By Raman sir

9988179237
Assignment
Gravitation
1. The largest and shortest distance of earth from
the sun are r1 and r2. Its distance from the sun when 5. Two spheres of masses m and M are situated in
it is perpendicular to the major axis of the orbit air and the gravitational force between them is F.
drawn from the sun The space around the masses is now filled with
liquid of specific gravity 3. The gravitational force
will now be
(a) 3F
(b) F
(c) F/3
(d) F/9

6. A satellite is moving in a circular orbit at a height

2. The distance of two planets (neptune and saturn) 100 km above the earth's surface. A person inside
form sun are 10^13 and 10^12 m respectively. The the satellite feels weightless because
ratio of time period of planets is (a) acceleration due to gravity is almost zero at
(a) 100 such a height
(b) 1 / √10 (b) the earth does not exert any force on the
(c) √10 person.
(d) 10√10 (c) the centripetal force makes the satellite move
in a circular orbit.
3. The period of revolution of a certain planet in an (d) the forces due to earth and moon are almost
orbit of radius R is T. Its period of revolution in an
compensated at such a height.
orbit of radius 4R will be
(a) 2T 7. The density of a newly discovered planet is twice
that of earth. The acceleration due to gravity at the
(b) 2 √2 T
surface of the planet is equal to that at the surface
(c) 4T
of the earth. If the radius of the earth is R, the
(d) 8T radius of the planet would be

4. If the radius of earth were to increase y 1%, its (a) 2R

mass remaining the same, the acceleration due to (b) 4R
gravity on the surface of the earth will (c) R/4
(a) increase by 1% (d) R/2
(b) decrease by 2%
8. Average density of the earth
(c) decrease by 1%
(a) is directly proportional to g
(d) increase by 2%
(b) is inversely proportional to g
(c) is complex function of g
(d) does not depend on g
9. Choose the correct statement/(s) (a) (3/2)v
(a) Weight of a body is greater on planes and less (b) √(3/2)v
on hill tops. (c) √(2/3)v
(b) Weight of a body is greater at the poles and (d) (2/3)v
less at the equator.
14. The change in potential energy, when a body of
(c) Weight of a body on the moon is less than mass m is raised to a height nR from earth’s surface
that on the earth. is (R= radius of earth)
(d) Weight of a body on the moon is same as that
at a height, equal to radius of moon from the
surface of earth.

10. A simple pendulum is suspended from the roof of

a trolley which moves in a horizontal direction with
an acceleration a, then the time period is given by
, where g' is equal to

15. If g is the acceleration due to gravity on the

earth's surface, the gain in the potential energy of
an object of mass m raised from the surface of earth
to a height equal to the radius R of the earth is
(a) 1/2 mgR
(b) 2 mgR
11. An artificial earth satellite of mass m is circling (c) mgR
round the earth in an orbit of radius R. If the mass (d) 1/4 mgR
of the earth is M, then the total energy of the
satellite is: 16. The escape velocity of earth is V. If the mass of
a certain planet is 3 times and radius 3 times than
(a) 3GMm/2R
that of the earth, then the escape velocity from the
(b) -GMm / 2R
planet will be
(c) GMm/R
(d) -GMm / R

12. The time period of a second’s pendulum in a

satellite is
(a) zero
(b) 2
17. A satellite orbits around the earth in a circular
(c) infinity
orbit with a speed v and orbital radius r. If it losses
(d) depends on mass of body
some energy, then v and changes as
13. The orbital speed of an artificial satellite in a (a) v decreases and r increases.
circular orbit just above the earth's surface is v. For (b) both v and r decreases.
a satellite orbiting at an altitude of half the earth's (c) v increases and r decreases.
radius the orbital speed is (d) both v and r increases.
18. A satellite S is moving in an elliptical orbit 22. The gravitational field due to a mass
around the earth. The mass of the satellite is very distribution is I = K/r³ in the X-direction. (K is a
small compared to the mass of the earth. constant). Taking the gravitational potential to be
zero at infinity, its value at a distance x is:
(a) The acceleration of S is always directed
(a) K/x
towards the centre of the earth.
(b) K/2x
(b) The angular momentum of S about the centre
(c) K/x²
of the earth changes in direction but its
(d) K/2x²
magnitude remains constant.
(c) The total energy of S varies periodically with
time. 23. Escape velocity of a planet is v. If radius of the
planet remains same and mass becomes 4 times, the
(d) The linear momentum of S remains constant
escape velocity becomes
in magnitude.
(a) 4 v
19. A satellite is orbiting just above the surface of a (b) 2 v
planet of average density p with period T. If G is the (c) v
universal gravitational constant, the quantity T^2 p (d) v / 2
is equal to
24. The square of the period of revolution of a
planet around the sun is proportional to the _______
of the semimajor axis of its elliptical orbit.
(a) square
(b) cube
(c) square root
(d) cube root

20. A ring has a total mass M but non-uniformly

distributed over its circumference. The radius of the 25. The orbit at which the satellite will remain static
ring is R. A point mass m is placed at the centre of according to earth is called
the ring. Work done in taking away this point mass (a) polar orbit
from centre to infinity is (b) stationary orbit
(a) -GMm / R (c) parking orbit
(b) GMm / R (d) outer orbit
(c) - GMm/ 2R
26. Suppose universal gravitational constant starts
(d) GMm / R^2
to decrease, then
21. The gravitational potential at a plane varies (a) length of the day, on earth, will decrease.
inversely proportional to x²(i.e., V = k/x²), then (b) length of the year will decrease.
gravitational field intensity at the place is
(c) earth will follow a spiral path of increasing
(a) -k/x radius.
(b) k/x (d) kinetic energy of earth will decrease.
(c) -2k/x³
(d) 2k/x³
27. The earth is an approximate sphere. If the (d) will move in orbits like planets and obey
interior contained matter which is not of the same Keplers's laws.
density everywhere, then on the surface of the earth,
the acceleration due to gravity 31. Choose the wrong option
(a) will be directed towards the centre but not the (a) Inertial mass is a measure of difficulty of
same everywhere. accelerating a body by an external force whereas
(b) will have the same value everywhere but not the gravitational mass is relevant in determining
directed towards the centre. the gravitational force on it by an external mass.
(c) will be same everywhere in magnitude (b) The gravitational mass and inertial mass are
directed towards the centre. equal is an experimental result.
(d) cannot be zero at any point. (c) The acceleration due to gravity on earth is the
same for all bodies is due to the equality of
28. As observed from the earth, the sun appears to
move in an approximate circular orbit. For the gravitational mass and inertial mass.
motion of another planet like mercury as observed (d) Gravitational mass of a particle like proton
from earth. this would can depend on the presence of neighbouring
(a) be similarly true, heavy objects but the inertial mass cannot.
(b) not be true because the force between earth
32. Particles of masses 2M, m and M are
and mercury is not inverse square law.
respectively at points A, B and C with AB = 1/2
(c) not be true because the major gravitational (BC). m is much- much smaller than M and at time
force on mercury is due to sun. = 0, they are all at rest (Fig. 8.1). At subsequent
(d) not be true because mercury is influenced by times before any collision takes place:
forces other than gravitational forces.

29. Both the earth and the moon are subject to the
gravitational force of the sun. As observed from the
sun, the orbit of the moon
(a) m will remain at rest.
(a) will be elliptical.
(b) m will move towards M.
(b) will not be strictly elliptical because the total
(c) m will move towards 2M.
gravitational force on it is not central.
(d) m will have oscillatory motion.
(c) is not elliptical but will necessarily be a closed
curve.
33. Satellites orbiting the earth have finite life and
(d) deviates considerably from being elliptical sometimes debris of satellites fall to the earth. This
due to influence of planets other than earth. is because,
30. In our solar system, the inter-planetary region (a) the solar cells and batteries in satellites run
has chunks of matter (much smaller in size
out.
compared to planets) called asteroids. They
(b) the laws of gravitation predict a trajectory
(a) will not move around the sun since they have
spiralling inwards.
very small masses compared to sun.
(c) of viscous forces causing the speed of satellite
(b) will move in an irregular way because of their
and hence height to gradually decrease.
small masses and will drift away into outer space.
(d) of collisions with other satellites.
(c) will move around the sun in closed orbits but
not obey Kepler's laws.
For following questions, two statements are given-
40. Assertion: The value of acceleration due to
one labelled Assertion (A) and the other labelled
gravity decreases with height as well as depth.
Reason (R). Select the correct answer to these
Reason: At the centre of earth, acceleration due to
questions from the codes (a), (b), (c) and (d) as
gravity is infinite.
given below.
(a) Both A and R are true and R is the correct
explanation of A. 41. Assertion: We can shield a body from
(b) Both A and R are true but R is NOT the gravitational influence of nearby matter by
correct explanation of A. putting it inside a hollow sphere.
(c) A is true but R is false. Reason: This property of gravitational forces is
(d) A is false and R is also false. similar to electrical forces.

34. Assertion: According to Newton's law of

gravitation, the acceleration action on the moon
due to earth should be 1 /(60)^2 times the 42. If the earth stops rotating about its own axis,
acceleration action on a body near the surface of what is the effect on the value of weight of any
earth. object on the surface of earth?
Reason: Distance of the moon from the centre of
the earth is 60 times the distance of a body placed
43. A graph was plotted taking gravitational force
on the surface of the earth from the centre.
(F) along y-axis and the square of the distance (d²)
along x-axis, what is the nature of graph?
35. Assertion: Standard value of acceleration due
to gravity is taken at sea level at a latitude of 30°.
44. Can a satellite be in an orbit in a plane not
passing through the earth's centre? Explain your
Reason: Value of g do not change from place to
answer.
place at the surface of the earth and also in going
above or below, the surface.
45. If earth be at half of its present distance from the
sun, how many days will there be in a year?
36. Assertion: Gravitational potential is always
negative.
46. State Newton's law of gravitation in vector form.
Reason: The gravitational potential energy at
infinity is assumed to be zero.
47. A planet reduces its radius by 1% with its mass
remaining same. How acceleration due to gravity
37. Assertion: Earth is flat at the poles. varies?
Reason: This is due to rotation of earth about its
equatorial axis. 48. What is the gravitational force on a body inside a
spherical shell? Why is it so?
38. Assertion: Heavier bodies have more inertia
and lighter bodies have less inertia. 49. Planet Mars has two moons - phobos and deimos.
Reason: Inertial mass is the ratio of force applied Phobos has a period of 7 hours 39 minutes and
to acceleration caused. orbital radius of 9.4 × 103 km. Calculate the mass of
Mars.
39. Assertion: For orbits close to earth, orbital
velocity of a satellite is given by
50. The change in the value of g at a height h above
the earth is same as at a depth d below it. If /h and d
Reason: Torque on a body about the centre of
are small as compared to the radius of the earth,
mass is zero.
what is the ratio (h/d)?
51. While approaching a planet circling a distant
61. If the radius of the earth were increased by a
star, á space traveller determines the planet's radius
factor of 3, by what factor would its density have to
to be half that of the earth. After Innding on the
be changed to keep 'g' the same?
surface, he finds the acceleration due to gravity to
be twice that on the surface of the earth. Find the
62. If the earth has a mass nine times and radius
ratio of the mass of the planet to that of the earth.
twice that of the planet Mars, calculate the
maximum velocity required by a rocket to pull out
52. Draw the graph showing the variation of
of the gravitational force of Mars. Given escape
acceleration due to gravity with
velocity on the surface of earth is 11.2 km/sec.
(a) height above the earth's surface.
(b) depth below the earth's surface.
63. Suppose there existed a planet that went around
the sun twice as fast as the earth. What would be its
53. The radii of two planets are R and 2R
orbital size as compared to that of the earth?
respectively and their densities p and p/2
respectively. What is the ratio of acceleration due to
64. How will you 'weigh the Sun', that is estimate its
gravity at their surfaces?
mass? The mean orbital radius of the Earth around
the Sun is 1.5 × 10^8 km.
54. Why does the earth have an atmosphere and the
moon does not? 65. A Saturn year is 29.5 times the Earth year. How
far is the Saturn from the Sun if the Earth is 1.50 ×
55. A small mass is released by an astronaut in a 10^8 km away from the Sun?
satellite in space. Will it fall on the earth?
66. A body weighs 63 N on the surface of the earth.
56. A black hole is a body from whose surface What is the gravitational force on it due to the Earth
nothing may ever escape, What is the condition for at a height equal to half the radius of the earth?
a uniform spherical mass M to be a black hole?
67. Assuming the earth to be a sphere of uniform
What should be the radius of such a black hole if its
mass density, how much would a body weigh half way
mass is the same as that of the Earth?
down to the centre of the earth if it weighed 250 N on
57. What is gravitational potential energy at a the surface?
point? How much of work is done in shifting a mass 68. Is it possible for a body to have inertia but no
from the surface to a height equal to its radius? weight?

58. The radius of the earth is reduced by 4%. The 69. Out of aphelion and perihelion, where is the speed
mass of the earth remains unchanged. What will be of Earth more and why?
the change in escape velocity?
70. Two identical heavy spheres are separated by a
59. The mass and diameter of a planet are twice of distance 10 times their radius. Will an object placed
those of the earth. What will be the period of at the mid-point of the line joining their centres be in
oscillation of a pendulum on this planet, if it is a stable equilibrium or unstable equilibrium? Give
second's pendulum on the earth? reason for your answer
71. Write Kepler’s laws for planetary motion.
60. Satellite A is in a certain circular orbit about a
72. State Newton's law of Gravitation. Find the
planet, while satellite B is in a larger circular orbit.
percentage decrease in the weight of the body when
Which satellite has (i) the longer period and (ii) the
taken to a height of 16 km. above the surface of the
greater speed?
earth. Radius of the earth is 6400 km.
73. Three masses, each equal to M, are placed at
83. To what height a mass can go, when sent up with
the three corners of a square of side 'a'. Calculate
a velocity half of the escape velocity?
the force of attraction on unit mass at the fourth
corner 84. What happens to a body when it is projected
vertically upwards from the surface of the earth
74. Find the ratio of the acceleration due to gravity with a speed of 11200 m/s, and why? Compare
of two planets (surface) if their radii are in the ratio escape speeds for two planets of masses M and 4M
1: 2 under the condition, and radii 2R and R respectively.
(1) Mass remains same (ii) Material remains same.
85. Calculate the change in energy of a 500 kg
satellite when it falls from an altitude of 200 km to
75. A 10 kg mass is to be divided into two parts,
199 km. If this change takes place during one orbit,
such that the force of attraction between them is
calculate the retarding force on the satellite. [Given:
maximum. What is the mass of each portion?
mass of earth = 6 × 10^24 kg and radius of earth =
6400 km]
76. Two stationary particles of masses M₁ and M₂
are a distance 'd' apart. A third particle lying on the 86. A 400 kg satellite is in a circular orbit of radius
line joining the particles, experiences no resultant 2R about the earth. How much energy is required to
gravitational force. What is the distance of this transfer it to circular orbit of radius 4R? What are
particle from M₁? the changes in the kinetic energy and potential
energy?
77. How far above the earth's surface does the value
of g becomes 20% of its value on the surface? 87. A rocket is fired with a velocity 0.6 times the
escape velocity on the surface of earth. How high will
78. An astronaut, on his journey between the earth it go from the surface?
and the moon experience weightlessness at a point
88. Two masses each of 100 kg are separated by 1
P. Find the distance of the point P from the centre
metre. Find the gravitational (i) field (ii) potential at
of the earth. (Given: mass of earth is 80 times the
the mid-point of the line joining them.
mass of the moon and the distance between them is
3.84 x 10^5 km). 89. A stationary object is released from a point P a
distance 3R from the centre of the moon which has
79. What is the acceleration due to gravity at the radius R and mass M. Calculate the speed of the
bottom of a sea 30 km deep taking radius of the object on hitting the moon.
earth as 6.3 × 10^6 km?
90. If the earth supposed to be a uniform sphere,
contracts slightly so that its radius becomes less by
80. Suppose a hole was drilled completely through
(R/n) than before, show that the length of the day
the earth along a diameter. Show that the force on a
shortens by (48/n) hours.
mass m at a distance r from the centre of the earth
is assuming that the density of the earth in 91. A body is projected vertically from the surface of
uniform earth with a velocity equal to half of the escape
velocity. What is the maximum height reached by the
81. Prove that gravitational potential difference is body?
the work done in carrying a unit mass from one
point to another. 92. Two satellites A and B go around a planet Pin
circular orbits having radius 4R and R respectively.
82. The kinetic energy associated with a satellite is If the speed of the satellite A is 3V, find the speed of
E. What is the total energy associated? the satellite B.
93. The moon takes about 27 days to complete one
orbit around the earth. The orbit is nearly a circle of
radius 3.8 × 10^8 m. Calculate the mass of the
earth from this data.

94. Jupiter has a mass 318 times that of the earth,

and its radius is 11.2 times the earth's radius.
Estimate the escape velocity of a body from
Jupiter's surface given that the escape velocity from
the earth's surface is 11.2 km s¹.

95. A spaceship is launched into a circular orbit

close to earth's surface. What additional velocity
has to be imparted to the spaceship in the orbit to
overcome the gravitational pull? Radius of earth =
6400 km and g = 9.8 ms^-2.

96. A rocket is launched vertically from the surface

of the earth with an initial speed of 10 km/s. How
far above the surface of the earth would it go?
Ignore the atmospheric resistance. Radius of the
earth = 6400 km.

97. A comet orbits the sun in a highly elliptical

orbit. Does the comet have a constant (a) linear
speed, (b) angular speed, (c) angular momentum, (d)
kinetic energy, (e) potential energy, (f) total energy
throughout its orbit? Neglect any mass loss of the
comet when it comes very close to the sun.

98. Draw areal velocity versus time graph for mars.

99. How is the gravitational force between two point

masses affected when they are dipped in water
keeping the separation between then the same?

100. Six point masses of mass m each are at the

vertices of a regular hexagon of side 1. Calculate
the force on any of the masses.