) straight path (b) circular path (c) elliptical path (d) hyperbolic path
29. Kepler's second law is based on
(a) Newton's first law(b) Newton's second law
(c) Special theory of relativity(d) conservation of angular momentum.
30. The radius vector, drawn from the sun to aplanet sweeps out equal areas in equal times. This is the
statement of
(a) Kepler's first law (b) Kepler's second law (c) Kepler's third law (d) Newton's third law
31. The orbital speed of Jupiter is
(a) greater than the orbital speed of earth (b) less than the orbital speed of earth
(c) equal to the orbital speed of earth (d) proportional to distance from the earth.
32. For a planet moving around the sun in an elliptical orbit of semimajor and semiminor axes a and b
respectively and period T,
(a) the torque acting on the planet about the sun is non-zero
(b) the angular momentum of the planet about the sun is constant
(c) the planet moves with a constant speed around the sun
(d) the areal velocity is πab/T
33. An artificial satellite moving in a circular orbitaround the earth has a total (kinetic + potential) energy E 0.
Its potential energy is
(a) -E0 (b) 1.5 E0 (b)2E0 (d) E0 [AIIMS 12]
Assertions and Reasons
Directions. In the following questions (34 - 49), a statement of assertion is followed by a statement of reason.
Mark the correct choice as
(a) If both assertion and reason are true and reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not correct explanation of the assertion.
(c) If assertion is true, but reason is false.
(d) If both assertion and reason are false.
34. Assertion. The stars twinkle, while the planets do not.
Reason. The stars are much bigger in size than the planets. [AIIMS 03]
35. Assertion. A planet is a heavenly body revolving round the sun.
Reason. Star is a self-luminous body made of gaseous material. [AIIMS 02]
36. Assertion. The comets do not obey Kepler's laws of planetary motion.
Reason. The comets do not have elliptical orbits.[AIIMS 95]
37. Assertion. The square of the period of revolution of a planet is proportional to the cube of its distance from
the sun.
Reason. Sun's gravitational field is inversely proportional to the square of its distance from the planet.
38. Assertion. The earth is slowing down and as a result, the moon is coming nearer to it.
Reason. The angular momentum of the earth-moon system is not conserved. [AIIMS 03]
39. Assertion. The length of the day is slowly increasing.
Reason. The dominant effect causing a slow down in the rotation of the earth is the gravitational pull of
other planets in the solar system. [AIIMS 03,11]
40. Assertion. The earth without its atmosphere would be inhospitably cold.
Reason. All heat would escape in the absence of atmosphere.
41. Assertion. The time-period of pendulum on a satellite orbiting the earth is infinity.
Reason. Time-period of a pendulum is inversely proportional to √g. [AIIMS 02]
42. Assertion. If a pendulum falls freely, then its time period is infinite.
Reason. Free falling body has acceleration equal to g. [AIIMS 97]
43. Assertion. Am astronaut experiences weightlessness in a space satellite.
Reason. When a body falls freely, it does not experience gravity. [AIIMS 07]
44. Assertion. The difference in the value of acceleration due to gravity at pole and equator is proportional
to square of angular velocity of earth.
Reason. The value of acceleration due to gravity is minimum at the equator and maximum at the
pole.
45. Assertion. At the centre of earth a body has centre of mass, but no centre of gravity.
Reason. This is because g = 0 at the centre of earth.
46. Assertion. A planet moves faster, when it is closer to the sun in its orbit and vice-versa.
Reason. Orbital velocity in orbit of planet is constant. [AIIMS 12]
47. Assertion. A satellite moving in a circular orbit around the earth has a total energy E0, then its potential
energy is -E0.
GMm
Reason. Potential energy of the body at a point in agravitational field of orbit is - .
R

48. Assertion. An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason. An object moving around the earth under the influence of earth's gravitational force is in a
 state of 'free fall'.

CHAPTER 8 GRAVITATION
(MOTS AND LOTS TYPE)
1.Two spheres of masses m and M are situated in air and the gravitational force between them is F.
The space around the masses is now filled with a liquid of specific gravity 3.
The gravitational force will now be
(a)3F (b) F (c) F/3 (d) F /9 [CBSE PMT 03]
2. The earth (mass = 6 × 1024 kg) revolves around the sun with an angular velocity of 2 × 10 -7 rad/s in a circular
orbit of radius 1.5 × 10s km. The force exerted by the sun on the earth, in newton, is
(a)36×1021 (b)27×1039 (c) zero (d)18 × 1025 [CBSE PMT 03]
3. Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational
attraction. The speed v of each particle is
1 Gm 4Gm 1 1 Gm
(a) √ (b) √ (c) √ (d) √ [CBSE PMT 95]
2 R R 2R Gm R

4. If the gravitational force between two objects were proportional to 1/ R (and not as 1/ R2), where R is the
distance between them, then a particle in a circular path (under such a force) would have its orbital speed v,
proportional to
(a) R (b) R0 (independent of R) (c) 1 / R2 (d) 1 / R [CBSE PMT 89, 94]
5. Gravitational force is required for
(a) stirring of liquid (b) convection (c) conduction (d) radiation [CBSE PMT 06]
6. What will be the formula of mass of the earth in terms of g, R and G ?
R R2 R g
(a) G g
(b)g G
(c)g2G (d)G R

7. The acceleration due to gravity g and mean density of the earth ρ are related by which of the following
relations ? (where G is the gravitational constant and R is the radius of the earth)
3g 3g 4πgR2 4πgR3
(a) ρ = (b)ρ= (c)ρ = (d)ρ = [CBSE PMT95]
4πGR 4πGR3 3G 3G

8. The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface
of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet
would be
1 1
(a) 2 R (b) 4 R (c) 4 R (d) 2 R [CBSE PMT 04]
9. 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
(a)g'=g/9 (b)g'=27g (c)g'=9g (d)g'=3g
10. A spherical planet has a mass Mp and diameter Dp. A particle of mass mfalling freely near the surface of
this planet will experience an acceleration due to gravity, equal to
 (a)4GMp/D2p (b)GMpm/D2p (c) GMp/D2p (d) 4GMpm/D2p
11. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A
man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet
B?
(a) (2/9) m (b) 18 m (c) 6 m (d) (2/3) m [CBSE PMT 03]
12. A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then
gravitational force exerted on it will be
(a) 36 N (b) 32 N (c) 144 N (d) 50 N[CBSE PMT 2K]
13. The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is about 10 times
mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be
(a) 20 N (b) 8 N (c) 80 N (d) 40 N
14. The height at which the weight of a body becomes 1/16th, its weight on the surface of earth (radius R), is
(a) 5 R (a) 15 R (c) 3R (d)4R
15. A body of mass m is placed on earth surface which is taken from earth surface to a height of h =3R. Then
change in gravitational potential energy is
mgR 2 3 mgR
(a) 4
(b) 3 mgR (c) 4 mgR (d) 2

16. A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth.
The change in potential energy of body will be
2 1
(a) mg2 R (b) mgR (c)3mgR (d) mgR
3 3

17. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravita-
tional potential at a point situated at a 12 distance from the centre, will be
3 GM 2 GM GM 4 GM
(a) - a
(b) - a
(b) - a
(d) - a

18. Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m, ...
respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
8 4
(a) - G (b)- 3 G (b) -3 G (d) -4G
19. Dependence of intensity of gravitational Held (E) of earth with distance (r) from centre of earth is correctly
represented by

20. Which one of the following plots represents the variation of gravitational Held on a particle with distance r
due to a thin spherical shell of radius R ? (ris measured from the centre of the spherical shell)
21. The escape velocity of a sphere of mass m is given by (G = universal gravitational constant ; M e = Mass of
the earth and R, - Radius of the earth)
2GMem 2GMe GMe 2GMe+Re
(a)√ Re
(b)√ R𝑒
(c)√ Re
(d)√ Re

22. For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical,
then escape velocity will be
11
(a) 11 km/s (b) 11√3 km/s (a) km/s (d) 33 km/s
√3

23. The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45°
to the vertical, then the escape velocity is
(a) 11.2 × 2 km/s (b) 11.2 km/s (c) 11.2/√2 km/s (d) 11.2 √2 km/s
24. The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to
twice its present value and radius of the earth becomes half, the escape velocity becomes
(a) 22.4 km/s (b) 44.8 km/s (c) 5.6 km/s (d) 11.2 km/s [CBSE PMT 97]
25. For a planet having mass equal to mass of the earth, the radius is one fourth of radius of the earth. Then
escape velocity for this planet will be
(a) 11.2 km/sec (b) 22.4 km/sec (c) 5.6 km/sec (d) 44.8 km/sec
26. With what velocity should a particle be projected so that its height becomes equal to radius of earth ?
GM
1⁄2 8GM
1⁄2 2GM
1⁄2 4GM
1⁄2
(a)( ) (b)( ) (c)( ) (d)( )
R R R R

27. The earth is assumed to be a sphere of radius R. A plateform 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 off is
(a) 1/2 (b)√2 (c) 1/√2 (d) 1/3 [CBSE PMT 06]
28. A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the
radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity
on the surface of the earth. The minimum value of u so that the particle does not return to earth, is
2GM 2GM 2gM
(a)√2gR2 (b)√ R2
(c)√ R
(d)√ R2

29. If ve is escape velocity and v0 is orbital velocity of a satellite for orbit close to the earth' surface, then these
are related by
(a)v0 = √2ve (b) v0 = ve (c) ve = √2v0 (d) ve = √2v0
30. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To
what approximate radius would earth (mass = 5.98 × 10 24kg) have to be compressed to be a black hole ?
(a)10-9m (b) 10-6m (c) 10-2m (b)100m [AIPMT 14]
31. A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25×10 6m above the surface of
earth. If earth's radius is 6.38×10 6m and g =9.8 ms-2, then the orbital speed of the satellite is
(a) 6.67 km s-1 (b) 7.76 km s-1 (c) 8.56 km s-1 (d) 9.13 km s-1
32. The radii of circular orbits of two satellites A and B of the earth are 4R and R, respectively. If the speed of
satellite A is 3 V, the the speed of satellite B will be
(a) 3 V/4 (b)6V (c) 12 V (d) 3 V / 2
33. A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass2m is
at a distance of 2 r from the earth's surface. Their time periods are in the ratio of
(a) 1 : 2 (b) 1 : 16 (c) 1 : 32 (d) 1 : 2√2
34. The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at
earth's surface is g. What will be the radius of the orbit of a geostationary satellite ?
(a) (R2g/ω2)1/3 (b)(Rg/ω2)1/3 (c)(R2ω2/g)1/3 (d)(r2g/ω)1/3
35. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
(a) 1/2 (b)1/√2 (c) 2 (d)√2
36. The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total
energy ?
(a) (3/4)mv2 (b) (1/2 )mv2 (c) mv2 (d) -(1/2 )mv2
37. A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to
the ball ?
(a) it will fall down to the earth gradually (b) it will go very far in the space
(c) it will continue to move with the same speed along the original orbit of spacecraft
(d) it will move with the same speed, tangentially to the spacecraft.
38. The largest and the shortest distances of the earth from the sun are r ↑ and r2. Its distance from the sun
when it is at perpendicular to the major-axis of the orbit drawn from the sun, is
r1+r2 r +r 2r1r2 r1+r2
(a) 4
(&) r1−r2 (c) r (d) [CBSE PMT 88]
1 2 1 +r2 3

39. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is
how many times greater than that of B from the sun ?
(a) 4 (b) 5 (c) 2 (d) 3 [CBSE PMT 97]
40. The distances of two planets from the sun are1013 m and 1012mrespectively.Theratio of
timeperiods of the planets is
(a) √10 (b) 10√10 (c) 10 (d) 1 / √10
41. A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth, Rbeing the
radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth
6
is (a) 5 (b) 10 (c)6√2 (d)
√2

42. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small
compared to mass of the earth. Then,
(a) the acceleration of S is always directed towards the centre of the earth
(b) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains
constant
(c) the total mechanical energy of S varies periodically with time
(d) the linear momentum of S remains constant in magnitude
43. Two satellites of earth, S1 and S2 are moving in the same orbit. The mass of S 1 is four times the mass of
S2. Which one of the following statements is true ?
(a) The potential energies of earth and satellite in the two cases are equal
(b) S1 and S2 are moving with the same speed
(c) The kinetic energies of the two satellites are equal
(d) The time period of S1 is four times that of S2
44. A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand respectively for its kinetic
energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of
force, which of the following is correct ?
(a) T is conserved (b) V is always positive (c) E is always negative
(d) L is conserved but direction of vector L changescontinuously [CBSE PMT 90]
45. A satellite in force free space sweeps stationaryinterplanetary dust at a rate of dM / dt = αv, where M is
mass and v is the speed of satellite and α is a constant. The acceleration of satellite is
−αv2 −2αv2 −αv2
(a) 2M
(b) -αv2 (c) M
(𝑑) M
[CBSE PMT 94]

46. The figure shows elliptical orbit of a planet m about the sun S. The shaded area of SCD is twice the

shaded area SAB. If t1 is the time for the planet to move from C to D and t 2 is the time to move from A to B,
then
(a) t1 = 4t2 (b) t1=2t2 (c) t1= t2 (d) t1> t2
47. Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to
third power of average distance r between sun and planet i.e., T 2 = Kr3, here K is constant.
If the masses of sun and planet are M and m respectively, then as per Newton' law of gravitation force of
GMm
attraction between them is F = r2 , here G is gravitational constant. The relation between G and K is
described as
1
(a) GMK = 4π2 (b) K = G (c) K = G (d) GK = 4π2 [AIPMT 15]