# Gravitation Questions

We provide gravitation practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on gravitation skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of gravitation Questions

Question NoQuestionsClass
1Make a list of the uses of artificial
satellites.
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2A geostationary satellite is orbiting the earth at a height ( 6 mathrm{R} ) above the surface of earth, where ( R ) is the radius of the
earth. The time period of another satellite at a height of ( 2.5 mathrm{R} ) from the surface of earth in hour is
В. ( 1.5 sqrt{2} h )
c. ( 6 sqrt{2} h )
D. ( 12 sqrt{2} h )
11
3An artificial satellite moving in a circular orbit around the earth has a
total ( (K . E .+P . E .) ) is ( E_{0} . ) Its potential
energy is
A. ( -E_{0} )
в. ( 1.5 E_{0} )
c. ( 2 E_{0} )
D. ( E_{0} )
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4A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth
is ( 11 k m s^{-1}, ) the escape velocity from
the surface ofthe planet would be
A. ( 110 k m s^{-1} )
B. ( 0.11 k m s^{-1} )
c. ( 1.1 k m mathrm{s}^{-1} )
D. ( 11 k m s^{-1} )
11
5Variation in the Acceleration Due to
Gravity:

Outside the earth ( : g=g_{0}left(frac{R_{e}}{x}right)^{2} )

11
6The direction of acceleration due to
gravity depends:
A. on the direction of motion of a body
B. on the direction of motion of body’s acceleration
c. on the direction of motion of body’s velocity
D. none of these
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7Which of the following statements is
true?
A. The satellite ( A ) has a shorter period than the satellite ( B )
B. The satellite ( B ) has a shorter period than the satellite ( A )
C. The two satellites must have the same period
D. The two satellites must have the same linear speed
E. The two satellites must have the same period and the same linear speed
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8Acceleration due to gravity as a
function of ( r ) is given by
A ( cdot frac{4}{3} pi G r(A-B R) )
B . ( 4 pi G r(A-B R) )
c. ( frac{4}{3} pi G rleft(A-frac{3}{4} B Rright) )
D ( cdot frac{4}{3} pi G rleft(A-frac{4}{3} B Rright) )
11
9Write the formula to find the magnitude of the gravitational force between the
earth and an object on the surface of the earth.
11
10A satellite of the earth is revolving in circular orbit with a uniform velocity ( V )
If the gravitational force suddenly disappears, the satellite will
A. continue to move with the same velocity in the same orbitt
B. move tangentially to the original orbit with velocity ( v ).
c. fall down with increasing velocity.
D. come to a stop somewhere in its original orbit.
9
11A tunnel is dug along a diameter of the Earth. The force on a particle of mass ( boldsymbol{m} )
placed in the tunnel at a distance ( x )
from the centre is:
A ( cdot frac{G M_{e} m}{R^{3}} x )
в. ( frac{G M_{e} m}{R^{2}} x )
c. ( frac{G M_{e} m}{R^{3} x} )
D. ( frac{G M_{e} m R^{3}}{x} )
11
12Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when
he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g
is greater at the poles than at the equator.
11
13Four particles, each of mass ( mathrm{m}, ) are placed at the four corners of a square of side ‘a’. Force exerted by this system on another particle of mass ( mathrm{m} ) placed at the midpoint of a side of square is –
A ( cdot frac{16 G m^{2}}{5 sqrt{5 a^{2}}} )
в. ( frac{16 G m^{2}}{5 sqrt{3 a^{2}}} )
c. ( frac{16 G m^{2}}{5 a} )
D. zero
11
14Read the given statements and mark
the correct option
Statement 1: If an earth satellite is on a
lower orbit, the speed of satellite increases
Statement 2: The speed of satelite is a constant quantity for all orbits of earth
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. both statements 1 and 2 are true but statement 2 is not correct explanation of statement
c. statement 1 is true but statement 2 is false
D. Both statements 1 and 2 are false
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15How orbital and escape velocities are
related?
A ( cdot v_{e}=2 v_{0} )
B ( cdot v_{e}=sqrt{3} v_{0} )
c. ( v_{e}=1.31 v_{0} )
D. ( v_{e}=1.41 v_{0} )
11
16A geo-stationary satellite is orbiting the earth at a height of 6 R above the
surface of earth, R being the radius of earth. The time period of another satellite at a height of ( 2.5 mathrm{R} ) from the surface of earth is
A. 10 hr
B ( cdot(-6 / sqrt{2}) h r )
( c cdot 6 h r )
D. ( 6 sqrt{2} h r )
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17If the distance of Earth from the Sun
were half the present value, how many days will make one year?
11
18Calculate the force of gravitation between the earth and the sun, given that the mass of the earth ( =6 times 10^{24} k g )
and of the ( operatorname{Sun}=2 times 10^{30} k g . ) The
average distance between the two is
( 1.5 times 10^{11} m )
11
19The acceleration due to gravity on the moon is one sixth that on the earth. ( A )
high jumper canjump ( 2 mathrm{m} ) on earth. What distance can he jump on the moon?
( A cdot 2 m )
B. ( 6 mathrm{m} )
( c cdot 12 m )
D. 18
9
20Choose the correct statement among
the following options.
A. All bodies repel each other in this universe.
B. Our earth does not behave like a magnet.
C. Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} )
D. All bodies fall at the same acceleration in vacuum in
state of free fall.
11
21Two persons having mass ( 50 mathrm{kg} ) each,
are standing 1 m apart from each other
Calculate the force of gravitation and also calculate the force of gravity on each. (Take ( G=6.67 times 10^{-11} N m^{2} k g^{-2} )
mass of earth ( M=6 times 19^{24} k g )
Radius of earth ( boldsymbol{R}=mathbf{6 . 4} times mathbf{1 0}^{mathbf{6}} boldsymbol{m} ) )?
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22If ( A ) is the areal velocity of planet of
mass ( M . ) its angular momentum is
( mathbf{A} cdot M )
B. ( 2 M A )
c. ( A^{2} M )
D. ( A M^{2} )
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23( mathbf{1} boldsymbol{g} boldsymbol{f}= )
A. ( 250 N )
B. 980 dynes
c. 56 dynes
D. All
9
24Solve:
Estimate the mass of the earth, given,
radius of the earth ( =mathbf{6 . 4} times mathbf{1 0}^{mathbf{6}} mathbf{m} )
acceleration due to gravity ( =9.8 m / s^{2} )
and gravitational constant ( =6.67 times )
( 10^{-11} S . I . ) units.
11
25At a place, value of acceleration due to
gravity ( g ) is reduced by ( 2 % ) of its value
on the surface of the earth (Radius of
earth ( =6400 mathrm{km} ). The place is:-
A. ( 64 mathrm{km} ) below the surface of the earth
B. ( 64 mathrm{km} ) above the surface of the earth
( mathrm{c} .32 mathrm{km} ) above the surface of the earth
D. ( 32 mathrm{km} ) below the surface of the earth
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26Which of the following laws are conserved, if the areal acceleration is
zero
A. Law of conservation of angular velocity
B. Law of conservation of angular momentum
c. Law of conservation of angular acceleration
D. Law of conservation of angular displacement
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27Keplers second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation
of:
A. Linear momentum
B. Angular momentum
c. energy
D. none of the above
11
28A research satellite of mass ( 200 mathrm{kg} ) circles the earth in an orbit of average radius ( frac{3 R}{2}, ) where ( R ) is the radius of the earth. Assuming the gravitational pull on a mass ( 1 mathrm{kg} ) on earth’s surface to be
( 10 mathrm{N}, ) the pull on this satellite will be:
A . ( 860 mathrm{N} )
B. 889 N
c. ( 827 mathrm{N} )
D. 798 N
11
29The moon is observed from two
diametrically opposite points ( A ) and ( B ) on earth. The angle ( theta ) subtended at the
moon by the two directions of
observation is ( 1^{0} 54^{prime} . ) Given the diameter
of the earth to be about ( 1.276 times 10^{7} m )
compute the distance of the moon from
the earth.
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30A large spherical planet of radius ( mathrm{R} ) made of a material of density d, has a spherical cavity of radius R/2,with centre of cavity a distance R/2 from the
centre other planet. Find the gravitational force one small mass ( mathrm{m} ) at
the centre of the cavity.
A. 2 RGmd/3
B. RGmd/3
c. 2RGmd
D. 4 RGmd/3
11
31Acceleration due to gravity as a
function of ( r ) is given by :
A ( cdot frac{4}{3} pi G r(A-B r) )
B . ( 4 pi G r(A-B r) )
c. ( frac{4}{3} pi G rleft(A-frac{3}{4} B rright) )
D ( cdot frac{4}{3} pi G rleft(A-frac{3}{2} B rright) )
11
32How far must a particle be on the line joining earth to sun, in order that the gravitational pull on it due to sun is
counterbalanced by that due to earth.
Given orbital radius of earth is ( 10^{8} mathrm{Km} )
and ( M_{S}=3.24 times 10^{5} M_{E} )
A ( cdot 6.4 times 10^{5} mathrm{Km} )
В. ( 1.75 times 10^{2} mathrm{Km} )
( mathbf{c} cdot 1.75 times 10^{9} mathrm{Km} )
D. ( 6400 mathrm{Km} )
11
33A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then
A. the weight of body will become zero
B. the weight of body will become infinite
c. the mass of the body will become zero
D. the body will vanish in air
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34A spherical uparrow ole of radius ( mathbf{R} / mathbf{2} ) is
excavated from ( mathbf{t} uparrow ) e asteroid of mass
M as shown in fig. T Me gravitational
acceleration at a point on t ( uparrow mathbf{e} )
surf ace of ( mathbf{t} uparrow mathbf{e} ) asteroid just above ( mathbf{t} uparrow )
excavation is :
A. GM/R ( ^{2} )
B. ( mathrm{GM} / 2 mathrm{R}^{2} )
c. ( mathrm{GM} / 8 mathrm{R}^{2} )
D. ( 7 mathrm{gW} 8 mathrm{R}^{2} )
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35If the distance between the earth and
the Sun were half its present value, the number of days in a year would have
been
A . 64.5
в. 129
c. 182.5
D. 730
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36The value of acceleration due to gravity
is ( 980 mathrm{cm} s^{-2} ). What will be its value if
the unit of length is kilometer and that
of time is minute?
11
37A saturn year is 29.5 times the earth
year. How far is the saturn from the sun
if the earth is ( 1.50 times 10^{8} k m ) away from
the sun?
11
38Assertion
Kepler’s second law can be understood by conservation of angular momentum principle.
Reason
Kepler’s second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as ( (boldsymbol{d A} / boldsymbol{d t})=left(boldsymbol{r}^{2} boldsymbol{omega}right) / 2 )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
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39The time period of an earth satellite in
circular orbit is independent of:
A. the mass of the satellite
c. both the mass and radius of the orbit
D. neither the mass of the satellite nor the radius of its orbit
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40Moon is revolving in a circular orbit with
a uniform velocity ( V_{0} ). If the
gravitational force suddenly disappears, the moon will
A. continue to move in the same orbit
B. move with a velocity ( V_{0} ) tangentially to the orbitt
c. fall down freely
D. ultimately comes to rest
9
41At what altitude will the acceleration
due to gravity be ( 25 % ) of that at the earth’s surface (given radius of earth is
( R) ? )
A. ( R / 4 )
в. ( R )
c. ( 3 R / 8 )
D. ( R / 2 )
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42Gravitational force between two point masses ( mathrm{m} ) and ( mathrm{M} ) separated by a distance ( r ) is ( F . ) Now if a point mass ( 3 mathrm{m} ) is placed next to ( mathrm{m} ), what will be the (a) force on M due to ( m,(b) ) total force on M?
A. ( F=4 F )
B. ( F=5 F ).
( mathbf{c} cdot F=6 F )
( mathbf{D} cdot F=7 F )
11
43The escape velocity of an object on a planet whose radius is 4 times that of
the earth and ( g ) value 9 times that on
the earth, in ( mathrm{kms}^{-1} ) is
A. 33.6
B. 67.2
c. 16.8
D. 25.2
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44A stone drop from height ‘h’ reaches to Earth surface in 1 sec. If the same stone
taken to Moon and drop freely then it will reaches from the surface of the
Moon in the time(The ‘g’ of Moon is ( 1 / 6 ) times of Earth)
A. ( sqrt{6} ) second
B. 9 second
c. ( sqrt{3} ) second
D. 6 second
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45The earth’s radius is ( mathrm{R} ) and acceleration
due to gravity at its surface is g. If a
body of mass ( m ) is sent to a height ( h= ) ( boldsymbol{R} )
( frac{i}{5} ) from the earth’s surface, the
potential energy increases by
A . mgh
в. ( frac{4}{5} m g h )
c. ( frac{5}{6} ) mgh
D. ( frac{6}{7} ) mgh
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46A bomb blasts on moon. Its sound will
be heard on earth after
A. 3.7 minutes
B. 10 minutes
c. 138 minutes
D. sound will never be heard
11
47The mass of the earth is ( 6 times 10^{24} mathrm{kg} ) and
that of the moon is ( 7.4 times 10^{22} mathrm{kg} )
distance between the earth and the
moon be ( 3.84 times 10^{5} mathrm{km}, ) calculate the
force exerted by the earth moon. ( (G= ) ( left.6.7 times 10^{-11} N m^{2} k g^{-2}right) )
11
48Let ( ^{prime} boldsymbol{A}^{prime} ) be the area swept by the radial vector connecting the earth and the sun in April and May months. Then, find the area swept by the same radial vector connecting the earth and the sun in
November and December months
interms of ( boldsymbol{A} )
A. ( A )
в. ( 2 A )
c. ( frac{30 A}{31} )
D. ( frac{31 A}{30} )
11
49When a satellite going round the earth
in a circular orbit of radius ( r ) and speed
( v, ) loses some of its potential energy, then :
A. both ( r ) and ( v ) will increase
B. both ( r ) and ( v ) will decrease
c. ( r ) will decrease and ( v ) will increase
D. ( r ) will increase and ( v ) will decrease
11
50The escape velocity from the earth for a rocket is ( 11.2 mathrm{km} / mathrm{s} ) ignoring air resistance. The escape velocity of ( 10 mathrm{mg} ) grain of sand from the earth will be
( mathbf{A} cdot 0.112 mathrm{km} / mathrm{s} )
B. ( 11.2 mathrm{km} / mathrm{s} )
c. ( 1.12 mathrm{km} / mathrm{s} )
D. ( 0.0112 mathrm{kms}^{-1} )
11
51The gravitational field intensity at a point ( 10,000 mathrm{km} ) from the centre of the
earth is ( 4.8 N k g^{-1} . ) The gravitational
potential at the point is
A ( .-4.8 times 10^{7} J k g^{-1} )
B . ( -2.4 times 10^{7} mathrm{Jkg}^{-1} )
C ( .4 .8 times 10^{6} mathrm{Jkg}^{-1} )
D. ( 3.6 times 10^{6} mathrm{Jkg}^{-1} )
11
52In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times
of its present value, then how would the weight of any object on the surface of the earth be affected?
A. Weight is doubled
c. weight becomes 16 times
D. Weight remains same
11
53The escape velocity of a body from earth is about ( 11.2 mathrm{km} / mathrm{s} ). Assuming the mass and radius of the earth to be about 81
and 4 times the mass and radius of the
moon, the escape velocity in ( mathrm{km} / mathrm{s} ) from the surface of the moon will be:
A . 0.54
B. 2.48
( c cdot 11 )
D. 49.5
11
54If masses of two point objects are tripled and distance between them is doubled,then gravitational force of attraction between them will
A. Increase by 225%
B. Decrease by 56%
c. Increase by 125%
D. Decrease by 144%
11
55The Jupiter’s period of revolution around
the Sun is 12 times that of the

Earth. Assuming the planetary orbits to be circular, find the acceleration of Jupiter in the heliocentric reference frame.
A ( cdot 2 times 10^{-4} mathrm{m} / mathrm{s}^{2} )
B. ( 4.2 times 10^{-4} mathrm{m} / mathrm{s}^{2} )
C ( .2 .2 times 10^{-4} mathrm{m} / mathrm{s}^{2} )
D. ( 4 times 10^{-4} mathrm{m} / mathrm{s}^{2} )

11
56The height at which the value of acceleration due to gravity becomes ( 50 % ) of that at the surface of the earth.
(radius of the earth ( =mathbf{6 4 0 0 k m} ) ) is
A . 2650
в. 2430
c. 2250
D. 2350
11
57A ball thrown up vertically returns to the thrower after 6 s. Find
(a) The velocity with which it was
thrown up,
(b) The maximum height it reaches, and
(c) Its position after 4 s.
11
58Assuming the mass of Earth to be ten times the mass of Mars, its radius to be
twice the radius of Mars and the
acceleration due to gravity on the
surface of Earth is ( 10 mathrm{m} / mathrm{s}^{2} ). Then the
acceleration due to gravity on the surface of Mars is given by.
A ( cdot 0.2 m / s^{2} )
B. ( 0.4 m / s^{2} )
c. ( 2 m / s^{2} )
D. ( 4 m / s^{2} )
E ( .5 mathrm{m} / mathrm{s}^{2} )
11
59Two planets have masses ( M_{1} ) and ( M_{2} )
and radii ( boldsymbol{R}_{1} ) and ( boldsymbol{R}_{2} ) respectively. Then
the time periods of near surface satellite of the two planets will be equal if
A. ( M_{1} R_{2}^{2}=M_{2} R_{1}^{2} )
B. ( M_{1} R_{2}^{3}=M_{2} R_{1}^{3} )
( mathbf{c} cdot M_{1}^{2} R_{2}=M_{2}^{2} R_{1} )
D. ( M_{1} R_{1}^{3}=M_{2} R_{2}^{3} )
11
60Consider a planet in some system
which has a mass double the mass of
the earth and density equal to the average density of the earth. If an object weighs ( mathrm{W} ) on the earth, then its weight on the planet is:
( mathbf{A} cdot W )
в. ( 2 W )
c. ( frac{w}{2} )
D. ( 2^{1 / 3} W )
9
61When an object moves with a constant acceleration, under the influence of force of gravitation of the earth only, the object is said to have:
A . free fall
B. accelerated fall
c. projectile motion
D. constant velocity
11
62Imagine 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 the planet and the star is
proportional to ( r^{5 / 2}, ) then the square of the time period will be proportional to.
A ( cdot r^{3} )
в. ( r^{2} )
( c cdot r^{2.5} )
D. ( r^{3.5} )
11
63Imagine a light planet revolving around a very massive star in a circular orbit of
radius R with a speed of revolution T. If the gravitational force of attraction between the planet and the star is proportional to ( boldsymbol{R}^{-5 / 2}, ) then
A ( cdot T^{2} ) is proportional to ( R^{2} )
B . ( T^{2} ) is proportional to ( R^{7 / 2} )
c. ( T^{2} ) is proportional to ( R^{3 / 2} / 2 ) proportional
D. ( T^{2} ) is proportional to ( R^{3.75} )
11
64Assertion
On satellites we feel weightlessness. Moon is also a satellite of earth. But we
do not feel weightlessness on moon.
Reason
Mass of moon is considerable.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
65Two spherical bodies of masses ( 2 M )
and ( M ) and of radii ( 3 R ) and ( R )
respectively are held at a distance ( 16 R )
from each other in free space. When they are released, the start approaching
each other due to the gravitational force of attraction, then find
(a) the ratio of their accelerations
during their motion
(b) their velocities at the time of
impact.
11
66Out of the following statements, the one which correctly describes a satellite
A. There is no force acting on the satellite
B. The acceleration and velocity of the satellite are roughly in the same direction
c. The satellite is always accelerating about the earth
D. The satellite must fall, back to earth when its fuel is exhausted
11
67The gravitational force of attraction between two masses depend on the distance between them is ( G= )
gravitaional constant ( =boldsymbol{k} times )
( 10^{-11} N m^{2} k g^{-2} . ) what is the value of ( k ? )
11
68What is the magnitude of the gravitational force between the earth and a ( 1 k g ) object on its surface? (Mass
of the earth is ( 6 times 10^{24} k g ) and radius of
the earth is ( 6.4 times 10^{6} ) m.)
11
69If the radius of the earth were to shrink
by ( 1 % ) its mass remaining the same, the acceleration due to gravity on the earths surface would
A. decrease by ( 2 % )
B. remain unchanged
c. increase by ( 2 % )
D. will increase by ( 9.8 % )
11
70A double star system consists of two stars ( A ) and ( B ) which have time periods
( T_{A} ) and ( T_{B} . ) Radius ( R_{A} ) and ( R_{B} ) and
( operatorname{mass} M_{A} ) and ( M_{B}, ) choose the correct
A ( cdotleft(T_{A} / T_{B}right)^{2}=left(R_{A} / R_{B}right)^{3} )
B. If ( T_{A}>T_{B} ) then ( R_{A}>R_{B} )
( mathbf{c} cdot T_{A}=T_{B} )
D. ( T_{A}>T_{B} ) then ( M_{A}>M_{B} )
11
71A body is weighed at the poles and at the equator. The weight:
A. at the equator it will be more than at the poles
B. at the poles it will be greater than at the equator
C. at the poles it will be equal to the weight at the equator
D. depends upon the object
11
72What is the tension between her ears?
A ( .2 .1 k N )
B. ( 2.6 k N )
c. ( 2.9 k N )
D. None
11
73Mercury orbits the sun in about one-
fifth of the earth year. If ( 1 A U ) is defined
as the distance from the earth to the
sum, what is the approximate distance between mercury and the sun?
A ( cdot 1 / 25^{1 / 3} A U )
B . ( 1 / 9^{1 / 3} A U )
( mathbf{c} cdot 1 / 5^{1 / 3} A U )
D. ( 1 / 3^{1 / 3} ) AU
11
741 kgwt is equal to
A .980000 dynes
B. 9.80 dynes
c. 98 dynes
D. none of these
9
75The value of G depends on
A. the nature of the interacting bodies
B. the size of the interacting bodies
C. the mass of the interacting bodies
D. none of these
11
76Two planets are revolving around a star in circular orbits. If the ratio of radii of
orbit is ( 1: 4, ) then ratio of their time
period will be
A . 1: 1
B. 1: 4
c. 1: 8
D. 1: 16
11
77A planet’s density is 3 times that of the Earth. But the acceleration due to
gravity on its surface is exactly the same as on the Earth’s surface. The
radius of the planet in terms of the Earth’s radius ( R ) is
A ( .2 . R )
в. ( 3 R )
c. ( frac{R}{3} )
D. none of the above
11
78The ratio of value of gravitational constant ( G ) between Earth and Moon
system and Earth and Sun system is-
( A cdot>1 )
в. ( <1 )
c. 1
D. can't be calculated
11
79What is the minimum energy required to launch a satellite of mass ( mathrm{m} ) from the
surface of a planet of mass ( mathrm{M} ) and
radius ( mathrm{R} ) in a circular orbit at an
altitude of 2R.
( mathbf{A} cdot frac{5 G m M}{6 R} )
B. ( frac{G m M}{2 R} )
( mathbf{c} cdot frac{G m M}{3 R} )
( mathbf{D} cdot frac{5 G m M}{7 R} )
11
80In MKS, the gravitational unit of force is
A. ( k g f )
в. ( g f )
( c . N )
D. dyne
9
81KEPLER’S LAWS
A planet revolves around the sun in an
elliptical orbit. If ( v_{p} ) and ( v_{a} ) are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by
A. ( frac{v_{p}}{v_{n}} )
в. ( frac{v_{a}-v_{p}}{v_{a}+v_{p}} )
c. ( frac{v_{p}+v_{a}}{v_{p}-v_{a}} )
D. ( frac{v_{p}-v_{a}}{v_{p}+v_{a}} )
11
82Two identical spheres are placed in contact with each other. The force of
gravitation between the spheres will be proportional to (R = radius of each sphere ( ) )
( A cdot R )
B . ( R^{3} )
( c cdot R^{4} )
D. None of these
11
83An object has a mass ( m ) kg on earth.
What will be its mass on the moon?
A. ( m ) kg
в. ( 6 m ) кg
c. ( frac{m}{6} ) kg
D. zero
9
84An object is taken to height ( 2 mathrm{R} ) above the surface of earth, the increase in potential energy is [R is radius of earth]
( ^{mathrm{A}} cdot frac{m g R}{2} )
в. ( frac{m g R}{3} )
c. ( frac{2 m g R}{3} )
D. 2 mgR
11
85( left[M^{-1} L^{3} T^{-2}right] ) are the dimensions of
A. Acceleration due to gravity
B. Gravitational constant
c. Gravitational force
D. Gravitational potential energy
11
86A particle falling down freely under the influence of gravity covers a distance of ( 20 mathrm{m} ) in 4 secs. Find its acceleration
A ( cdot 9.8 m / s^{2} )
B . ( 15 mathrm{m} / mathrm{s}^{2} )
( mathrm{c} cdot 5 mathrm{m} / mathrm{s}^{2} )
D. ( 3 m / s^{2} )
11
87The mass of planet Jupiter is ( 1.9 times 10^{27} )
kg and that of the Sun is ( 1.99 times 10^{30} mathrm{kg} )
The mean distance of Jupiter from the
Sun is ( 7.8 times 10^{11} ) m. Calculate the
gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also
calculate the speed of Jupiter. ( boldsymbol{G}= )
( mathbf{6 . 6 7} times mathbf{1 0}^{-mathbf{1 1}} mathbf{N m}^{mathbf{2}} mathbf{k g}^{-mathbf{2}} )
( mathbf{A} cdot=5 times 10^{23} mathrm{N} )
B. ( =4.15 times 10^{23} mathrm{N} )
( mathbf{C} .=15 times 10^{23} mathbf{N} )
D. ( =1 times 10^{23} mathrm{N} )
11
88Describe kepler’s law of planetrary
motion?
11
89The time period of an earth’s satellite in
circular orbit is independent of:
A. the mass of the satellite
c. both the mass and radius of the orbit
D. neither the mass of the satellite nor the radius of its orbit
11
90As the distance of the planet from the sun increases, the period of revolution decreases.
A. True
B. False
11
91The distances of Neptune and Saturn
from the Sun are respectively ( 10^{13} ) and
( 10^{12} ) meters and their periodic times
are respectively ( T_{n} ) and ( T_{S} ). If their orbits are assumed to be circular, the value of ( frac{T_{n}}{T_{S}} ) is :
A. 100
в. ( 10 sqrt{10} )
c. ( frac{1}{10 sqrt{10}} )
D. 10
11
92A body of mass ‘m’ is raised from the surface of the earth to a height ‘nR’ (Rradius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)
A ( cdotleft(frac{n}{n+1}right) m g R )
B ( cdotleft(frac{n-1}{n}right) m g R )
c. ( frac{m g R}{n} )
D. ( frac{m g R}{(n-1)} )
11
93A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is ( r ) and the
farthest distance is ( R ). If the velocity of
the planet nearest to the sun be ( v ) and
that farthest away from the sun be ( boldsymbol{V} )
then ( boldsymbol{v} / boldsymbol{V} ) is :
A ( cdot frac{R^{2}}{r^{2}} )
B. ( frac{r^{2}}{R^{2}} )
( mathbf{c} cdot frac{R}{r} )
D. ( frac{r}{R} )
11
94Two masses ( M_{1} ) and ( M_{2} ) at an infinite
distance from each other and initially at rest, start interacting gravitationally. Find their velocity of approach when they are distances apart.
11
95State whether true or false.
The weight of a body on the surface of the moon is ( frac{1}{6} t h ) of that on the earth’s surface. It is because acceleration due
to gravity on the surface of the moon is six times that on the surface of the
earth.
A. True
B. False
9
96A ball with a weight of 20 N is thrown vertically upward. What is the acceleration of the ball just as it
reaches the top of its path?
A. ( 10 m / s^{2} ) downward
B. ( 10 mathrm{m} / mathrm{s}^{2} ) upward
c. ( 20 m / s^{2} ) downward
D. ( 20 m / s^{2} ) upward
E. zero
11
97A stone weight ( 100 mathrm{N} ) on the surface of the earth. The ratio of its weight at a height of half the radius of the earth to
its weight at a depth of half the radius of the earth will be approximately
A. 3.6
B. 2.2
( c cdot 1.8 )
D. None of these
11
98A particle of mass ( 10 g ) is kept on the surface of a uniform sphere of mass
100 ( k g ) and radius ( 10 c m . ) Find the work
to be done against the gravitational force between them to take the particle far away from the
sphere
A ( cdot 13.34 times 10^{-10} mathrm{J} )
B . ( 13.33 times 10^{-10} J )
c. ( 6.67 times 10^{-9} mathrm{J} )
D. ( 6.67 times 10^{-10} J )
11
99Two particles of equal mass go around in a circle of radius ( r ) under the action
of their mutual gravitational attraction. If the mass of each particle is ( m ), the
speed of each particle is
A ( cdot sqrt{frac{G m}{r}} )
в. ( sqrt{frac{G m}{2 r}} )
c. ( sqrt{frac{G m}{4 r}} )
D. ( sqrt{frac{2 G m}{r}} )
11
100Assertion
The value of acceleration due to gravity does not depend upon the mass of the body.
Reason
Acceleration due to gravity is a constant quantity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
101If a satellite is revolving very close to the surface of earth, then its orbital
velocity does not depend upon
A. mass of satellite
B. mass of earth
11
102The Sl unit of gravitational potential is
( A . J )
B. ( J k g^{-1} )
c. ( J k g )
D. ( J k g^{-2} )
11
103If ( v_{e} ) is the escape velocity for earth when a projectile is fired from the surface of earth. Then the escape velocity if the same projectile is fired from its centre is
A ( cdot sqrt{frac{3}{2}} v_{e} )
в. ( frac{3}{2} v_{e} )
c. ( sqrt{frac{2}{3}} v_{e} )
D. ( frac{2}{3} v_{e} )
11
104The minimum and maximum distances
of a planet revolving around sun are ( r ) and ( R ) If the minimum speed of
planet on its trajectory is ( v_{0}, ) then its
maximum speed will be:
A ( cdot frac{v_{0} R}{r} )
B. ( frac{v_{0} r}{R} )
c. ( frac{v_{0} R^{2}}{r^{2}} )
D. ( frac{v_{0} r^{2}}{R^{2}} )
11
105Calculate the force of gravitation between two objects of masses ( 80 mathrm{kg} ) and ( 1200 mathrm{kg} ) kept at a distance of ( 10 mathrm{m} ) from each other.Given ( (G=mathbf{6 . 6 7} times )
( left.10^{-11} N m^{2} / k g^{2}right) )
11
106Suppose the gravitational potential due to a small system is ( k / r^{2} ) at a distance from it. What will be the gravitational field ? Can you think of any such system? What happens if there were negative masses?11
107The figure shows a planet in elliptical orbit around the sun S. The kinetic
energy of the planet will be maximum
when the planet is at:
( A cdot P_{1} )
в. ( P_{2} )
( c cdot P_{3} )
( mathbf{D} cdot P_{4} )
11
108If the distance of earth from the sun
reduces to one fourth of its present
value then the length of the year will become
A . ( 1 / 6 ) of present year
B. 1/8 of present year
c. ( 1 / 4 ) of present year
D. ( 1 / 2 ) of present year
11
109Show that period of a satellite revolving around the Earth depends upon mass of
the Earth.
11
110When the earth is far away from the
sun, its travels slower. This is due to
A. Potential energy is higher, hence it travels slower
B. Inertia of the earth make it to go in straight line
C. Kinetic energy is lower and hence it travels slower
D. tend to get attracted by other planets and hence it becomes slower
11
111How the gravitational constant will change if a brass plate is introduced between two bodies?
A. No change
B. Decreases
c. Increases
D. No sufficient data
11
112Two artificial satellites of unequal
masses are revolving in a circular orbit around the earth with a constant speed.
Their time periods.
A. will be different.
B. will be same
c. will depend on their masses
D. will depend upon the place of their projection
11
113If the radius of earth shrinks by ( 1.5 % ) mass remaining same ), then the value of gravitational acceleration changes by
A. 2 %
B . – 2 %
c. 3 %
D. -3 %
11
114The average density of the earth in terms of ( g, ) Gand ( R ) is:
A ( cdot frac{4 pi G R}{3 g} )
в. ( frac{3 g}{4 pi G R} )
c. ( frac{3 g}{4 pi G R^{2}} )
D. ( frac{4 pi G R^{2}}{3 g} )
11
115A boy can jump to a height ( h ) from ground on earth. What should be the
radius of a sphere of density ( delta ) such that on jumping on it, he escapes out of the gravitational field of the sphere?
A. ( sqrt{frac{4 pi G delta}{3 g h}} )
B. ( sqrt{frac{4 pi g h}{3 G delta}} )
c. ( sqrt{frac{3 g h}{4 pi G delta}} )
D. ( sqrt{frac{3 G delta}{4 pi g h}} )
11
116A body weighs ( 63 mathrm{N} ) on the surface of the earth. What is the gravitational force (in
N) on it due to the earth at a height equal to half the radius of the earth?
11
117Imagine a new planet having the same density as that of the earth but it is 3
times bigger than the earth in size. If
the acceleration due to gravity on the
surface of the earth is ( g ) and that on the
new planet is ( g^{prime} ), then what is the value of ( frac{boldsymbol{g}^{prime}}{boldsymbol{g}} )
11
118Value of ‘g’ on moon is of
the value of ‘g’ on earth. Fill in the blank.
A. One third
B. One sixth
c. one fourth
D. one tenth
9
119If ( T ) be the period of revolution of ( a )
planet revolving around sun in an orbit of mean radius ( R ), then identify the correct graph from the following.
This question has multiple correct options
( A )
B.
( c )
D. None of these
11
120A uniform sphere of mass ( mathrm{M} ) and radius
( mathrm{R} ) is surrounded by a concentric spherical shell of same mass but
radius ( 2 mathrm{R} . ) A point mass ( mathrm{m} ) is kept at a distance ( x(>R) ) in the region bounded by spheres as shown in the figure. The net
gravitational force on the particle is
A ( cdot frac{operatorname{CMm}}{frac{pi^{2}}{n}} )
B. ( frac{G M m}{R^{3}} )
( c cdot frac{G(M+m)}{x^{2}} )
D. zer
11
121Which of the following are not correct?
This question has multiple correct options
A. The escape velocity for the Moon is ( 6 k m s^{-1} )
B. The escape velocity from the surface of Moon is ( v ). The orbital velocity for a satellite to orbit very close to the surface of Moon is ( v / 2 )
C. When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases
D. The orbital velocity of a satellite revolving in a circular path close to the planet is independent of the density of the planet.
11
122If the ratio of the masses of two plane
what will be the ratio of their accelera
11
123Assuming the earth to be a sphere of uniform density, how much could a body weigh at a height equal to radius of earth when it weighs ( 250 mathrm{N} ) on the surface of the earth.11
124The possible relationship between
magnitudes of ” ( V_{1} ) ” and ” ( V_{2} ) ” is:
A ( cdot V_{1}>V_{2} )
в. ( V_{1}<V_{2} )
( c cdot V_{1}=V_{2} )
D. Both (A) and (C)
11
125A rocket is launched to travel vertically
upward with a constant velocity of 20 ( mathrm{m} / mathrm{s} . ) After travelling for 35 seconds, the rocket develops a snag and its fuel supply is cut off. The rocket then travels like a free body. The height achieved by
it is:
11
126A small mass and a thin uniformed rod
each of mass ‘m’ are positioned along the same straight line as shown. find the forced of gravitational attraction exerted by the rod on the small mass.
11
127f a body be projected vertically upward from the surface of the earth so as to
reach a height ( n R ) above the surface;
the increase in its potential energy is ( left(frac{n}{n+a}right) m g R, ) where ( a=? )
11
128The force acting on a mass of 1g due to the gravitational pull on the earth is called lgwt. One gwt equals:
( A cdot 1 N )
B. ( 9.8 mathrm{N} )
c. 980 dyne
D. none of these
9
129Mass of moon is ( 7.34 times 10^{22} k g ). If the
acceleration due to gravity on the moon is ( 1.4 m s^{-2}, ) the radius of the moon is:
( left[G=6.667 times 10^{-11} N m^{2} k g^{-2}right] )
A ( cdot 0.56 times 10^{4} m )
В. ( 1.87 times 10^{6} mathrm{m} )
c. ( 1.92 times 10^{6} m )
D. ( 1.01 times 10^{8} mathrm{m} )
11
130If mass ( mathrm{M} ) is split into two parts, ( mathrm{m} ) and ( (M-m) ) which are then separated by a
certain distance. What ratio of ( mathrm{m} / mathrm{M} )
maximizes the gravitational force between the two parts.
A . ( 1 / 3 )
B. ( 1 / 2 )
c. ( 1 / 4 )
D. ( 1 / 5 )
11
131A small mass ( m ) is moved slowly from the surface of the earth to a height ( h ) above the surface. The work done (by an external agent) in doing this is
This question has multiple correct options
A. ( m g h, ) for all values of ( h )
B. ( m g h, ) for ( h<<R )
c. ( frac{1}{2} ) mgR, for ( h=R )
D. ( -frac{1}{2} ) mgR, for ( h= )
11
132If the time taken by the planet to move
from position ( mathrm{P} ) to ( mathrm{X} ) and ( mathrm{Q} ) to ( mathrm{Y} ) is equal
then the ratio of ( A_{1} ) to ( A_{2} ) is:
A. Greater than one
B. Less than one
c. Equal to one
D. Data insufficient
11
133The acceleration due to gravity at a depth of ( 1600 k m ) inside the earth is
( mathbf{A} cdot 6.65 mathrm{ms}^{-2} )
B. ( 7.35 mathrm{ms}^{-2} )
c. ( 8.65 mathrm{ms}^{-2} )
D. ( 4.35 mathrm{ms}^{-2} )
11
134The ratio of acceleration due to gravity at a depth ( h ) below the surface of earth
and at a height ( h ) above the surface for ( boldsymbol{h}<<boldsymbol{R} )
A. constants only when ( h<<R )
B. increases linearly with ( h )
C. increases parabolically with ( h )
D. decreases
11
135If a body is sent with a velocity of ( mathrm{km} mathrm{sec}^{-1} ), it would leave the earth
forever.
A . 11.9
в. 11.6
c. 11.4
D. 11.2
11
136Two planets of radii ( r_{1} ) and ( r_{2} ) are made from the same material. The ratio of the
acceleration due to gravity ( g_{1} / g_{2} ) at the
surfaces of the two planets is:
A ( cdot r_{1} / r_{2} )
в. ( r_{2} / r_{1} )
C ( cdotleft(r_{1} / r_{2}right)^{2} )
D. ( left(r_{2} / r_{1}right)^{2} )
11
137At the Earth, a block of mass ( m ) which
rest on the frictionless table, let ( boldsymbol{F} ) be
the force required to produce acceleration ( a ). Calculate the force at
the Moon to produce same acceleration
if ( g_{m o o n} ) is one sixth of ( g_{e a r t h} )
A ( cdot frac{F}{12} )
в. ( frac{F}{6} )
c. ( frac{F}{3} )
D. ( F )
E . ( 6 F )
9
138The universal law of gravitation must be applicable to
A. The earth and the moon
B. The planets around the sun
c. Any pair of bodies.
D. The earth and the apple.
11
139Keplers second law regarding constancy of arial velocity of a planet is a consequence of the law of conservation
of
A. energy
B. angular momentum
c. linear momentum
D. none of these
11
140As you have learnt in the text, a
geostationary satellite orbits the earth at a height of nearly ( 36,000 mathrm{km} ) from the
surface of the earth. What is the
potential due to earth’s gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the earth ( =6.0 times 10^{24} k g, ) radius ( =6400 )
( mathbf{k m} )
11
141Linear momentum of the planet is
This question has multiple correct options
A. Different for different points of the orbitt
B. Conserved
c. Not conserved
D. None of these
11
142The ratio of the radii of the planets ( P_{1} )
and ( P_{2} ) is ( k_{1} . ) The corresponding ratio of the acceleration due to the gravity on
them is ( k_{2} ). The ratio of the escape velocities from them will be
A ( cdot k_{1} k_{2} )
в. ( sqrt{k_{1} k_{2}} )
( mathbf{c} cdot sqrt{left(k_{1} / k_{2}right)} )
D. ( sqrt{left(k_{2} / k_{1}right)} )
11
143A particle is dropped under gravity from
rest from a height ( hleft(g=9.8 m / s^{2}right) ) and it travels a distance ( frac{mathbf{9 h}}{mathbf{2 5}} ) in the last second the height ‘h’ is:
( mathbf{A} cdot 100 m )
B. ( 125 mathrm{m} )
( mathbf{c} cdot 145 m )
D. ( 167.5 mathrm{m} )
11
144The value of gravitational acceleration ‘g’ at a height ‘h’ above the earth’s surface is ( frac{g}{4} ) then ( (R= ) radius of earth)
( mathbf{A} cdot h=R )
в. ( h=frac{R}{2} )
( c cdot h=frac{R}{3} )
D. ( h=frac{R}{4} )
11
145Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the
periods of revolution of Mercury, Earth, Jupiter and Neptune are nearly 0.24,1 11.8 and 165 years. It follows that the period of revolution of
A. Venus is less than 0.24 years
B. Mars is less than 12 years.
C. Uranus is more than 165 years
D. Uranus is less than 165 years but
more than 12 years. Of these the correct statement(s) is 1
are :
A. A and C
B. D only
c. c only
D. B and D
11
146The force of attraction between the two
bodies ( (A, B) ) depend upon:
A. mass of ( A )
B. mass of ( B )
c. distance between them
D. all of the above
11
147A sphere of mass ( 40 mathrm{kg} ) is attracted by a
second sphere of mass ( 15 mathrm{kg} ), when their
centres are ( 20 mathrm{cm} ) apart, with a force of
0.1 milligram weight. Calculate the value of gravitational constant.
( mathbf{A} cdot=8.53 times 10^{-11} N m^{2} k g^{-2} )
B. ( =6.53 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{-2} )
( mathbf{c} .=7.53 times 10^{-11} mathrm{Nm}^{2} mathrm{kg}^{-2} )
D. ( =9 times 10^{-11} N m^{2} k g^{-2} )
11
148Are the equations of motion applicable to bodies projected vertically up with
any velocity, say ( 8 k m s^{-1}, ) for
determining the maximum height? And why?
11
149In Sl unit gravitational unit of force is called
A. ( G f )
в. ( K g f )
( c . N )
D. All
9
150Assertion
An astronaut in an orbiting space
station above the earth experience
weightlessness.
Reason
An object moving around the earth
under the influence of earth’s
gravitational force is in a state of ‘free
fall’.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
151An artificial satellite moving in circular orbit around the earth has a total
kinetic + potential ) energy ( boldsymbol{E}_{0} ). Its
potential energy and kinetic energy respectively are
A ( cdot 2 E_{0} ) and ( -2 E_{0} )
B . ( 2 E_{0} ) and ( 3 E_{0} )
( mathbf{c} cdot 2 E_{0} ) and ( -E_{0} )
D. ( -2 E_{0} ) and ( -E_{0} )
11
152Which of the following quantities remain constant in a planetary system when seen from the surface of the sun.
This question has multiple correct options
A . KE
B. angular speed
c. speed
D. angular momentum
E. binding energy
11
153On the surface of the earth, force of gravitational attraction between two masses kept at distance dapart is 6
Newtons. If these two masses are taken
to the surface of the moon and kept at
the same distance d, the force between
them will be
A . ( 1 mathrm{N} )
B. 36N
( c cdot frac{1}{6} N )
D. 6N
9
154On the pole of the Earth a body is
imparted velocity ( v_{0} ) directed vertically
up. Knowing the radius of the Earth and
the free-fall acceleration on its surface,
the height to which the body will ascend is given as ( h=frac{R v_{0}^{2}}{x g R-v_{0}^{2}} . ) The air drag
is to be neglected. Find ( x )
11
155The possible relationship between
magnitudes of ( ” boldsymbol{V}_{1} ) ” and ( ” boldsymbol{V}_{2} ) ” is :
( mathbf{A} cdot V_{1}>V_{2} )
( mathbf{B} cdot V_{1}<V_{2} )
( mathbf{c} cdot V_{1}=V_{2} )
D. Both A and C
11
156Consider the following statements about acceleration due to gravity on earth and mark the correct
statement(s):
A. The value of ( g ) is constant throughout
в. ( g^{prime}=gleft(1-frac{d}{r}right) )
( mathrm{c} . g ) is slightly less (by about ( 1 % ) ) when distance ( <200 mathrm{m} )
D. ( g ) is slightly greater when distance ( <200 m )
11
157Which of the following quantities does not depends upon the orbital radius of the satellite?
A ( cdot frac{T}{R} )
в. ( frac{T^{2}}{R} )
c. ( frac{T^{2}}{R^{2}} )
D. ( frac{T^{2}}{R^{3}} )
11
at a height ( boldsymbol{H} ) on the roof a building, tries to catch it. He misses the catch,
the ball overshoots and simultaneously
the person starts a stop-watch. The ball
reaches its highest point and he
manages to catch it upon its return. By this time, a time interval ( T ) has elapsed
as recorded by the stop watch. If ( g ) is the
acceleration due to gravity at this place, the speed with which the ball was
thrown from point ( boldsymbol{A} ) will be
( mathbf{A} cdot sqrt{g H+g T} )
( frac{(sqrt{g^{2} T^{2}+4 g H})}{2} )
( frac{(sqrt{g^{2} T^{2}+8 g H})}{2} )
D. ( (sqrt{g^{2} T^{2}+2 g H}) )
11
159The gravitational force of attraction between two bodies at a certain
distance is ( 10 mathrm{N} ). If the distance
between them is doubled, the force of
attraction:
A. decreases by ( 50 % )
B. decreases by ( 75 % )
C. increases by ( 50 % )
D. increases by ( 75 % )
11
160Value of ( g ) on the surface of earth is
( 9.8 m / s^{2} . ) Value of ( g ) on the surface of earth is ( 9.8 m / s^{2} . ) At height ( h=R ) from the surface the value of ( g ) is ( frac{g}{x} . ) Find ( x )
11
161Let ( V ) and ( E ) denote the gravitational potential and gravitational field at a point. It is possible to have This question has multiple correct options
A. ( V=0 ) and ( E=0 )
B. ( V=0 ) and ( E neq 0 )
c. ( V neq 0 ) and ( E=0 )
D. ( V neq 0 ) and ( E neq 0 )
11
162Given that mass of earth is ( M ) and its
radius ( R ) body is dropped from a height equal to the radius of the earth above
the surface of the earth. When it
reaches the ground velocity of body will be
( ^{A} cdot frac{G M}{R} )
( ^{text {В. }}left(frac{G M}{R}right)^{1 / 2} )
c. ( frac{2 G M}{R} )
( ^{mathrm{D} cdot}left(frac{2 G M}{R}right)^{1 / 2} )
11
163The 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.
11
164Assertion
The value of acceleration due to gravity does not depend upon the mass of the body.
Reason
Acceleration due to gravity is a constant quantity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
165The moon’s radius is ( 1 / 4 ) times that of the earth and its mass ( 1 / 80 ) times that
of the earth. If ( g ) represents the acceleration due to gravity on the surface of the earth, then on the surface
of the moon its value is :
( mathbf{A} cdot g / 4 )
в. ( g / 5 )
c. ( g / 6 )
D. ( g / 8 )
9
166Four point masses each of mass ( mathrm{m} ) are kept at the vertices of a square. A point mass ( m ) is kept at the point of intersection of the diagonal of a square What will be the force experienced by
central mass ( m ? )
11
167The value of G does not depend upon:
A. nature of the interacting bodies
B. size of the interacting bodies
c. mass of the interacting bodies
D. all of these
11
168Four particles each of mass ‘m’ are placed at the four vertices of a square of side ‘a’. Find the net force on any one of
the particle.
11
169The depth at which the value of acceleration due to gravity becomes ( frac{1}{n} ) times the value at the surface is (R be
A ( cdot frac{R}{n} )
в. ( frac{R}{n^{2}} )
c. ( frac{R(n-1)}{n} )
D. ( frac{R n}{(n-1)} )
11
170If the diameter of the earth becomes
half of the present value but its average
density remains unchanged then how would be the wieght of an object on earth been affected
11
171If two stars of masses in the ratio 2: 3
become black holes, their radii will be in
the ratio of:
A .4: 9
B. 3: 2
c. 2: 3
D. 9: 4
11
172Cavendish Experiment to measure ( boldsymbol{G} )
uses the concept of
A. Torque
B. Force
c. Force-Torque Equilirium
D. None of these
11
173The power of water pump is The power
of water pump is ( 4 k W . ) If
( left(g=10 m s^{-2}right), ) the amount of water it
can raise in 1 minute to a height of ( 20 m )
is:
A. 100 litre
B. 1000 litre
c. 1200 litre
D. 2400 litre
11
174A tunnel is dug along a diameter of earth. The force on a particle of mass ( boldsymbol{m} )
and distance ( x ) from the centre in this
tunnel will be :
A ( cdot frac{G M_{e} m}{R^{3} x} )
в. ( frac{G M_{e} m R^{3}}{x} )
c. ( frac{G M_{e} m x}{R^{2}} )
D. ( frac{G M_{e} m x}{R^{3}} )
11
175A bomb blasts on the Moon. Its sound
reaches the Earth
A. after 10 minutes
B. after 24 hours and 10 minutes
c. after 3.7 minutes.
D. cannot reach.
11
176A ( 60 k g ) man is inside a lift which is moving up with an acceleration of
( 2.45 m s^{-2} . ) The apparent percentage change in his weight is:
A . ( 20 % )
B. 25%
c. ( 50 % )
D. ( 75 % )
11
177A body has a weight of ( 10 k g ) on the
surface of the Earth. What will be its
mass and weight when taken to the centre of the Earth?
A. ( 10 mathrm{kg} ), zero
B. zero, zero
c. ( 10 mathrm{kg}, 10 mathrm{g} )
D. zero, ( 10 g )
11
178( mathrm{R} ) is a radius of a planet and ( rho ) is its
density. The escape velocity on its surface will be
A ( cdot R^{2} sqrt{4 pi G rho / 3} )
в. ( R sqrt{4 pi G rho / 3} )
c. ( R^{2} sqrt{8 pi G rho / 3} )
D. ( R sqrt{8 pi G rho / 3} )
11
179If the escape velocity on earth is 11.2km / sec, its value for a planet having double the radius and 8 times the mass of earth is ( ldots . boldsymbol{m} / boldsymbol{s e c} )
A . ( 11.2 mathrm{km} / mathrm{sec} )
B. 22.4 km/sec
c. ( 5.6 mathrm{km} / mathrm{seco} )
D. ( 8 mathrm{km} / mathrm{sec} )
11
180toppr
quantities in relation to the energy of the comet-star system-kinetic energy
(KE) gravitational potential energy
( (G P E), ) speed of comet (Speed), and mechanical energy of system (ME) Choose the table that is correctly filled
in with ( x ) ‘s.

Notice that in some boxes for certain
quantities neither box is checked, indicating that the particular quantities is the same at both
positions. Assume any loss of mass of the comet or the star is insignificant.
0 ( G ) ( because . . . . )
4
begin{tabular}{|l|l|l|}
hline & Position 1 & Position 2 \
hline KE greater & ( mathrm{x} ) & \
GPE greater & ( mathrm{x} ) & \
Speedgreater & ( mathrm{x} ) & \
MEgreater & ( mathrm{x} ) & \
hline
end{tabular}
B.
begin{tabular}{|l|l|l|}
hline & Position 1 & Position 2 \
hline KE greater & & ( mathrm{x} ) \
GPE greater & & ( mathrm{x} ) \
Speed greater & & ( mathrm{x} ) \
MEgreater & & ( mathrm{x} ) \
hline
end{tabular}
( c )
begin{tabular}{|l|l|l|}
hline & Position 1 & Position 2 \
hline KE greater & ( mathrm{x} ) & \
GPE greater & ( mathrm{x} ) & \
Speedgreater & ( mathrm{x} ) & \
ME greater & & \
hline
end{tabular}
( D )
begin{tabular}{|l|l|l|}
hline & Position 1 & Position 2 \
hline KE greater & ( times ) & \
GPE greater & & ( times ) \
Speedgreater & ( times ) & \
MEgreater & & \
hline
end{tabular}
E begin{tabular}{|l|l|l|}
hline & Position 1 & Position 2 \
hline KEgreater & & ( times ) \
GPEgreater & ( times ) & \
Speedgreater & & ( times ) \
ME greater & & \
hline
end{tabular}

11
181If the radius of the earth be increased by
a factor of 5 by what factor its density be changed to keep the value of ( g ) the
same?
A ( cdot frac{1}{25} )
B. ( frac{1}{5} )
c. ( frac{1}{sqrt{5}} )
( D )
11
182Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in ( mathrm{N} ) ) half way down to the center of the earth if it weighed 250 N on the surface?11
183From a solid sphere of mass ( M ) and
radius ( R ) a spherical portion of radius ( boldsymbol{R} )
( frac{1}{2} ) is removed, as shown in the figure. Taking gravitational potential ( V=0 ) at
( r=infty, ) the potential at the centre of the
cavity thus formed is : ( (G= ) gravitational constant)
( ^{A} cdot frac{-2 G M}{3 R} )
в. ( frac{-2 G M}{R} )
( c cdot frac{-G M}{2 R} )
D. ( frac{-G M}{R} )
11
184Weightlessness in a satellite is experienced because
A . of inertia
B. the gravitational force acting on the satellite is zero
c. of centre of gravity
D. centrifugal acceleration negates the acceleration due to gravity
11
185Kepler’s second law states that the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time.This law is a
consequence of the conservation of
A . Time
B. Mass
c. Angular momentum
D. Linaer momentum
11
186If 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:
A. Decrease by ( 1 % )
B. Remain unchanged
C. Increase by ( 1 % )
D. Increase by 2%
11
187The image shows an outline for which
experiment?
A. Cavendish Experiment
B. Newton’s Experiment
C. Kepler’s Experiment
D. None of these
11
188What is the effect of the shape of Earth
on value of ‘ ( g ) ‘?
11
189If a body is sent with a velocity of ( mathrm{km} mathrm{sec}^{-1} ), it would leave the earth
forever.
A . 11.9
в. 11.6
c. 11.4
D. 11.2
11
190The force primarily responsible for the existence of the solar system is the
A. force of friction
B. gravitational force
c. electrostatic force
D. magnetic force
11
191A spring balance is calibrated at sea
level. If this balance is used to measure
the weight of a body at successive increasing heights from the surface of the earth, then the weight indicated by spring balance will
A. decrease continuously
B. increase continuously
c. first decrease, then increase
D. remains constant
11
192Magnitude of binding energy of satellite is ( boldsymbol{E} ) and kinetic energy is ( boldsymbol{K} ). The ratio ( boldsymbol{E} / boldsymbol{K} ) is :
A . ( 2 / 1 )
B . ( 1 / 4 )
( c .1 )
D. ( 1 / 2 )
11
193If the earth has no rotational motion, the
weight of a person on the equator is ( W )
Determine the speed with which the earth would have to rotate about its
axis so that the person at the equator will weight ( frac{3}{4} W . ) Radius of the earth is ( 6400 k m ) and ( g=10 m / s^{2} )
11
194The gravitational force of each planet in our solar system is different.The diagram below shows four planets listed in order from least amount of relative gravity to greatest amount of relative gravity. A person would weigh the most standing on which planet?
Mercury

Least Relative Gravity
Venus
Earth
Jupiter Greatest Relative Gravity
A. Mercury
B. Venus
c. Earth
D. Juipter

11
195Assertion
The length of the day is slowly increasing.
Reason
The dominant effect causing a
slowdown in the rotation of the earth is
the gravitational pull of other planets in the solar system.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
196The density of newly discovered planet is twice that of the 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 It the radius of the plane would be
A ( .2 . R )
в. ( 4 R )
c. ( frac{1}{4} R )
D・( frac{1}{2} R )
11
197The value of universal gravitational constant on earth for a particle of mass
5 kgs is
В. ( 6.67 times 10^{-7} )
c. ( 5 times 6.67 times 10^{-11} )
D. ( 6.67 times 10^{-23} )
11
198If ( V_{e} ) is the escape velocity of a body from a planet of mass ( M ) and radius ( R ) Then, the velocity of satellite revolving at height ( h ) from the surface of planet
will be
A ( cdot V=V_{e} sqrt{frac{R}{(R+h)}} )
B ( cdot V=V_{e} sqrt{frac{2 R}{(R+h)}} )
( ^{mathbf{c}} cdot_{V}=V_{e} sqrt{frac{(R+h)}{R}} )
D. ( V=V_{e} sqrt{frac{R}{2(R+h)}} )
11
199The height at which the weight of a body becomes ( frac{1}{16} t h, ) its weight on the surface of earth (radius ( boldsymbol{R} ) ), is
( A .3 R )
в. ( 4 R )
( c .5 R )
D. ( 15 R )
11
200If ( g ) is the acceleration due to gravity at
the Earths, surface, the gain of the potential energy of an object of mass ( mathrm{m} )
raised from the surface of the Earth to
height equal to the radius ( mathrm{R} ) of the Earth
is :
A ( cdot frac{m g R}{4} )
в. ( frac{m g R}{2} )
( mathrm{c} cdot m g R )
D. ( 2 m g R )
11
201Two fishes are ( 1 m ) apart underwater
The gravitational force between them is
( F_{1}, ) Theyjump above the surface of water keeping the same distance (i.e 1 m)
between them. The new gravitational
force between them is ( F_{2} ). The
relationship between ( boldsymbol{F}_{1} ) and ( boldsymbol{F}_{2} ) is
A ( cdot F_{1}>F_{2} )
B. ( F_{1}<F_{2} )
c. ( F_{1}=F_{2} )
D. ( F_{1}: F_{2}=1: 2 )
11
202Two metal spheres of radius ( r ) are kept
in contact. If ( ^{prime} d^{prime} ) is the density of each sphere material, the gravitational force between them is proportional to
( mathbf{A} cdot d^{2} r^{6} )
B. ( d^{2} r^{4} )
c. ( frac{d^{2}}{r^{4}} )
D. ( frac{r^{4}}{d^{2}} )
11
203Explorer ( 38, ) a radio-astronomy satellite of mass ( 200 k g ) circles the earth in an orbit of average radius ( frac{3 R}{2}, ) where ( R ) is the radius of the earth. Assuming the gravitational pull on the mass of ( 1 k g ) at
the earth’s surface to be ( 10 N ), calculate
the pull on the satellite.
( mathbf{A} cdot 889 N )
B. ( 8.89 N )
( c .8889 N )
D. ( 88.9 N )
11
204The ratio of Sl unit of G to its CGS unit is
A . 100: 1
в. 1000: 1
c. 10: 1
D. 10000: 1
11
205The force of gravitation between two
bodies can be zero if the separation
between the bodies becomes
( A )
B.
( c cdot-1 )
D. infinity
11
206In the above diagram the shaded
regions ( A ) and ( B ) are the areas covered by
planet around the sun. ( boldsymbol{d}_{A} ) and ( boldsymbol{d}_{B}, boldsymbol{t}_{boldsymbol{A}} )
and ( t_{B} ) are the distances traveled by the
planet and the time taken by it to cover
the paths PQ and RS respectively.
Choose the correct statement.
( mathbf{A} cdot d_{A}=d_{B} ) if ( t_{4}=t_{B} )
B ( cdot d_{4}t_{B} )
( mathbf{c} cdot d_{A}=d_{B} ) if ( t_{A}d_{B} ) if ( t_{A}=t_{B} )
11
207A wooden plank of length 1 m and
uniform cross section is hinged at one
end to the bottom of a tank as shown in
the figure. The tank is filled with water
up to a height of 0.5 m. The specific
gravity of the plank is ( 0.5 . ) If the angle ( theta ) by the inclination of that the plank
makes with the vertical in the
equilibrium position (exclude the case
( theta=0 ) ). Find the value of ( frac{1}{cos ^{2} theta} )
11
208A satellite is revolving around earth in a
circular orbit. The radius of orbit is half
of the radius of theorbit of moon.

Satellite will complete one revolution in.
A ( cdot 1 / 2^{3 / 2} ) lunar month
B . ( 1 / 2^{2 / 3} ) |unar month
C. ( 2^{3 / 2} ) lunar month
D. ( 2^{2 / 3} ) lunar month

11
209A particle is projected vertically upwards from the surface of teh earth
(radius ( R_{e} ) ) with a kinetic energy equal to half of the minimum value needed for
it to escape. The height to which it rises above the surface ot the earth is ( frac{boldsymbol{R}}{boldsymbol{n}} ) where ( n ) is:
11
210A planet is revolving in an elliptical orbit around the Sun. Its closest
distance from the Sun is ( r_{text {min }} ) and the
farthest distance is ( r_{m a x} ). If the velocity
of the planet at the distance of the
closest approach is ( nu_{1} ) and that at the
farthest distance from the Sun is ( nu_{2} )
( operatorname{then}left{nu_{1}right} /left{nu_{2}right} )
A ( cdot frac{r_{max }}{r_{min }} )
B ( cdot frac{r_{min }}{r_{max }} )
C. ( frac{r_{min }+r_{max }}{r_{max }-r_{min }} )
D. none
11
211A fisherman lifts a fish of mass ( 250 g )
from rest through a vertical height of 1.8 ( m ). The fish gains a speed of
( 1.1 m s^{-1} )
What is the energy gained by the fish?
A. ( 0.15 J )
в. 4.3 .5
c. ( 4,4 J )
D. 4.6 .5
11
212Inside a horizontally moving box, an
experimenter finds that when an object
is placed on a smooth horizontal table
and is released, it moves with an
acceleration of ( 10 m s^{-2} . ) In this box, if
1 kg body is suspended with a light string, the tension in the string in equilibrium position. (w.r.t. experimenter) will be (take ( g=10 m s^{-2} )
A ( cdot 10 m s^{-2} )
B . ( 10 sqrt{2} mathrm{ms}^{-2} )
c. ( m s^{-2} )
D. Zero
11
213Two equal point charges ( Q=sqrt{2} mu C ) are
placed at each of the two opposite
corners of a square and equal point –
charges ( q ) at each of the other two
corner.What must be the value of ( boldsymbol{q} ) so
that the resultant force on ( Q ) is zero?
11
214What is the percentage change in the value of ( g ) on shifting from equator to poles on the Earth’s surface? Difference in radius of Earth at poles
and equator is ( 21 mathrm{km} )
A . 4.5%
B . 0.65%
c. 0.05%
D. 0.43%
11
215Estimate whether it takes more energy
to get a satellite upto ( 1600 mathrm{km} ) above the earth than to put in orbit there
earth’s radius is ( 6400 mathrm{km} ). Does your
answer remain same for height ( 3200 mathrm{km} )
or for height ( 4800 mathrm{km} ? )
11
216( frac{sqrt{4}}{frac{4}{4}} )9
217A planet has mass and radius both half
of earth. Acceleration due to gravity ( (g) )
at its surface should be
A ( cdot 29.4 m / s^{2} )
в. ( 19.6 m / s^{2} )
C. ( 9.8 m / s^{2} )
D. ( 4.9 mathrm{m} / mathrm{s}^{2} )
11
218Give the dimensional formula for
Gravitational constant ( G )
11
219The gravitational force between two stones of mass ( 1 k g ) each, separated by
a distance of ( 1 mathrm{m} ) in vacuum is
A . zero
B . ( 6.675 times 10^{-5} N )
c. ( 6.675 times 10^{-8} N )
D. ( 6.675 times 10^{-11} N )
11
220The 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 the earth.
When both ( d ) and ( h ) are much smaller
than the radius of earth, then which one
of the following is correct
A ( cdot d=frac{h}{2} )
B. ( d=frac{3 h}{2} )
( c ldots d=2 h )
( mathbf{D} cdot d=h )
11
221If a planet consists of a satellite whose
mass and radius were both half that of
the earth, then the acceleration due to
gravity at the surface of the planet would be
A. ( 5.0 mathrm{ms}^{-2} )
B. ( 6.5 mathrm{ms}^{-2} )
c. ( 7.9 mathrm{ms}^{-2} )
D. ( 19.6 mathrm{ms}^{-2} )
11
222Two metal spheres each of radius ‘r’ are kept in contact with each other. If d is
the density of the material of the sphere, then the gravitational force between those spheres is propositional
to
( mathbf{A} cdot d^{2} r^{6} )
B. ( d^{2} r^{4} )
c. ( frac{d^{2}}{r^{4}} )
D. ( frac{r^{4}}{d^{2}} )
11
223Imagine 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^{prime} ), then:
A ( cdot g^{prime}=3 g )
B. ( g^{prime}=frac{g}{3} )
c. ( g^{prime}=9 g )
D. ( g^{prime}=27 g )
11
224The energy required to remove a body of mass ( m ) from earth’s surface is/are
equal to:
A. ( frac{-G M m}{R} )
в. ( m g R )
c. ( -m g R )
D. none of these
11
225Which of the following hypotheses was made by Newton?
A. Heavier body in the universe exerts a gravitational force on the lighter bodies.
B. Every body in the universe exerts a gravitational force on every other body.
c. Only the sun gravitational force is responsible for all the motion in this universe
D. None of the above
11
226Find the value of ( theta ) such that the
acceleration of ( boldsymbol{A} ) is ( boldsymbol{g} / boldsymbol{6} ) downward
along the incline plane. (All surfaces are
smooth)
A ( cdot theta=10^{circ} )
B . ( theta=60^{circ} )
( mathbf{c} cdot theta=45^{circ} )
D. ( theta=53^{circ} )
11
227The period of a simple pendulum inside a satellite orbiting earth is
A . zero
B. ( infty )
c. can be any integer
D. cant say
11
228The mass of the jupiter is ( 1.9 times 10^{2} mathrm{kg} )
and that of sun is ( 1.99 times 10^{30} ) kg. The
mean distance of jupiter from the sun is ( 7.8 times 10^{11} mathrm{m} . ) Speed of jupiter is
(assuming that jupiter moves in circular orbit around the sun)
11
229Choose the correct statements from the
following
This question has multiple correct options
A. The gravitational forces between two particles are an action and reaction pair
B. Gravitational constant ( (G) ) is scalar but acceleration due to gravity ( (g) ) is a vector
C. The values of ( G ) and ( g ) are to be determined
experimentally
D. ( G ) and ( g ) are constant everywhere
11
230Value of universal gravitational
constant ( G ) in ( mathrm{CGS} ) unit is-
A ( cdot 6.67 times 10^{8} mathrm{cm}^{3} g^{1} s )
B . ( 6.67 times 10^{8} mathrm{cm}^{3} g^{-1} s^{-2} )
c. ( 6.67 times 10^{9} mathrm{cm}^{3} g^{1} s^{2} )
D. ( 6.67 times 10^{7} mathrm{cm}^{3} g^{-1} s^{2} )
11
231State whether true or false.
As a planet moves around the sun it
sweeps equal areas in equal intervals of time.
A. True
B. False
11
232Can a satellite move in a stable orbit in
a plane not passing through the earth’s centre? Explain.
11
233The 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 the earth.When both ( h ) and ( d ) are
much smaller than the radius of
earth,then which one of the following is
true?
A ( . a=h / 2 )
В. ( d=3 h / 2 )
c. ( d=2 h )
( mathbf{D} cdot h=d )
11
234In case of an orbiting satellite, if the radius of orbit is decreased
A . its ( K E ) decreases
B. its ( P E ) decreases
c. its ( M E ) is doubled
D. it stops moving in the orbit
11
235A man of mass ( m ) starts falling towards
a planet of mass ( M ) and radius R. As he
reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass ( 2 M / 2 ) and a point
mass ( M / 3 ) at the centre. Change in the force of gravity experienced by the man is
A ( cdot frac{2 G M m}{3} frac{G M m}{R^{2}} )
B. 0
c. ( frac{1}{3} frac{G M m}{R^{2}} )
D. ( frac{4 G M m}{3} frac{G M m}{R^{2}} )
11
236Identify which of the following
statement is correct for acceleration
due to gravity on earth:
A. It is abbreviated with the letter ( R )
B. It has a magnitude of ( 9.8 mathrm{cm} / mathrm{sec}^{2} ) away from the center of earth
C. It has a magnitude of ( 9.8 mathrm{m} / mathrm{sec}^{2} ) toward the center of earth
D. Acceleration tends to increase with a greater mass
E. Acceleration tends to decrease with force
11
237An object is weighed at the North pole by a beam balance and a spring
balance, giving readings of ( W_{B} ) and ( W_{S} )
respectively. It is again weighed in the same manner at the equator, giving
readings of ( W_{B}^{prime} ) and ( W_{S}^{prime} ) respectively. Assume that the acceleration due to
gravity is the same everywhere and that the balances are quite sensitive. This question has multiple correct options
A ( . W_{B}=W_{S} )
В. ( W_{B}^{prime}=W_{S}^{prime} )
( mathbf{c} cdot W_{B}=W_{B}^{prime} )
D. ( W_{S}^{prime}=W_{S} )
11
238Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth is size. If
the acceleration due to gravity on the surface of the earth is ( g ) and that on the
new planet is ( g^{prime} ), then what is the value of g’lg?
( A cdot 3 )
B. 4
( c cdot 5 )
D. 6
11
239Two planets ( A ) and ( B ) have their radii in
the ratio of 2: 5 and densities in the
ratio of 1: 6 respectively. Which of the
following statements is NOT true regarding the given information?
A. The ratio of acceleration due to gravity on them is 1 :
15
B. For the same volume of planets, mass of planet ( A ) is greater than that of planet ( B )
c. A body weighs 15 times more on planet ( B ) than on planet ( A )
D. Planet ( B ) has greater volume than planet ( A )
11
240A planet in its elliptical orbit has the
farthest distance from the sun(r, ( ) )
equal to three times its nearest
distance from the sun(r ( _{2} ) ). Will the
orbital speed of the planet be different
at those points?
A. Orbital velocity at nearest point will be twice that at farthest point
B. orbital velocity at nearest point will be thrice that at farthest point
c. orbital velocity at farthest point will be thrice that at nearest point
D. orbital velocity will be same, since no other force acts on the planet
11
241Consider a satellite moving in a circular orbit around Earth. If ( mathrm{K} ) and ( mathrm{V} ) denote its
kinetic energy and potential energy respectively, then(Choose the convention, where ( V=0 text { as } r rightarrow infty) )
A ( . K=V )
в. ( K=2 V )
( mathbf{c} cdot V=2 K )
D. ( K=-2 V )
E . ( V=-2 K )
11
242At what height ( ^{prime} h^{prime} ) from the earth
surface, acceleration due to gravity
becomes half as that of acceleration
due to gravity on the surface of earth. ( [R=text { Radius of earth }] )
( mathbf{A} cdot h=R )
в. ( h=frac{R}{2} )
c. ( h=frac{R}{3} )
D. ( h=frac{R}{4} )
11
243A spring balance is graduated on sea level. If a body is weighted at consecutively increasing heights from earth’s surface, the weight indicated by the balance:
A. Will go on increasing continuously
B. Will go on decreasing continuously
c. will remain same
D. Will first increases and then decreases
11
244Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?11
245The speed of a falling body increases continuously. This is because:
A. No force acts on it
B. It is very light
c. Air exerts a frictional force along the direction of motion
D. The earth attracts it
11
246Fill in the blanks:
Value of gravitational constant (G) on moon is
A. Greater
B. Smaller
c. same
D. None
9
247If density of the earth is doubled keeping its radius constant, then acceleration due to gravity (present
value ( 9.8 m / s^{2} ) ) will be:
A ( cdot 2.45 mathrm{m} / mathrm{s}^{2} )
B . ( 4.9 mathrm{m} / mathrm{s}^{2} )
c. ( 9.8 mathrm{m} / mathrm{s}^{2} )
D. ( 19.6 mathrm{m} / mathrm{s}^{2} )
11
248The value of ( G ) for two bodies in vacuum
is ( 6.67 times 10^{-11} N / m^{2} / K g^{2} . ) Its value in
a dense medium of density
( 10^{10} g m / c m^{3} ) will be:
A ( .6 .67 times 10^{-11} N / m^{2} / K g )
B. ( 6.67 times 10^{-31} N / m^{2} / K g )
c. ( 6.67 times 10^{-21} N / m^{2} / K g )
D. ( 6.67 times 10^{-10} N / m^{2} / K g )
11
249Kepler’s law of area is based on
A. Conservation of linear momentum
B. Conservation of angular mementium
c. conservation of energy
D. both(1) and ( mid(2) )
11
250A body of mass ( mathrm{m} ) is dropped from a
height h equal to the radius of the earth
(R) above the tunnel dug through the
earth as shown in the figure. Ignore the
effect of earths rotation and air
resistance, M is mass of earth. Choose
the correct alternative(s):
A. body will oscillate through the earth to a height hon both sides
B. body will execute simple harmonic motion.
c. Motion of the body is periodic.
D. body passes the center of earth with a speed ( sqrt{frac{2 G M}{R}} )
11
251Suppose the earth shrinks such that its
radius decreases to half the present
value. What will be the acceleration due
to gravity on the surface of the earth?
11
252The Jupiter’s period of revolution around
the Sun is 12 times that of the

Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and
the Sun.
A . 5.2 times
B. 10.2 times
c. 6.4 times
D. 3 times

11
253For a satellite moving in an orbit around the earth, the ratio of K.E to P.E is:
A ( -frac{1}{2} )
B. ( -frac{1}{sqrt{2}} )
( c cdot 2 )
D. ( sqrt{2} )
11
254Which of the following is correct?
A. The value of ( g ) is constant throughout
B. ( g propto frac{1}{r^{2}} )
C ( . g ) is slightly less (by about ( 1 % ) ) when distance ( <200 m )
D. ( g ) is slightly greater when distance ( <200 m )
11
255The escape velocity for a planet is ( boldsymbol{v}_{e} cdot mathbf{A} ) tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
A ( cdot v_{c} )
в. ( frac{v_{e}}{sqrt{2}} )
c. ( frac{v_{e}}{2} )
D. zero
11
256If ( F ) is the force between two bodies of
masses ( m_{1} ) and ( m_{2} ) at certain
separation, then the force between ( sqrt{2} m_{1} ) and ( sqrt{3} m_{2} ) at same separation
is:
A ( cdot sqrt{6} F )
в. ( sqrt{26} F )
( c .6 F )
D. ( sqrt{216} F )
11
257Which of the following Kepler’s laws is also known as harmonic law?
A. First law
B. Second law
c. Third law
D. None of these
11
258(a) Explain Newton’s first law of motion with an example.
(b) ( F=frac{G m_{1} m_{2}}{d^{2}} ) is the mathematical
form of Newton’s law of gravitation. Give the statement of Newton’s law of
gravitation.
11
259Four particles each of mass ( M, ) are located at the vertices of a square with
side ( L . ) The gravitational potential due
to this at the centre of the square is
A ( cdot-sqrt{32} frac{G M}{L} )
в. ( -sqrt{64} frac{G M}{L^{2}} )
c. zero
D. ( sqrt{32} frac{G M}{L} )
11
260Find the amount of work done by friction and gravity till the chain leaves the table, if the hanging part is pulled gently and released
A ( cdot frac{5 m g ell}{18} )
в. ( frac{18 m g ell}{5} )
c. ( frac{m g ell}{5} )
D. ( frac{m g ell}{18} )
11
261Assertion
Water kept in an open vessel will quickly evaporate on the surface of the
moon.
Reason
The temperature at the surface of the moon is much higher than the boiling point of water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
262Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The
two will.
A. Will become stationary
B. Keep floating at the same distance between them
c. Move towards each other
D. Move away from each other
11
263Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution.
Reason
According to Kepler’s third law of
planetary motion, square of the time period is proportional to the cube of the mean distance from the sun.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
264A satellite is going around the earth. Which of the following statement is not
correct?
A. It is freely falling body
B. It experiences no acceleration
c. It is moving with constant speed
D. Its angular momentum is constant
11
265A satellite is revolving in a circular orbit at a distance of ( 2620 mathrm{km} ) from the
surface of the earth. The time period of
revolution of the satellite is
(Radius of the earth ( =mathbf{6 3 8 0} ) km, mass
of the earth ( =mathbf{6} times mathbf{1 0}^{mathbf{2 4}} mathbf{k g}, mathbf{G}=mathbf{6 . 6 7} times )
( left.mathbf{1 0}^{-11} mathbf{N}-boldsymbol{m}^{mathbf{2}} / boldsymbol{k g}^{2}right) )
( mathbf{A} cdot 2.35 ) hours
B. 23.5 hours
c. 3.25 hours
D. 32.5 hours
11
266The escape velocity for the earth is 11.2 ( mathrm{km} / mathrm{s} . ) The mass of another planet 100 times mass of earth and its radius is 4
times radius of the earth. The escape
velocity for the planet is
( A cdot 280 mathrm{km} / mathrm{s} )
в. 56.0 km/s
c. ( 112 mathrm{km} / mathrm{s} )
D. 24 km/s
11
267The force of attraction between two unit
point masses separated by a unit distance is called:
A . gravitational potential
B. acceleration due to gravity
c. gravitational field
D. universal gravitational constant
11
268At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be ( frac{g}{100} ? )
A. ( 10 R )
( R )
в. ( 9 R )
c. ( 100 R )
D. ( R / 100 )
11
269The weight of a person on Earth is 600
N. His weight on Moon will appear as:
A . zero
B. 100 N
c. 600 N
D. 6300 N
9
270At noon, the sun and the earth pull the objects on the earth’s surface in opposite directions. At midnight, the ( mathrm{gm} ) and the earth pull these objects in the same direction. Is the weight of an object, as measured by a string balance on the earth’s surface, more at midnight
as compared to its weight at noon?
11
271The separation between two masses is reduced to half. How is the magnitude of gravitational force between them affected?
A. Force will become four times
B. Force will remains same
c. Force will become twice
D. Force will become eight times
11
272The work done in rearranging a system of 3 identical particles of mass 1kg on a right angled triangle to an equilateral triangle is (length of the side in both the configuration is ( 1 mathrm{m} ) )
A. ( W=G(1+1 sqrt{2}) )
в. ( W=G(1-1 sqrt{(} 2)) )
c. ( W=G(1-2 sqrt{(} 2)) )
D. ( W=G(1+2 sqrt{(} 2)) )
11
273The centripetal force acting on a
satellite revolving round the earth is ( boldsymbol{F} ) The gravitational force on that planet is also ( F . ) The resultant force on the
satellite is
A . zero
в. ( F )
c. ( 2 F )
D. ( frac{F}{2} )
11
274A planet is revolving in an elliptical orbit around the sun. Its closest
distance from the sun is ( r ) and the
farthest distance is ( R ). If the velocity of
the planet nearest to the sun be ( v ) and
that farthest away from the sun be ( V )
then ( boldsymbol{v} / boldsymbol{V} ) is :
A ( cdot R^{2} / r^{2} )
B . ( r^{2} / R^{2} )
c. ( R / r )
D. ( r / R )
11
275A spherical planet far out in space has a
( operatorname{mass} M_{0} ) and diameter ( D_{0} . ) A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to:
A ( cdot frac{G M_{0}}{D_{0}^{2}} )
в. ( frac{4 m G M_{0}}{D_{0}^{2}} )
c. ( frac{4 G M_{0}}{D_{0}^{2}} )
D. ( frac{G m M_{0}}{D_{0}^{2}} )
11
276The relation connecting acceleration due to gravity and gravitational constant is:
A ( cdot g=frac{G M}{R^{2}} )
В . ( g=frac{G M}{R} )
c. ( g=G M R^{2} )
D. ( g=G M R )
11
277The ratio of the value of ( g ) in Sl units to
CGS units is.
( mathbf{A} cdot 10^{2}: 1 )
B. 10: 1
( c cdot 10^{-1}: 1 )
1
D. ( 10^{-2}: 1 )
11
278WEIGHTLESSNESS
An astronaut experiences weightlessness in a space satellite. It is because
A. the gravitational force is small at that location in space
B. the gravitational force is large at that location in space
c. the astronaut experiences no gravity.
D. the gravitational force is infinitely large at that location in space
11
279Two satellites are revolving around the earth in circular orbits of same radii.
Mass of one satellite is 100 times that
of the other. Then their periods of revolution are in the ratio:
A . 100: 1
B. 1: 100
c. 1: 1
D. 10: 1
11
280The inward force required to keep a satellite moving a circular orbit is?
A. Gravitational field
B. Centripetal force
c. centrifugal force
D. Aerodynamic forç
11
281What would be the length of a sec. A pendulum at a planet (where acc, due to gravity is ( g / 4 ) ) if it’s length on earth is ( l )
A ( . l / 2 )
в. ( 2 l )
( c cdot l / 4 )
D. 4
11
282If the mass of a planet is ( 10 % ) less than that of the earth and the radius is ( 20 % )
greater than that of the earth, the
acceleration due to gravity on the planet will be.
A. ( 5 / 8 ) times that on the surface of the earth
B. ( 3 / 4 ) times that on the surface of the earth
c. ( 1 / 2 ) times that on the surface of the earth
D. ( 9 / 10 ) times that on the surface of the earth
11
283In the region of only gravitational fields of mass ‘ ( M^{prime} ) a particle is shifted from ( boldsymbol{A} )
to ( B ) via three different paths of length
( 5 m, 10 m ) and ( 25 m . ) The work done in
different paths is ( W_{1}, W_{2}, W_{3} ) respectively then:
A. ( W_{1}=W_{2}=W_{3} )
В. ( W_{1}>W_{2}>W_{3} )
C ( . W_{1}=W_{2}>W_{3} )
D. ( W_{1}<W_{2}<W_{3} )
11
284Two blocks ( A ) and ( s ) of masses ( 100 k g )
and ( 20 k g ) respectively, separated by a
distance of 5 in are kept on a smooth
surface. A mass of 60kg is then added
to the block ( A . ) Now, in order to
experience same attractive force as before, the two blocks should be separated by a distance of :
11
285The radius of the earth is ( R ) and
acceleration due to gravity at its surface is ‘g’. If a body of mass ‘ ( m ) ‘ is
sent to a height of ( boldsymbol{R} / mathbf{4} ) from the earth’s surface, the potential energy is:
( A cdot m g R / 3 )
в. ( m g R / 4 )
c. ( m g R / 5 )
D. ( m g R / 16 )
11
286A body weighs ( 900 mathrm{N} ) on the earth. Find its weight on a planet whose density is ( mathbf{1}^{s} )
( frac{1}{3} ) the density of earth and radius is 1
( t h )
( frac{1}{4} ) that of the earth.
A . ( 75 mathrm{N} )
в. 500 N
c. 62 N
D. 320N
11
287On the earth surface, ‘g’ is a vector and its direction is oriented towards the
centre of the
( A cdot ) body
B. sun
c. earth
D. none of these
11
288Explain why an astronaut in an orbiting satellite has a feeling of
weightlessness.
11
289If the density of a small planet is the same as that of earth, while the radius
of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is:
A ( .0 .2 mathrm{g} )
в. 0.4 g
( c cdot 2 g )
D. 4 g
11
290If the distance between Arun and Ajay becomes 10 times of initial value, then
the gravitational force between them becomes ( _{-1-} ) times of the initial
value.
A. 100
B. 10
c. ( frac{1}{100} )
D. ( frac{1}{10} )
11
291Where is the intensity of the gravitational field of the earth maximum?
A. Centre of earth
B. Equator
c. Poles
D. Same everywhere
11
292Write the three laws given by Kepler.11
293The earth’s gravitational force at some place in space causes an acceleration
of ( 7 m / s^{2} ) in a ( 1 k g ) mass.What will be
the acceleration of a ( 5 k g ) mass.What
will be the acceleration of a ( 5 k g ) mass
at the same place?
A ( cdot 7 m / s^{2} )
B. ( 35 m / s^{2} )
c. ( 1.4 m / s^{2} )
D. ( 3.5 m / s^{2} )
11
294toppr
B.
( c )
( D )
11
295A hypothetical planet has density ( rho ) radius ( R, ) and surface gravitational acceleration g. If the radius of the
planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be?
11
296What is the magnitude of the gravitational force between the earth and a ( 1 mathrm{kg} ) object on its surface? (Mass
of the earth is ( 6 times 10^{24} ) kg and radius of
the earth is ( left.6.4 times 10^{6}right) )
11
297A particle is projected upward from the surface of earth (radius ( =boldsymbol{R} ) ) with a
speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is
A ( cdot sqrt{2} R )
в. ( frac{R}{sqrt{2}} )
( c . R )
D. 2 ( R )
11
298The escape velocity from the earth is
( 11 k m s^{-1} . ) The escape velocity from a
planet having twice the radius and same mean density as that of earth is
( mathbf{A} cdot 5.4 mathrm{kms}^{-1} )
B . ( 11 k m s^{-1} )
( mathbf{c} cdot 22 k m s^{-1} )
D. None of the above
11
299A black hole is an object whose
gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth
( left(m a s s=5.98 times 10^{24} k gright) ) have to be
compressed to be a black hole?
( A cdot 10^{-9} m )
B. ( 10^{-6} mathrm{m} )
( c cdot 10^{-2} m )
D. ( 100 m )
11
300Can you think of two particles which do
not exert gravitational force on each
other?
11
301The motion of planets in the solar
system is an example of the conservation of
A . mass
B. linear momentum
c. angular momentum
D. energy
9
302A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to
the rock.
A. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite
B. As the rock cannot generate its own force, it will slow down
c. Gravity will pull the rock towards earth
D. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity
E. As the rock is smaller than the satellite, its inertia will pull it further away from earth
11
303The Jupiter’s period of revolution around the Sun is 12 times that of the

Earth. Find the ratio gravitational force exerted on Earth to that on Jupiter
A. 27.47
в. ( frac{1}{27.47} )
c. 16.2
D. ( frac{1}{16.2} )

11
304Find the distance between the centre of
gravity and centre of mass of a twoparticle system attached to the ends of
light rod. Each particle has the same
mass. Length of the rod is ( R ), where ( R ) is the radius of the earth.
( A cdot R )
в. ( frac{R}{2} )
( c . ) zer
D. ( frac{R}{4} )
11
305If ( g ) on the surface of the Earth is 9.8
( m s^{-2}, ) then it’s value at a depth of 3200
( k m ) (Radius of the earth ( =6400 mathrm{km} ) ) is
( mathbf{A} cdot 9.8 m s^{-2} )
в. zero
C ( .4 .9 mathrm{ms}^{-2} )
D. ( 2.45 mathrm{ms}^{-2} )
11
306The minimum and maximum speeds
are
( ^{mathbf{A}} cdot sqrt{frac{G M}{9 R}}, sqrt{frac{2 G M}{R}} )
в. ( sqrt{frac{G M}{5 R}}, sqrt{frac{3 G M}{2 R}} )
c. ( sqrt{frac{G M}{6 R}}, sqrt{frac{2 G M}{3 R}} )
D. ( sqrt{frac{G M}{3 R}}, sqrt{frac{5 G M}{2 R}} )
11
307In case of a planet revolving around the sun, the net torque is
A. zero
B. Maximum
c. Minimum
D. Depends on the shape of the orbit
11
308At a certain height above the earth surface the gravitational acceleration is ( 4 % ) of its value at the surface of the
earth find the height above the earth surface:
11
309If the mass of one particle is increased by ( 50 % ) and the mass of another particle is decreased by ( 50 % ), the gravitational force between them
A. decreases by 25%
B. decreases by 75 %
c. increases by 25%
D. does not change
11
310When an object is in a bond state in a field, its total energy is
A. positive
B. negative
c. zero
D. infinite
11
311A planet of mass ( M ) has uniform
density in a spherical volume of radius
( R ) Calculate the work done by the
external agent to de-assemble the planet in eight identical spherical part against gravitational pull amongst its constitute particle.
11
312The moon’s radius is ( 1 / 4 ) that of the
earth and its mass ( 1 / 80 ) times that of
the earth. If ( g ) represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is:
( A cdot g / 4 )
B. ( g / 5 )
( c cdot g / 6 )
D. g/8
11
313Dimensional formula of universal
gravitational constant ( G ) is-
A ( cdot M^{-1} L^{3} T^{-2} )
B . ( M^{-1} L^{2} T^{-2} )
c. ( M^{-2} L^{3} T^{-2} )
D. ( M^{-2} L^{2} T^{-2} )
11
314A spherical ball is dropped in a long column of viscous liquid. Which of the
following graphs represent the variation of
i) The gravitational force with time
ii) The viscous force with time
iii) The net force acting on the ball with time
A. ( Q, R, P )
B. R, Q, P
c. ( P, Q, R )
D. R, P, Q
9
315Let a star be much brighter than our
sun but its mass is same as that of sun
If our earth has average life span of a man as 70 years, then on earth like
planet of this star system at double the distance between our earth and sun will
have an average life span of a man as
A. 25 planet years
B. 20 planet years
c. 70 planet years
D. 15 planet years
11
316The velocity with which it must be projected is ( sqrt{frac{2 n g R}{n+1}}, ) where ( R ) is the radius of the earth and ( m ) the mass of
body.
11
317The weight of a satellite on earth is 100
kN. What is the gravitational force on the satellite when it orbits the earth at a
distance of ( 12800 mathrm{km} ) from the center of
the earth?
A. 11 kilo-newtons
B. 25 kilo-newtons
c. 50 kilo-newtons
D. 100 kilo-newtons
E. 200 kilo-newtons
11
318Planets A and B have same average density. Radius of ( A ) is twice that of ( B ) The ratio of acceleration due to gravity
on the surface of ( A ) and ( B ) is
A . 2:
B. 1:
( c cdot 1: 4 )
D. 4:
11
319Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of ( 200 mathrm{Km} ), the height of the other satellite is (Radius of the earth is ( R=6400 mathrm{Km} )
A. ( 8450 K m )
в. 845 Кт
c. ( 84.5 K m )
D. ( 84500 K m )
11
320Three uniform sphere, each having mass ( m ) and radius ( r, ) are kept in such a way that each touches the other two.
The magnitude of the gravitational force on any sphere due to the other two is
A ( cdot frac{G m^{2}}{r^{2}} )
в. ( frac{G m^{2}}{4 r^{2}} )
c. ( frac{sqrt{3} G m^{2}}{4 r^{2}} )
D. ( frac{sqrt{3} G m^{2}}{r^{2}} )
11
321If the distance between two particles is doubled,then the gravitational force becomes
A . Half
B. One fourth
c. Double
D. one eighth
11
322The ratio of the gravitational force between the Earth and the satellite ( A ) to
the gravitational force to the satellite ( boldsymbol{B} )
is equal to :
A ( cdot frac{1}{4} )
B. ( frac{1}{2} )
c. 1
D. 2
( E . )
11
323Four particles of masses ( m, m, 2 m ) and
( 2 m ) are placed at the four corners of a
square of side ( a ) as shown in the figure.
The magnitude of the gravitational
force acting on a particle of mass ( boldsymbol{m} )
placed at the centre of the square is
( ^{mathbf{A}} cdot frac{2 G m^{2}}{a^{2}} )
в. ( frac{G m^{2}}{sqrt{2} a^{2}} )
c. ( frac{G m^{2}}{2 a^{2}} )
( D )
11
324Planet moves in an elliptical orbit around one of the foci. The ratio of
maximum velocity ( V_{max } ) and minimum
velocity ( V_{min } ) ansd eccentricity e of the
ellipse is given by
A ( cdot frac{1-e}{1+e e} )
В ( cdot frac{e-e}{e+e e} )
c. ( frac{1+e}{1-e-e} )
D. ( frac{e}{e-e} )
11
325Three planets of same density have
radii ( boldsymbol{R}_{1}, boldsymbol{R}_{2} ) and ( boldsymbol{R}_{3} ) such that ( boldsymbol{R}_{1}= )
( 2 R_{2}=3 R_{3} ) The gravitational field at
their respective surfaces are ( g_{1}, g_{2} ) and
( g_{3} ) and escape velocities from their
surfaces are ( boldsymbol{v}_{1}, boldsymbol{v}_{2} ) and ( boldsymbol{v}_{3} ) then
This question has multiple correct options
A. ( g_{1} / g_{2}=2 )
В ( cdot g_{1} / g_{3}=3 )
c. ( v_{1} / v_{2}=1 / 4 )
D. ( v_{1} / v_{3}=3 )
11
326Suppose the distance between earth
and sun becomes half of its present
distance. What is likely to happen to
life?
11
327The escape velocity for a planet is ( boldsymbol{v} . mathbf{A} )
particle starts from rest at large
distance from the planet The planet only under gravitational attraction and passes through a smooth tunnel through its centre, speed at the centre of the planet will be:
11
328The acceleration due to gravity
with an increase in height
and depth.
11
329How are ( g ) and ( G ) related?
A ( cdot g=frac{G M}{R^{3}} )
в. ( g=frac{M}{G R^{2}} )
c. ( _{g}=frac{G M}{R^{2}} )
D. ( g=frac{G M}{R} )
11
330If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into the sun in a time ( boldsymbol{T} times ) ( left(frac{sqrt{2}}{8}right), ) where ( T ) is the time period of revolution.11
331The change in the gravitational potential energy when a body of mass ( mathrm{m} ) is raised to a height ( n R ) above the surface of the Earth is (Here R is the
A ( cdotleft(frac{n}{n+1}right) ) mgR
в. ( left(frac{n}{n-1}right) ) тg ( R )
c. ( n m g R )
D. ( frac{m g R}{n} )
11
332A meteor of mass ( M ) breaks up into two
parts. The mass of one part is ( m ). For a
given separation ( r ) the mutual
gravitational force between the two parts will be maximum if
A. ( m=(M / 2) )
в. ( m=(M / 3) )
c. ( _{m}=frac{M}{sqrt{2}} )
D. ( _{m}=frac{M}{2 sqrt{2}} )
11
333The semi-major axes of the orbits of Mercury and Mars in the astronomical units are 0.387 and 1.524
respectively. If the time period of Mercury is 0.241 year, then the time period of mars will be
A. 0.9 Year
B. 0.19 Year
c. 1.9 Year
D. 2.9 Years
11
334A planet of mass ( M=2.4 times 10^{14} k g ) is
orbiting a star in time ( boldsymbol{T}=boldsymbol{3} times mathbf{1 0}^{4} boldsymbol{s} )
sweeps an area of ( boldsymbol{A}=mathbf{6 . 9} times mathbf{1 0}^{mathbf{8}} boldsymbol{m}^{mathbf{2}} )
Calculate Angular Momentum of Planet
11
335Which among these is required in the experiment to measure Gravitational Constant?
This question has multiple correct options
A. 2 big spheres
B. 2 small spheres
c. a rod
D. physical balance
11
336A satellite of mass m goes around the earth along a circular path of radius ( r ) (from the center of Earth), let me is the
mass of the earth and ( R ), its radius. Then
the linear speed of the satellite depends
on:
( mathbf{A} cdot m_{e} ) and ( r )
B . ( m_{e} ) only
( mathbf{c} cdot mu, m_{e}, V )
D. ( m_{e}, R_{e} ) and ( r )
11
337Acceleration due to gravity on the moon
is ( 1 / 6 t h ) of the acceleration due to
gravity on the earth. If the ratio of densities of the earth and the moon is
( 5 / 3, ) then radius on the moon in terms of radius of earth will be
9
338Which of the following statement is
true?
( mathbf{A} cdot g ) is same at all places on the surface of earth.
B. g has its maximum value at the equator.
C. ( g ) is less at the earth’s surface than at a height above it or a depth below it.
D. ( g ) is greater at the poles than at the equator.
11
339If 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
( mathbf{A} cdot d propto r )
B. ( d propto r^{1 / 2} )
c. ( d propto 1 / r )
D. ( d propto frac{1}{r^{2}} )
11
340Two satellites of the same mass are
launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is
A. ( -frac{2 G M m}{r} )
в. ( -frac{G M m}{r} )
c. ( frac{G M m}{2 r} )
D. ( frac{G M m}{4 r} )
11
341An asteroid is moving directly towards the centre of the earth. When at a
distance of ( 10 R(R ) is the radius of the
earth) from the earth centre, it has a
speed of ( 12 k m / s . ) Neglecting the effect of the earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is ( 11.2 k m / s ) )? Give your answer to the nearest integer in kilometer/s
11
342If the distance between the centres of
earth and moon is ( mathrm{D} ) and mass of earth
is 81 times that of moon. At what
distance from the centre of earth
gravitational field will be zero:
A ( cdot frac{D}{2} )
в. ( frac{3 D}{2} )
c. ( frac{4 D}{5} )
D. ( frac{D}{10} )
11
343The largest and the shortest distance of
the earth from sun are a and b,
respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on
the major axis meets the orbit is
A ( cdot frac{a b}{a+b} )
в. ( frac{a b}{2(a+b)} )
c. ( frac{2 a b}{a+b} )
D. ( frac{a+b}{2 a b} )
11
344A body weighs ( 160 N ) on the earth. Find
its weight on another planet whose mass is ( frac{5}{2} ) times mass of earth and radius ( frac{4}{5} ) times that of earth.
A . ( 125 N )
B. ( 625 N )
c. ( 225 N )
D. 25 N
11
345Identify the incorrect statement about a
planet revolving around Sun
A. The gravitational attraction provides the centripetal force for a revolving planet
B. The total energy of a planet is always negative
c. The total energy of a planet is always more than potential energy of the system
D. Kinetic energy of revolving planet is sometimes zero
11
346The average value of acceleration due to gravity on the surface of the earth is
equal to:
A. ( 9.8 mathrm{ms}^{-2} )
B. ( 9.8 mathrm{ms}^{-1} )
c. ( 19.6 mathrm{ms}^{-2} )
D. ( 9.8 s^{-2} )
11
347The normal force of an object of mass 5 kg , measured by a force metre is seen to be 50 N. Determine the acceleration
due to gravity in ( mathrm{cm} / mathrm{s}^{2} )
A. 1000
B. 100
c. 0.01
D. ( 0 . )
11
348Assertion
An astronaut inside a massive
spaceship orbiting around the earth will experience a finite but smal
gravitational force.
Reason
The centripetal force necessary to keep the spaceship in orbit around the earth is provided to keep the spaceship in orbit.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
349A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is ( V ). Due to the rotation of
planet about its axis the acceleration due to gravity ( g ) at equator is ( frac{1}{2} ) of ( g ) at
poles. The escape velocity of a particle on the pole of planet in terms of ( V )
A. ( V_{e}=2 V )
B . ( V_{e}=V )
( mathbf{c} cdot V_{e}=V / 2 )
D. ( V_{e}=sqrt{2} V )
11
350A man of weight mg is moving upwards in a rocket with acceleration 4 g. His
apparent weight in side the rocket will
be?
A. zero
B. ( 4 mathrm{mg} )
( mathrm{c} cdot 5 mathrm{mg} )
D. ( 2 mathrm{mg} )
11
351For moon its mass is ( frac{1}{81} ) of earth’s mass
and its diameter is ( frac{1}{3.7} ) of earth’s
diameter. If acceleration due to gravity of earth surface is ( 9.8 m / s^{2}, ) then at moon its value is
A ( cdot 2.86 m / s^{2} )
B . ( 1.65 m / s^{2} )
( mathbf{c} cdot 8.65 m / s^{2} )
D. ( 5.16 m / s^{2} )
9
352How much below the surface of the
earth does the acceleration due to
gravity become ( 70 % ) of its value at the surface of earth? (Take ( boldsymbol{R}=mathbf{6 4 0 0 k m} ) )
11
353A satellite in earth orbit experiences a
small drag force as it enters the earth’s atmosphere. Two students were asked consequence of this Student-A : The satellite would slow
down as, it spirals towards earth due to work of frictional force.

Student-B : The satellite speed up due
to earths gravitational pull as it spirals
towards earth.
A. A is correct, B is wrong
B. B is correct, A is wrong
c. both are correct
D. both are wrong

11
354The figure shows the elliptical orbit of a
area SCD is a twice shaded area SAB. if
( t_{1} ) is the 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 ( cdot t_{1}=t_{2} )
( mathbf{B} cdot t_{1}=2 t_{2} )
( mathbf{c} cdot t_{1}=4 t_{2} )
( mathbf{D} cdot t_{1}>t_{2} )
11
3551 ( g ) force is the force due to gravity on a mass of
( mathbf{A} cdot 1 k g )
в. ( 0.1 k g )
c. ( 0.01 k g )
D. ( 0.001 k g )
9
356An Earth’s satellite is moving in a circular orbit with a uniform speed ( boldsymbol{v} ). If
the gravitational force of the Earth suddenly disappears, the satellite will
A. vanish into outer space
B. continue to move with velocity ( v ) in original orbit
c. fall down with increasing velocity.
D. fly off tangentially from the orbit with velocity ( v )
9
3575. Given that acceleration due to gravity varies inversely as
the square of the distance from the center of earth, find its
value at a height of 64 km from the earth’s surface, if the
value at the surface be 9.81 ms-2. Radius of earth = 6400
km.
11
358A satellite is launched into a circular
orbit of radius ( R ) around the earth.
Another second satellite is launched
into an orbit of radius ( 1.01 R ). The
period of the second satellite is longer than that first by approximately
A . ( 0.5 % )
в. ( 1.0 % )
c. ( 1.5 % )
D. 3.0%
11
359An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface
of the earth of two earth radii ( (h=2 R )
where ( R ) is the radius of the earth.
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)
A. 81 pounds
B. 40.5 pounds
c. 18 pounds
D. 54 pounds
E. 0 pounds (astronaut is weightless
11
360Choose the correct statement:
A. All bodies repel each other in this universe
B. Our earth does not behave like a magnet
C. Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} )
D. All bodies fall at the same rate in vacuum
11
361The kinetic energies of a planet in an elliptical orbit about the Sun, at
positions ( A, B ) and ( C ) are ( K_{A}, K_{B} ) and
( K_{C} ) respectively. ( A C ) is the major axis and ( S B ) is perpendicular to ( A C ) at the position of the Sun ( S ) as shown in the
figure. Then.
A ( cdot K_{B}<K_{A}<K_{C} )
B. ( K_{A}<K_{B}K_{A}>K_{C} )
D. ( K_{A}>K_{B}>K_{C} )
11
362Rockets are lunched in Eastward
A. The clear sky on Eastersn side
B. The thinner atmosphere on this side
c. both A and B
D. non of the above
11
363A body of mass ( 5 k g ) is cut into two
parts of masses
(a) ( frac{m}{4} ; frac{3 m}{4} )
(b) ( frac{m}{7} ; frac{5 m}{7} )
(c) ( frac{boldsymbol{m}}{2} ; frac{boldsymbol{m}}{boldsymbol{2}} )
(d) ( frac{boldsymbol{m}}{mathbf{5}} ; frac{boldsymbol{4} boldsymbol{m}}{mathbf{5}} . ) When these two
pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?
A. In case a
B. In case ( c )
c. In case d
D. In case b
9
364A satellite of mass ( 1000 k g ) is supposed
to orbit the earth at a height of ( 2000 k m )
above the earth’s surface. Find the
potential energy of the earth-satellite
system.
11
365State whether true or false.
The weight of a freely falling body from a very large height is always constant
A. True
B. False
11
366A satellite is moving in a circular orbit round the earth. If gravitational pull suddenly disappears,then it
A. Continuous to move with the same speed along the same path
B. Moves with the same velocity tangential to original orbit
c. Falls down with increasing velocity.
D. comes to rest after moving certain distance along original path.
9
367A body of mass ( m ) is moving in a circular orbit of radius ( boldsymbol{R} ) about a planet
of mass ( M . ) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius ( frac{boldsymbol{R}}{longrightarrow} ) ( overline{2} )
and the other mass, in a circular orbit of radius ( frac{3 R}{2} . ) The difference between the final and initial total energies is:
A. ( -frac{G M m}{2 R} )
в. ( +frac{G M m}{6 R} )
c. ( frac{G M m}{2 R} )
D. ( -frac{G M m}{6 R} )
11
368At what height, the value of ‘g’ is half
that on the surface of the earth of
A. ( R )
в. ( 2 R )
c. ( 0.414 R )
D. ( 0.75 R )
11
369If ( G ) is the universal gravitation
constant and is the uniform density of a
spherical planet, then,
A. Time period of a planet will be independent of density of the planet
B. The shortest period of rotation of the planet will have very high density
c. The shortest period of rotation of the planet will have very low density
D. The shortest period of rotation of the planet depends on the radius of the planet
11
370State Kepler’s third law.11
371Kepler’s third law of planetary motion states that : (Symbols have their usual
meaning)
A. ( V_{0}=sqrt{R g} )
B . ( overrightarrow{F_{12}}=-overrightarrow{F_{21}} )
( mathbf{c} cdot r^{2} propto T^{3} )
( mathbf{D} cdot r^{3} propto T^{2} )
11
372The ratio of the value of ( G ) in ( S ) l units to
CGS units is
( mathbf{A} cdot 10^{3}: 1 )
B ( cdot 10^{2}: 1 )
( mathbf{c} cdot 10^{-2}: 1 )
D. ( 10^{-3}: 1 )
11
373An object takes ( 5 s ) to reach the ground
from a height of ( 5 m ) on a planet. What is
the value of ( g ) on the planet?
11
374Rank the arrangements of masses given in the table below according the
force between masses, greatest first. The first column in the table tells the
mass of one of the objects in each arrangements, the second column gives the mass of the second object, and the third column gives the distance between the centers of the objects.
( boldsymbol{m}_{1} ) , an a ( m_{2} )
Arrangement 1 M м
М 2M 1 Arrangement 2
зм 1 Arrangement 3 1 М
A .1,2,3
B. 1,2 and 3 tie
c. 1,3,2
D. 3, 2,1
E. 2 and 3 tie,
11
375The radius of a planet is 4 times the radius of the earth. The time period of revolution of the planet will be:
A . ( 1 y r )
B. 2 ( y r )
c. ( 4 y r )
D. ( 8 y r )
11
376The mass of the moon is about ( 1.2 % ) of
the mass of the earth. Compared to the gravitational force that earth exerts on the moon, the gravitational force of the moon exerted on earth:
A. Is the same
B. Is smaller
c. Is greater.
D. Varies with its phase
9
377A mass ( mathrm{M} ) is broken in two parts: ( mathrm{m} ) and ( (M-m) . ) Relation between ( m ) and ( M s o )
that the force of gravitation between the two parts is maximum is.
( A cdot m M=2 )
в. ( m=frac{M}{2} )
c. ( M=m^{2} )
D. None of these
11
378Assertion
Newton’s law of gravitation resembles Coulomb’s law of electrical forces.
Reason
Coulomb’s law has the product of two charges in place of the product of the masses, and the electrostatic constant
in place of the gravitational constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
379A bullet is fired vertically upwards with velocity ( v ) from the surface of a
spherical planet. When it reaches its maximum heights, its acceleration due
to the planet’s gravity is ( 1 / 4 ) th of its value at the surface of the planet. If the
escape velocity from the planet is ( boldsymbol{v}_{e s c}=boldsymbol{v} sqrt{boldsymbol{N}}, ) then the value of ( mathrm{N} ) is
(ignore energy loss due to atmosphere)
11
380On a planet where ( boldsymbol{g}_{text {planet}}=mathbf{0 . 2} boldsymbol{g}_{text {earth}} )
What will be the difference in the height of column filled with mercury in a closed end manometer when the gas is
filled withe pressure of ( 2 a t m ) on earth (Assuming:outside pressure to be 1 atm on both planet; Volume of gas remain constant)
A . ( 30.4 mathrm{cm} )
в. ( 760 mathrm{cm} )
c. ( 380 c m )
D. 152 ст
11
381ENERGY OF AN ORBITING SATELLITE
The change in potential energy is:
( ^{A} cdot frac{G M_{E} m}{2 R_{E}} )
в. ( frac{G M_{E} m}{4 R_{E}} )
c. ( frac{G M_{E} m}{8 R_{E}} )
D. ( frac{G M_{E} m}{R_{E}} )
11
382A 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 ( r_{1} ) and ( r_{2} ) respectively. The time period of the planet is proportional to:
( mathbf{A} cdot r_{1}^{3 / 2} )
B ( cdot r_{2}^{3 / 2} )
c. ( left(frac{r_{1}+r_{2}}{2}right)^{3 / 2} )
D. ( frac{left(r_{1}-r_{2}right)^{3 / 2}}{2} )
11
383The International Space Station is
currently under construction. Eventually, simulated earth gravity may become a reality on the space station. What would the gravitational field through the central axis be like under
these conditions?
A. zero
B. ( 0.25 g )
( mathrm{c} .0 .5 mathrm{g} )
D. ( 0.75 g )
E . ( 1 g )
11
384A particle would take time ( t_{1} ) to move
down a straight tube from the surface of earth (supposed to be homogeneous sphere) to its centre. If gravitational acceleration were to remain constant
time would be ( t_{2} ). The ratio ( t / t^{prime} ) will be
A ( cdot frac{pi}{2 sqrt{2}} )
в. ( frac{pi}{2} )
c. ( frac{2 pi}{3} )
D. ( frac{pi}{sqrt{3}} )
11
385Correct form of gravitational law is:
A ( cdot vec{F}=-frac{G m_{1} m_{2}}{r^{2}} )
В ( cdot vec{F}=-frac{G m_{2} m_{1}}{r^{2}} )
c. ( vec{F}=-frac{G m_{1} m_{2}}{r^{2}} hat{r} )
D・ ( vec{F}=-frac{G m_{1} m_{2}}{r^{3}} vec{r} )
11
386A body is lying on the surface of earth.Suppose that the earth suddenly loses its power of attraction, then
A. the weight of body will become zero
B. the weight of body will become infinite
c. the mass of the body will become zero
D. the body will vanish in air
11
387Time period of simple pendulum in a satellite is
A . Infinite
B. Zero
c. 2 sec
D. Cannot be calculated
11
388If the mass of a body is ( M ) on the
surface of the earth, the mass of the
same body on the surface of the moon is
A. ( M / 6 )
в. ( M )
( c cdot 6 M )
D. zero
11
389What is the minimum energy required to launch a satellite of mass ( m ) from the
surface of a planet of mass ( M ) and radius ( R ) in a circular orbit at an
altitude of ( 2 R ? )
A ( cdot frac{2 G m M}{3 R} )
в. ( frac{G m M}{2 R} )
c. ( frac{G m M}{3 R} )
D. ( frac{5 G m M}{6 R} )
11
390The acceleration due to gravity ( g ) and density of the earth ( p ) are related by which of the following relations? (Here ( G ) is the gravitational constant and ( R ) is the radius of the earth)
A ( cdot p=frac{4 pi}{3 G R d} )
в. ( _{p}=frac{3 g}{4 pi G R} )
c. ( _{p}=frac{3 G}{4 pi G R} )
D. ( p=frac{4 pi G R}{3 G} )
11
391The escape velocity of a particle of mass ( m ) varies as:
( mathbf{A} cdot m^{2} )
в. ( m )
c. ( m^{0} )
D. ( m^{-1} )
11
392The acceleration due to gravity:
A. has the same value everywhere is space
B. has the same value everywhere on the earth
C. varies with the latitude on the earth
D. is greater on the moon due to its smaller diameter
11
393Find the gravitational force between two atoms in a hydrogen molecule. Given that ( G=6.67 times 10^{-11} N m^{2} k g^{-2} ) and
mass of hydrogen atom ( 1.67 times 10^{-27} k g )
and the distance between the two
atoms1 ( ^{circ} A . ) The answer is ( 1.86 times )
( 10^{-x y} N ) then ( x+y= )
11
394A small mass ( m ) is moved slowly from the surface of the earth to a height ( h ) above the surface. The work done (by an external agent) in doing this is
This question has multiple correct options
A. ( m g h, ) for all values of ( h )
B. ( m g h, ) for ( h<<R )
c. ( frac{1}{2} ) mgR, for ( h=R )
D. ( -frac{1}{2} ) mgR, for ( h= )
11
395If the mass of the Sun were ten times
smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not
correct?
A. Time period of a simple pendulum on the Earth would decrease
B. Raindrops will fall faster
c. ‘g’on the Earth will not change
D. Walking on the ground would become more difficult
11
396Depth from the surface of the earth at which is acceleration due to gravity is ( 25 % ) of acceleration due to gravity at the
surface
A. ( 1200 mathrm{km} )
B. 4000 km
c. ( 3600 mathrm{km} )
D. ( 4800 mathrm{km} )
11
397Name two force in nature that have
longest and shortest range
9
398Earth radius is ( boldsymbol{R} ) and spin angular
velocity of Earth is ( omega . ) At what height
above the North pole the acceleration
due to gravity will be same as that at
the equation? ( (g ) is acceleration due to
gravity at North pole).
11
399The gravitational potential difference between the surface of a planet and a
point ( 20 m ) above the surface is
2Joule/Kg. If the gravitational field is uniform then the work done in carrying a ( 5 K g ) body to a height of ( 4 m ) above the
surface is
A . 2 Joule
в. 20Joule
c. 40 Joule
D. 10 Joule
11
400Net torque on the planet is
A. Constant at all points
B. Zero at all point
c. Maximum at ( A )
D. Minimum at ( D )
11
401The earth is an approximate sphere. If
the interior contained matter which is
not of the same density everywhere, then on the surface of the earth, the
acceleration due to gravity :
A. will be directed towards the centre but not the same everywhere
B. will have the same value everywhere but not directed towards the centre
c. will be same everywhere in magnitude directed towards the centre
D. cannot be zero at at point
11
402Escape velocity when a body of mass ( m ) is thrown vertically from the surface of the earth is ( v, ) what will be the escape
velocity of another body of mass ( 4 m ) if thrown vertically
( A )
B . ( 2 v )
c. ( 4 v )
D. None of these
11
403If the gravitational potential on the surface of earth is ( V_{0} ) then potential at a
point at height half of the radius of earth is
A ( cdot frac{V_{0}}{2} )
в. ( frac{2}{3} V_{0} )
c. ( frac{V_{0}}{3} )
D. ( frac{3 V_{0}}{2} )
11
404On the earth, a Sumo of ( 420 mathrm{kg} ) is checking his reading on a spring balance. To have the same reading of spring balance on the moon, how many Sumos of mass ( 420 mathrm{kg} ) each should stand on it. Explain. ( left(g=30 mathrm{m} mathrm{s}^{-2}right) )
( A cdot 6 )
B. 12
( c cdot 18 )
D.
9
405Figure shows position and velocities of two particles moving under mutual gravitational attraction in space at
time ( t=0 . ) The position of centre of
mass after one second is :
( mathbf{A} cdot x=4 m )
B . ( x=6 m )
( mathbf{c} cdot x=8 m )
D. ( x=10 m )
11
406Two identical solid copper spheres of
radius ( R ) are placed in contact with each other. The gravitational attraction between them is proportional to
( mathbf{A} cdot R^{2} )
B. ( R^{-2} )
( c cdot R^{-4} )
D. ( R^{4} )
11
407A spaceship moves in a circular orbit of
radius ( 7200 mathrm{km} ) round the earth. How
far does it travel while sweeping an
angle of ( 100^{circ} ? )
11
408Which of the following is true for universal law of gravitation?
(1) It acts on all the objects irrespective of their nature, shape and size
(2) ( boldsymbol{F} propto boldsymbol{M} times boldsymbol{m} )
(3) It acts along the line joining the centers of the two objects.
(4) ( boldsymbol{F} propto frac{1}{d^{2}} )
A . a and c
B. b and d
( c cdot a, b ) and ( d )
D. All of the above
11
409At what height from the surface of earth
will the value of ( g ) be reduced by ( 36 % )
from the value at the surface? ( boldsymbol{R}= )
( 6400 k m )
A . ( 400 k m )
B. ( 800 k m )
( c .1600 k m )
D. 3200km
11
410A body of mass ( m ) is moving in a circular orbit of radius ( boldsymbol{R} ) about a planet
of mass ( M . ) At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius ( frac{boldsymbol{R}}{longrightarrow} ) ( overline{2} )
and the other mass, in a circular orbit of radius ( frac{3 R}{2} . ) The difference between the final and initial total energies is:
A. ( -frac{G M m}{2 R} )
в. ( +frac{G M m}{6 R} )
c. ( frac{G M m}{2 R} )
D. ( -frac{G M m}{6 R} )
11
411The radius of a planet is ( R_{1} ) and ( a )
satellite revolves around it in a radius ( mathrm{R} )
2
Time period of revolution is ( T . ) Find the
acceleration due to gravity.
( ^{mathbf{A}} cdot frac{4 pi^{2} R_{2}^{3}}{R_{1}^{2} T^{2}} )
B. ( frac{4 pi^{2} R_{2}^{2}}{R_{1} T^{2}} )
( ^{mathrm{c}} cdot frac{2 pi^{2} R_{2}^{3}}{R_{1} T^{2}} )
D. ( frac{4 pi^{2} R_{2}}{T^{2}} )
11
412The angular velocity of the earth’s rotation about its axis is ( omega . ) An object
weighed by a spring balance gives the same reading at the equator as at height ( h ) above the poles, the value of ( h )
will be:
( ^{mathrm{A}} cdot frac{omega^{2} R^{2}}{g} )
В. ( frac{omega^{2} R^{2}}{2 g} )
c. ( frac{2 omega^{2} R^{2}}{g} )
D. ( frac{2 omega^{2} R^{2}}{3 g} )
11
413The time period of an earth satellite in
circular orbits is independent of
A. both the mass and radius of the orbit
c. the mass of the satellite
D. neither the mass of the satellite nor the radius of its orbit
11
414Obtain an expression for acceleration due to gravity at a height ( h ) above the
earth’s surface.
11
415Can a pendulum vibrate in an artificial
satellite?
11
416Find the work done to take a particle of mass ( mathrm{m} ) from surface of the earth to a
height equal to ( 2 R )
( mathbf{A} cdot 2 m g R )
в. ( frac{m g R}{2} )
c. ( 3 m g R )
D. ( frac{2 m g R}{3} )
11
417The relationship between acceleration due to gravity ( (g) ) and universal
gravitational constant( ( G ) ) may be
represented as:
( (M text { and } R ) are the mass and radius of
the earth respectively
A. ( G=frac{g M}{R^{2}} )
В. ( g=frac{G M}{R^{2}} )
c. ( g=frac{G}{R^{2}} )
D. None of these
11
418Solve:
A sphere of mass ( 10 mathrm{kg} ) is attracted by another sphere of mass ( 150 mathrm{kg} ), with a force equal to ( 1.28 times 10^{-6} N, ) when their
centers are separated by a distance of ( 0.28 mathrm{m} . ) Calculate the gravitational
constant.
11
419Sl unit of ( G ) is ( N m^{2} k g^{-2} . ) Which of the
following can also be used as the Sl unit
of G?
A ( cdot m^{3} k g^{-1} s^{-2} )
B . ( m^{2} k g^{-2} s^{-1} )
( mathbf{c} cdot m k g^{-3} s^{-1} )
D. ( m^{2} k g^{-3} s^{-2} )
11
420The escape velocity of a body thrown vertically upwards from the surface of
earth is
( 11.2 mathrm{Km} / mathrm{s} . ) If it is thrown in a
direction making an angle of ( 30^{0} ) from the vertical, the new escape velocity will
be
( mathbf{A} cdot 5.6 mathrm{Km} / mathrm{s} )
B. ( 11.2 mathrm{Km} / mathrm{s} )
c. ( 11.2 times sqrt{2} mathrm{km} / mathrm{s} )
D. ( _{11.2} times frac{sqrt{3}}{2} mathrm{km} / mathrm{s} )
11
421The angular velocity of rotation of a star (mass ( mathrm{M} ) and radius ( mathrm{R} ) ), such that the
matter will start escaping from its equator is:
A ( cdot sqrt{frac{2 G R}{M}} )
в. ( sqrt{frac{2 G M}{R^{3}}} )
c. ( sqrt{frac{2 G M}{R}} )
D. ( sqrt{frac{2 G M^{2}}{R}} )
11
422An artificial satellite moving in a circular orbit around the earth has a
total energy ( boldsymbol{E}_{0} . ) Its potential energy is
A. ( -E_{0} )
в. ( E_{0} )
c. ( 2 E_{0} )
D. ( -2 E_{0} )
11
423Kepler’s laws of planetary motion provides information about:
A. areal velocity of a planet
B. nature of motion of a planet
C. ratio of time periods of two planets
D. all the above
11
424The radius and acceleration due to
gravity of the moon are ( frac{1}{4} ) and ( frac{1}{5} ) that of
the earth, the ratio of the mass of the
earth to mass of the moon is :
( mathbf{A} cdot 1: 80 )
B. 80: 1
c. 1: 20
D. 20:1
11
425Two blocks ( A ) and ( B ) of masses ( M_{A} ) and
( M_{B} ) respectively, are located ( 1.0 m ) apart on a horizontal surface. The
coefficient of static friction ( mu_{s} ) between
the block and the surface is ( 0.50 . ) Block
( A ) is secured to the surface and cannot
move, what is the minimum mass of
Block ( A ) that provides enough gravitational attraction to move Block
B? The universal gravitation constant is ( 6.67 times 10^{-11} N m^{2} / k g^{2} .(g= )
( 9.8 m s^{-2} )
A ( cdot 7.5 times 10^{9} k g )
в. ( 7.3 times 10^{16} k g )
c. ( 14.7 times 10^{11} k g )
D. The problem cannot be solved without knowing the mass of Block ( B )
11
426Acceleration of particle moving rectilinearly is ( a=4-2 x ) (where ( x ) is
position in meter and ( a ) in ( m s^{-2} ) ). It is at
instantaneous rest at ( x=0 . ) At what
position ( x ) (in meter) will the particle again come to instantaneous rest?
11
427If the earth were to suddenly contract to ( frac{1}{m} ) th of its present radius without any ( boldsymbol{n} )
change in its mass then the duration of the new day will be close to
( ^{mathrm{A}} cdot frac{24}{n} ) hour
B. ( 24 n ) hour
c. ( frac{24}{n^{2}} ) hour
D. ( 24 n^{2} ) hour
11
428Calculate the gravitational field intensity and potential at the centre of the base of a solid hemisphere of mass
( mathrm{m}, ) radius ( mathrm{R} )
11
429Journey in a train is adventurous
particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically
down and touched the ground in ( 0.2 s )
After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. If a projectile has velocity greater than escape velocity which trajectory it
will follow
A. elliptic
B. hyperbola
c. vertical straight
D. parabolic
11
430Assertion
If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies.
Reason
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
431Two planets ( A ) and ( B ) have the same
average density. Their radii ( boldsymbol{R}_{A} ) and ( boldsymbol{R}_{B} )
are such that ( boldsymbol{R}_{boldsymbol{A}}: boldsymbol{R}_{boldsymbol{R}}=boldsymbol{3}: boldsymbol{1} ) If ( boldsymbol{g}_{A} ) and
( g_{B} ) are the acceleration due to gravity at
the surfaces of the planets, the ( g_{A}: g_{B} )
equals
A . 3: 1
B. 1: 3
c. 9: 1
D. 1: 9
E . ( sqrt{3}: 1 )
11
432What the decrease in weight ofa body of mass 600 kg when it is taken in a mine of depth ( 5000 mathrm{m} ) ? [Radius of earth a
( 6400 mathrm{km}, mathrm{g}=9.8 mathrm{m} / mathrm{s}^{2} )
11
433A geostationary satellite is orbiting the earth at a height of ( 5 R ) above the
surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of ( 2 mathrm{R} ) from
the surface of the earth is:
A ( cdot frac{6}{sqrt{2}} )
B. 5
c. 10
D. ( 6 sqrt{2} )
11
434Pick out the wrong statement from the following
A. The Sl unit of universal gravitational constant is ( N m^{2} k g^{-2} )
B. The gravitational force is a conservative force
C. The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero
D. The centripetal acceleration of the satellite is equal to acceleration due to gravity
E . Gravitational potential energy ( =frac{text { gravitation potential }}{text { mass of the body }} )
11
435An astronaut whose mass is ( 84 mathrm{kg} ) on earth will have a mass of approximately
( 14 mathrm{kg} ) on the moon.
A. True
B. False
9
436( R ) and ( r ) are the radii of the Earth and
the Moon respectively and ( rho_{e} ) and ( rho_{m} ) are
the densities of the Earth and Moon
respectively. The ratio of acceleration due to gravity on the surface of the
Earth to the Moon is:
A ( cdot frac{R}{r} cdot frac{rho_{e}}{rho_{m}} )
в. ( frac{r}{R} cdot frac{rho_{e}}{rho_{m}} )
c. ( frac{r}{R} cdot frac{rho_{m}}{rho_{e}} )
D. ( frac{R}{r} cdot frac{rho_{m}}{rho_{e}} )
11
437A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) The maximum height to which it rises.
( (i i) ) The total time it takes to return to
the surface of the earth.
11
438Imagine 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 the planet and the star is
proportional to ( r^{5 / 2}, ) then the square of the time period will be proportional to.
A ( cdot r^{3} )
в. ( r^{2} )
( c cdot r^{2.5} )
D. ( r^{3.5} )
11
439State whether the given statement is True or False :
The value of ( G ) is high if the radius of the body is more and less if radius is less.
A . True
B. False
11
440Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution
Reason
According to Kepler’s third law of
planetary motion, square of time period is proportional to cube of mean distance from sun
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
441If ( M_{E} ) is the mass of the earth and ( R_{E} )
its radius, the ratio of the acceleration
due to gravity and the gravitational constant is:
( ^{text {A }} cdot frac{R_{E}^{2}}{M_{E}} )
в. ( frac{M_{E}}{R_{E}^{2}} )
c. ( M_{E} R_{E}^{2} )
D. ( frac{M_{E}}{R_{E}} )
11
442The escape velocity on the surface of a
planet is ( V_{e} ) what would be the escape
velocity on the planet having the same radius but mass 4 times that of it.
( A cdot 2 V_{e} )
B. ( 4 V_{e} )
c. ( V_{c} )
( D cdot frac{V_{c}}{2} )
11
443Escape velocity at surface of earth is
11.2Km/s. Escape valocity from a planet whose mass is the same as that of earth and radius ( 1 / 4 ) that of earth, is?
A ( .2 .8 mathrm{km} / mathrm{s} )
B. ( 15.6 mathrm{km} / mathrm{s} )
c. ( 22.4 mathrm{km} / mathrm{s} )
D. ( 44.8 mathrm{km} / mathrm{s} )
11
444f a satellite is revolving around a planet of mass ( mathrm{M} ) in an elliptical orbit of semimajor axis a. Show that the orbital speed of the satellite when it is at a distance r from the focus will be given by ( boldsymbol{v}^{2}=boldsymbol{G} boldsymbol{M}left[frac{boldsymbol{2}}{boldsymbol{r}}-frac{mathbf{1}}{boldsymbol{a}}right] )11
445The average acceleration due to gravity is ( 8.9 mathrm{ms}^{-2} )
A. True
B. False
11
446Two satellites ( A ) and ( B ) revolve around a
planet in two coplanar circular orbits in
the same sense with radii ( 10^{4} mathrm{km} ) and
( 2 times 104 mathrm{km} ) respectively. Time period of
( A ) is 28 hours. What is time period of
another
satellite?
11
447How is the acceleration due to gravity on earth surface related to the mass ( M )
and radius ( R ) of earth?
A ( cdot g=frac{G}{M R^{2}} )
в. ( g=frac{M}{G R^{2}} )
c. ( _{g}=frac{G M}{R} )
D. ( g=frac{G M}{R^{2}} )
11
448A pendulum beats seconds on the earth. Its time period on a stationary satellite of the earth will be
A. zero
B. ( 1 s )
( c cdot 2 s )
D. Infinity
11
449If the earth stops rotating.then the value of acceleration due to gravity at a latitude ( 45^{circ} ) will increases by11
450Two spheres each of mass ( 10^{5} k g ) and
radius ( 10 m ) are kept in contact. Find the force of gravitation acting between them.
A ( cdot 5.67 times 10^{-3} N )
N ( .5 .67 times 10^{-3} .6 times 10^{-3} )
в. ( 6.67 times 10^{-3} N )
c. ( 3.67 times 10^{-3} N )
D. 2.67 ( times 10^{-3} N )
11
451The weight of a body on the surface of the moon is ( frac{1}{6} t h ) of that on the earth’s surface. It is because acceleration due
to gravity on the surface of the moon is
six times that on the surface of the
earth.
A . True
B. False
9
452What is the nature of relation
betweenthe kinetic energy ( left(mathbf{E}_{mathbf{k}}right) ) and
their orbitalradius (r) of the satellites revolvingaround the Earth?
( mathbf{A} cdot E_{k} propto 1 )
B . ( E_{k} propto frac{1}{r} )
( mathrm{c} cdot E_{k} propto r^{2} )
D. ( E_{k} propto frac{1}{r^{2}} )
11
453If the earth is at one fourth of its present
distance from the sun, the duration of
the year will be
A. Half the present year
B. One eighth of the present year
c. one fourth of the present year
D. One sixth of the present year
11
454A satellite is changes it orbit from
radius of ( mathrm{R} ) to radius of ( 2 mathrm{R} ). If its initial
kinetic energy is ( K_{1} ) then calculate the
new kinetic energy.
A ( cdot frac{K_{1}}{4} )
в. ( frac{K_{1}}{2} )
c. ( K_{1} )
D. ( 2 K_{1} )
E ( .4 K_{1} )
11
455If the weight of a body on the earth is 12 Newtons (N), its weight on the moon will be:
A. २N
B. 24 kg
c. 12N
D. ( 12 mathrm{kg} )
9
456The work done by external agent to shift a point mass from infinity to the centre of earth is :
( mathbf{A} cdot=0 )
( mathbf{B} cdot>0 )
( c cdot<0 )
( mathrm{D} cdot<0 )
11
457Calculate the value of ( g ) on the surface
of planet if the planet has ( 1 / 500 ) the mass and ( 1 / 15 ) the radius of the Earth
в. ( 1.6 m / s_{2} )
( mathrm{c} cdot 2.4 mathrm{m} / mathrm{s}_{2} )
D. ( 4.5 m / s_{2} )
E ( .7 .1 mathrm{m} / mathrm{s}_{2} )
11
458In the Newton’s gravitational law, ( boldsymbol{F}= ) ( frac{G M m}{d^{2}}, ) the quantity ( G )
A. depends on the value of ( g ) at the place of observation
B. is used only when the earth is one of the two masses
c. is greatest at the surface of the earth
D. is universal constant in nature
11
459Mass of the earth has been determined
through
A ( cdot ) use of Kepler’s ( frac{T^{2}}{R^{3}} ) constancy law
B. sampling the density of earth’s crust and using earth’s radius.
C. Cavendish’s determination of G and using earth’s radius and ( g ) at its surface.
D. use of periods of satellites at different heights above earth’s surface.
11
460If ( g ) is the acceleration due to gravity on the earth’s surface, the gain of the potential energy of an object of mass ( boldsymbol{m} )
raised from the surface of the earth to a
height equal to the radius ( R ) of the earth
will be :
A. ( 2 m g R )
в. ( m g R )
c. ( frac{1}{2} m g R )
D. ( frac{1}{4} m g R )
11
461The value of acceleration due to gravity:
A. is same on equator and poles
B. is least on poles
( mathrm{c} ). is least on equator
D. increases from pole to equator
11
462Which of the following statements
corresponds to Kepler’s laws of planetary motion?
A. A planet moves around the sun in a circular orbit
B. A planet moves around the sun in an elliptical orbit with the sun at the geometrical centre
c. A planet moves around the sun in an elliptical orbit with the sun at the focus
D. A planet moves around the sun in an elliptical orbit with uniform speed
11
463A particle hanging from a massless
spring stretches it by ( 2 c m ) at the eath’s surface. How much will the same
particle stretch the spring at a height of ( 2624 K m ) from the surface of the earth?
(Radius of the earth ( =6400 K m) )
( A cdot 1 c m )
B. ( 2 c m )
( c .3 c m )
D. ( 4 c m )
11
464A satellite is launched into a circular
orbit of radius r around the earth. ( mathbf{A} )
second satellite is launched into an
orbit of radius ( 1.01 mathrm{r} ). The period of the second satellite is larger than that of
first one by approximately.
( A cdot 0.5 % )
B . 1.0 %
c. ( 1.5 % )
D. 3.0 %
11
465Value of ( g ) on the surface of earth is
( 9.8 m / s^{2} . ) Find acceleration due to gravity at depth ( h=frac{R}{2} ) from the
surface ( (boldsymbol{R}= ) radius of earth)
11
466Suppose gravitational force between two masses were to be given by ( boldsymbol{F}= ) ( k frac{sqrt{m_{1} m_{2}}}{d^{3}} ) where ( k ) is some constant
two equal masses attract each other with a certain force when the distance
is d. If each of the masses is doubled,
than what value the distance between
them must be maintained for the force
to remain the same as earlier?
A. ( sqrt{3 d} )
B. “3/3d
( c cdot sqrt{2 d} )
D. ( sqrt{2 d} )
11
467A (nonrotating) star collapses onto
itself from an initial radius ( mathrm{R}_{i} ) with its
mass remaining unchanged. Which
curve in figure best gives the
gravitational acceleration ( a_{g} ) on the
surface of the star as a function of the
radius of the star during the collapse?
4
B.
( c )
D.
11
468A lead sphere of mass ( 20 k g ) has the same diameter as an aluminium
sphere of mass ( 72 k g ). The spheres are simultaneously dropped from a tower.
When they are ( 10 m ) from the ground, they have identical (neglect air resistance):
A. kinetic energy
B. potential energy
c. momentum
D. acceleration
11
469The distance between the two point
masses ( boldsymbol{m}_{1} ) and ( boldsymbol{m}_{2} ) is d. Now, the
distance between them is reduced by two-thirds, Calculate by which factor
new gravitational force would be change?
A. It increases by a factor of 9
B. It increases by a factor of ( frac{4}{9} )
c. It increases by a factor of 3
D. It decreases by factor of 9
E. It decreases by a factor of 3
11
470A man in a balloon rising vertically with an acceleration of ( 4.9 m / s e c^{2} ) releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is ( (g= )
( mathbf{9 . 8 m} / boldsymbol{s e c}^{2} )
A ( .14 .7 m )
B. ( 19.6 m )
( mathrm{c} .9 .8 mathrm{m} )
D. ( 24.5 m )
11
471A particle of mass ( mathrm{M} ) is placed at origin
and a small mass ( mathrm{m} ) is placed at ( mathrm{A}, ) at a distance of ( r ) from M. A force F is applied
to ( m ) to make it move from ( A ) to a nearby point B. When the force becomes zero, it
is observed that the mass m moves
from B back to A. This is due to the
reason
A. Potential of B is larger than potential of A
B. objects starts moving in gravitational field until constant potential difference exist
c. The line B to A is equipotential surface
D. The mass moves from B to A, since A is nearer to origir
11
472If the radius of the earth is reduced by ( 1 % ) keeping the mass constant. The escape velocity will :
A. increase by ( 0.5 % )
B. decrease by ( 0.5 % )
c. decrease by ( 11 % )
D. remain same
11
473Two lead spheres of ( 20 mathrm{cm} ) and ( 2 mathrm{cm} ) diameter are placed with their centres 1.0 ( m ) apart. Calculate the force of
attraction between the two spheres. The
radius of the earth is ( 6.37 times 10^{6} m ), its
density is ( 5.51 times 10^{3} k g / m^{2} ) and
relative density of lead is 11.5
11
474A 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 –
A. ( mathrm{mg} ) २R
в. ( frac{2}{3} m g R )
c. ( 3 mathrm{mgR} )
D. ( frac{1}{3} m g R )
11
475Gravitational unit of force produce an acceleration in a body equal to
( A cdot g )
B. 0
c. ( 2 g )
D. unit value
9
476A spherical planet, far out in space, has
a mass ( M_{0} ) and diameter ( D_{0} . ) A particle of mass ( m ) falling freely near the surface of this planet will experience acceleration due to gravity which is
equal to:
A ( cdot frac{G M_{0}}{left(D_{0}right)^{2}} )
в. ( frac{4 m G M_{0}}{left(D_{0}right)^{2}} )
c. ( frac{4 G M_{0}}{left(D_{0}right)^{2}} )
D. ( frac{G m}{left(D_{0}right)^{2}} )
11
477A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sun is
A ( cdot frac{T pi}{2 e} )
B ( cdot Tleft(frac{2 e}{pi}-1right) )
c. ( frac{T e}{2 pi} )
D ( cdot Tleft(frac{1}{4}-frac{e}{2 pi}right) )
11
478The gravitational force acting on a
particle of ( 1 g ) due to a similar particle is
equal to ( 6.67 times 10^{-11} ). Calculate the
seperation between the particles.
11
479On doubling the distance between two masses the gravitational force between them will
A. Remain unchanged
B. Become one-fourth
c. Become half
D. Become double
11
480The gravitational force of attraction between two bodies at a certain
distance is ( 10 mathrm{N} ). If the distance
between them is doubled, the force of
attraction:
A. decreases by ( 50 % )
B. decreases by ( 75 % )
C. increases by ( 50 % )
D. increases by ( 75 % )
11
481What is the escape velocity from the
surface of the earth of radius ( R ) and
density ( rho ? )
( ^{text {A }} cdot 2 R sqrt{frac{2 pi rho G}{3}} )
в. ( 2 sqrt{frac{2 pi rho G}{3}} )
c. ( 2 pi sqrt{frac{R}{g}} )
D. ( sqrt{frac{2 pi G rho}{R^{2}}} )
11
482A satellite of mass ( m ) moves along
an elliptical path around the earth. The areal velocity of the satellite is proportional to
A . ( m )
B. ( m^{-1} )
( c cdot m^{0} )
( D cdot m^{frac{1}{2}} )
11
483Suppose a planet exists whose mass
and radius both are half that of the
earth The acceleration due to gravity on
the surface of this planet will be double
( ? )
11
484It is found that the speed of the earth around the sun increases when it is
close to the sun.
A. Angular velocity of the earth is constant.
B. Areal velocity of the earth is not constant.
c. Areal velocity of the earth is constant
D. None of these.
11
485A body of mass ( m ) falls from rest
through a height ( h ) under gravitation acceleration ( g ) and is then brought to rest by penetrating through a depth ( d ) into some sand. The average
deceleration of the body during penetration into sand is
A ( frac{g h^{2}}{d^{2}} )
в. ( frac{g h^{2}}{2 d^{2}} )
c. ( frac{g h}{d} )
D. ( frac{g d}{h} )
11
486The time period of a simple pendulum at the center of the earth is:
A . zero
B. infinite
c. less than zero
D. none of these
11
487When ( A ) is given its first impulse at the
moment:
( A . A, B ) and centre of earth are in same straight line
B. ( B ) is ahead of ( A ) angularly
( mathrm{c} . B ) is behide ( A ) angularly
D. None of these
11
488The force of attraction between two
bodies at a certain separation is ( 10 N )
What will be the force of attraction
between them if the separation between them is reduced to half?
( mathbf{A} cdot 2.5 N )
B. ( 5 N )
( c .20 N )
D. ( 40 N )
11
489f ( r_{2}=3 r_{1} ) and time period of revolution
for ( B ) be ( T ) than time taken by ( A ) in
moving from position 1 to position 2 is :
( ^{A} cdot frac{sqrt{3}}{sqrt{2}} )
3. ( T frac{sqrt{3}}{2} )
c. ( frac{T sqrt{2}}{3 sqrt{3}} )
D. ( frac{T sqrt{2}}{3} )
11
490The gravitational force between two bodies is decreased by ( 36 % ) when the distance between them is increased by
( 3 m . ) The initial distance between them
is:
A. ( 6 m )
в. ( 9 m )
( c .12 m )
D. ( 15 mathrm{m} )
11
491Orbital speed of an artificial satellite very close to earth’s surface is V. Its orbital speed at a height equal to three
times the radius of the earth from the
earth’s surface is:
( A cdot v )
B. v/2
( c cdot 2 v )
( D cdot v / 4 )
11
492If ( R ) is the radius of a planet, ( g ) is the acceleration due to gravity then find the mean density of the planet
A ( cdot frac{3 g}{4 G pi R} )
в. ( frac{3 g}{8 G pi R} )
c. ( frac{2 g}{4 G pi R} )
D. ( frac{6 g}{4 G pi R} )
9
493A sky laboratory of mass ( 2 times 10^{3} K g )
is raised from a circular orbit of radius
( 2 mathrm{R} ) to a circular orbit of radius ( 3 mathrm{R} ). The
work done is (approximately):
( mathbf{A} cdot 10^{16} J )
В. ( 2 times 10^{10} J )
( mathbf{c} cdot 10^{6} J )
D. ( 3 times 10^{10} J )
11
494How much the surface of earth does the
acceleration due to gravity reduce by ( 36 % ) of its value on the surface of earth?
Radius of earth ( =mathbf{6 4 0 0 k m} )
11
495If the weight of a body on the surface of the moon is ( 100 mathrm{N} ), what is its mass?
( left.=1.6 mathrm{ms}^{-2}right) )
( A cdot 160 mathrm{kg} )
B. 62.5 kg
( c cdot 6.25 mathrm{kg} )
D. 625 kg
9
496State the Kelper’s law which is
represented by the relation ( r^{3} propto T^{2} )
11
497When will multiple objects of different nature, shape, size etc fall from the
same height at the same rate?
A. In the presence of vaccum
B. on the poles
c. on the equator
D. None of the above
11
498Acceleration due to gravity – – depth from the surface of the earth.
A. Decreases
B. Increases
c. Remains constant
D. Data insufficient
11
499If value of acceleration due to gravity changes from one place to another, which of the following force will undergo a change?
A. Viscous force
B. Buoyant force
c. Magnetic force
D. All of the above
11
500Choose the correct statement.
A. All bodies repel each other in this universe
B. Our earth does not behave like a magnet
C . Acceleration due to gravity is ( 8.9 mathrm{m} / mathrm{s}^{2} )
D. All bodies have the same acceleration due to gravity at the surface of the earth
11
501A particle hanging from a spring
stretches it by ( 1 mathrm{cm} ) at earth’s surface.
Radius of earth is ( 6400 k m . ) At a place
( 800 k m ) above the earths surface, the same particle will stretch the spring by
A ( .0 .79 mathrm{cm} )
B. ( 1.2 mathrm{cm} )
( c .4 c m )
D. ( 17 mathrm{cm} )
11
502( mathbf{1} boldsymbol{g} boldsymbol{f}= )
A. 980 dyne
B. 98 dyne
c. 9.8 dyne
D. 0.98 dyne
9
503Derivation for weight pf an object on the surface of the moon.9
504A body is suspended from a spring balance kept in a satellite. The reading
of the balance is ( W_{1}, ) when the satellite
goes in an orbit of radius ( boldsymbol{R} ) and is ( boldsymbol{W}_{2} )
when it goes in an orbit of radius ( 2 R )
A. ( W_{1}=W_{2} )
в. ( W_{1}W_{2} )
D. ( W_{1} neq W_{2} )
11
505Every planet revolves around the sun in a/an orbit.
A. elliptical
B. circular
c. parabolic
D. none of these
11
506A spring balance whose maximum extension of its spring is ( 20 mathrm{cm} ) can
sustain a maximum load of ( 20 k g_{w t} )
within its elastic limit on the surface of
the earth. Now the same balance
is taken to the moon. Given that
gearth ( =6 g_{text {moon }}, ) what is the maximum
mass of the load that can be attached to
the balance to have half its maximum
extension?
A . 76
B. 65
c. 60
D. 55
11
507A mass ( M ) at rest is broken into two
pieces having masses ( m ) and ( (M-m) )
The two masses are then separated by a distance ( r . ) The gravitational force between them will be the maximum
when he ratio of the masses ( [boldsymbol{m}:(boldsymbol{M}- )
( boldsymbol{m}) ) of the two parts is
A . 1:
B. 1: 2
( c cdot 1: 3 )
D. 1: 4
11
508The ratio of the radii of planets ( A ) and ( B )
is ( K_{1} ) and ratio of accelerations due to
gravity on them is ( K_{2} ) The ratio of escape velocities from them will be:
A. ( K_{1} K_{2} )
B. ( sqrt{K_{1} K_{2}} )
c. ( sqrt{frac{K_{1}}{K_{2}}} )
D. ( sqrt{frac{K_{2}}{K_{1}}} )
11
509What is value of gravitational acceleration at the center of the earth?
( mathbf{A} cdot 9.8 m s^{2} )
B. zero
c. infinite
D. ( 6.67 times 10^{-11} mathrm{ms}^{-2} )
11
510The Orbit of a planet moving around the
sun
Refer image.
Observe the given figure showing the orbit of a planet moving around the Sun
and write the three laws related to it:
11
511The acceleration due to gravity
A. Has the same value everywhere in space
B. Has the same value everywhere on the earth
C. varies with the latitude on the earth
D. is greater on the moon due to its smaller diameter
11
512From the centre of the earth to the
surface of the earth, the relation between the value of ( g ) and distance ( (r) ) represented as a proportionality, is given by
A ( cdot g propto frac{1}{r^{2}} )
В . ( g propto r )
c. ( g propto r^{2} )
D ( cdot g propto r^{o} )
11
513If the acceleration due to gravity at the
surface of the earth is ( g ), the work done
in slowly lifting a body of mass ( m ) from
the earth’s surface to a height ( boldsymbol{R} ) equal to the radius of the earth is
( ^{mathrm{A}} cdot frac{m g R}{2} )
в. ( 2 m g R )
( mathrm{c} cdot m g R )
D. ( _{m g} frac{R}{4} )
11
514The Sl unit of G is.
A ( cdot N^{2} m^{2} / k g )
B. ( N m^{2} / k g )
c. ( N ) ml ( k g )
D. ( N m^{2} / k g^{2} )
11
515Gravitational force between two point
masses ( m ) and ( M ) separated by a
distance ( r ) is ( F ). now if a point mass ( 3 m )
is placed very next to ( mathrm{m} ), the total force
on ( boldsymbol{M} ) will be
A. ( F )
в. ( 2 F )
( c .3 F )
D. ( 4 F )
11
516The diameters of two plantes are in the ration 4: 1 and their density in the ration 1: 2 The acceleration due to gravity on
the planets will be in ratio,
A ( cdot 1: 2 )
B. 2:3
( c cdot 2: )
( D cdot 4: )
11
517The scientist who gave me three laws of planetary motion was
A. Newton
B. Kepler
c. Galileo
D. Robert Boyle
11
518A satellite close to the earth is in orbit
above the equator with a period of
revolution of 1.5 hours in the same
sense as that of the earth. If it is above a
point ( boldsymbol{P} ) on the equator at some time, it will be above ( P ) again after a time.
A. 1.5 hours
B. 1.6 hours if it is rotating from west to east
c. ( frac{24}{27} ) hours if it is rotating from west to east
D. none of these
11
519A string tied on a roof can bear a maximum tension of 50kgwt. The
minimum acceleration that can be
acquired by a man of ( 98 k g ) to descend
will be (Take ( boldsymbol{g}=mathbf{9 . 8 m} / boldsymbol{s}^{2} ) )
A ( cdot 9.8 m / s^{2} )
в. ( 4.9 m / s^{2} )
c. ( 4.8 m / s^{2} )
D. ( 5 m / s^{2} )
11
520Two bodies of masses ( 2 k g & 1.8 k g ) are
separated by ( 20 m )
The force between them becomes 4
times at a distance of :
A . ( 5 m )
B. ( 10 m )
( c .20 m )
D. None of them
11
521A man weight ( W ) on the surface of the
earth and his weight at a height ( boldsymbol{R} ) from
surface of the earth is ( (R ) is radius of
the earth)
A ( cdot frac{W}{4} )
в. ( frac{W}{2} )
c. ( W )
D. ( 4 W )
11
522If an orbiting satellite comes to a
standstill suddenly,
A. the satellite will move along the tangent.
B. the satellite will move radically towards centre of the orbit
C. the satellite will go to outer space and will be lost.
D. the satellite will continue to move in the same orbit.
9
523The gravitational potential difference between the surface of a planet and a point ( 20 m ) above it is ( 16 J / k g . ) Then the
work done in moving a 2 kg mass by
( 8 m ) on a slope 60 degree from the
horizontal, is:
A . ( 11.1 mathrm{J} )
B. ( 5.5 J )
( c .16 J )
D. 27.7 J
11
524State whether the given statement is True or False:

Acceleration due to gravity, ( boldsymbol{g}=frac{G M}{R^{2}} )
where symbols have their usual meanings.
A. True
B. False

11
525A balloon filled with hydrogen gas is
carried from earth to moon. Then the
balloon will:
A. neither fall nor rise
B. fall with acceleration less than ( g )
c. fall with acceleration g
D. rise with acceleration g
11
526A man weighs ( 600 N ) on earth. What
would be his approximate weight on
moon?
A . ( 100 N )
B. ( 200 N )
( c .50 N )
D. ( 600 N )
9
527The escape velocity of a body depends upon its mass as
( mathbf{A} cdot m^{0} )
B . ( m^{text {। }} )
( mathrm{c} cdot m^{3} )
D. ( m^{2} )
11
528The force acting on a mass of ( 1 g ) due to the gravitational pull on the earth is called 1 gw ( t . ) One ( g w t ) equals
A. ( 1 N )
в. ( 9.8 N )
c. 980 dyne
D. None of these
11
529As a planet moves around the sun it
sweeps equal areas in equal intervals of time.
A. True
B. False
11
530Two identical spherical masses are kept at some distance. Potential energy when a mass ( m ) is taken from the
surface of one sphere to the other
A. increases continuously
B. decreases continuously
c. first increases, then decreases
D. first decreases, then increases
11
531A rain drop starts falling from a height of ( 2 k m . ) It falls with a continuously decreasing acceleration and attains its terminal
velocity at a height of ( 1 k m . ) The ratio of
the work done by the gravitational force in the first half to the that in the second
half to the drops journey is
A. 1: 1 and the time of fall of the drop in the two halves is ( a: 1 text { (where } a>1) )
B. 1: 1 and the time of fall of the drop in the two halves is
( a: 1 text { (where } a1 ) ) and the time of fall of the drop in
the two halves is 1: 1
D. ( a: 1 ) (where ( a<1 ) ) and the time of fall of the drop in the two halves is 1: 1
11
532The evidence to show that there must
be force acting on Earth and directed
towards the Sun is.
A. phenomenon of day and night
B. apparent motion of the Sun around the Earth
c. revolution of Earth around the sun
D. deviation of the falling bodies towards east
11
533The force of gravity cannot act at a distance.
A . True
B. False
11
534State whether the given statement is True or False:
The equation ( F=frac{G M_{1} M_{2}}{r^{2}} ) is valid for all bodies.
A. True
B. False
11
535The height above the surface of earth at which acceleration due to gravity is half the acceleration due to gravity at
surface of earth is ( left(R=6.4 times 10^{6} mright) )
A ( cdot 6.4 times 10^{6} m )
В. ( 2.6 times 10^{6} mathrm{m} )
c. ( 12.8 times 10^{6} m )
D. ( 19.2 times 10^{6} mathrm{m} )
11
536A small satellite revolves around a
planet in an orbit just above planet’s surface. Taking the mean density of the planet ( 8000 mathrm{kg} m^{-3} ) and ( G=6.67 times )
( 10^{-11} mathrm{N} m^{-2} / k g^{-2}, ) find the time period
of the satellite.
11
537At a given place where acceleration due
to gravity is ( g m / s e c^{2}, ) a sphere of lead
of density ( d k g / m^{3} ) is gently released in
a column of liquid of density ( rho k g / m^{3} . ). ( boldsymbol{d}>boldsymbol{rho}, ) then immediately after the
sphere is released inside the liquid,
¡t will:
A . fall vertically with an acceleration of ( g ) m/ sec( ^{2} )
B. fall vertically with no acceleration
c. fall vertically with an acceleration ( gleft(frac{d-rho}{d}right) )
D. fall vertically with an acceleration ( (g rho) / d )
11
538The value of acceleration due to gravity
near the earth’s surface is
A ( cdot 8.9 m / s^{2} )
в. ( 7.9 m / s^{2} )
( mathrm{c} cdot 9.8 mathrm{m} / mathrm{s}^{2} )
D. ( 19.8 m / s^{2} )
11
539A straight tunnel is dug into the earth
as shown in figure at a distance ( b ) from
its center. A ball of mass ( m ) is dropped
from one of its ends. Find the time it
takes to reach the other end is
approximately.
11
540The value of acceleration due to gravity as we move from equator to
pole
A . increases
B. decreases
c. remains same
D. becomes zero
11
541The masses of sun and earth are ( M_{s} )
and ( M_{e}, ) respectively and the distance
between them is ( R_{e s} ) then, the distance
of a body of mass ( mathrm{m} ), from the earth
along the line towards the sun, where the sun’s gravitational pull balances that of the earth is
A ( cdot frac{R_{e s}}{sqrt{M_{s} / M_{e}}+1} )
В. ( frac{R_{e s}}{sqrt{M_{e} / M_{s}}+1} )
c. ( frac{R_{e s}}{sqrt{M_{s} / M_{e}}-1} )
D. ( frac{R_{e s}}{1-sqrt{M_{e} / M_{s}}} )
11
542Gravitational potential energy is
A. the product of force and velocity
B. the product of force and momentum
C. the product of weight and height lifted by an object
D. the product of force and displacement, if the particle is moving in a cirlce
11
543In case of a planet revolving around the sun, the angle between the gravitational force and the radial vector is
A. zero
B. 90
c. 180
D. 45
11
544At what height above the earth’s
surface, the value of ( g ) is same as that
at a depth of ( 100 k m ? )
Hint: Take ( g_{h}=g_{d} )
11
545A small body starts falling onto the Sun
from a distance equal to the radius of
the Earth’s orbit. The initial velocity of the body is equal to zero in the heliocentric reference frame.
Making use of Kepler’s laws, how long the body will be falling in days
A . 64.5
B. 65
c. 60
D. None of these
11
546When the radius of earth is reduced by
( 1 % ) with out changing the mass, then the acceleration due to gravity will
A. increase by ( 2 % )
B. decrease by 1.5%
C. increase by ( 1 % )
D. decrease by 1%
11
547At a point very near earth’s surface, the acceleration due to gravity is g. What will be the acceleration due to gravity at the same point if the earth suddenly shrinks to half its radius without any
change in its mass?
( A cdot 28 )
B. 48
c. ( g )
D. 3
11
548A feather of mass ( m ) and a hammer of
mass ( 100 m ) are both released from rest
from the same height on the surface of the moon. Mass of moon is ( M ) and
radius of moon is ( R ). Both feather and
hammer are released simultaneously. What is the acceleration of the
hammer?
A ( cdot frac{m v^{2}}{r} )
в. ( frac{G M}{R^{2}} )
c. ( frac{G M m}{R^{2}} )
D. ( _{100} frac{G M}{R^{2}} )
E ( cdot_{100} frac{G M m}{R^{2}} )
11
549An astronaut,inside an earth’s satellite
experiences weightlessness because
A. he is falling freely
c. no reaction is exerted by the floor of the satellite
D. he is far away from the earth’s surface
11
550What is the range of gravitational force.
( ? )
( A cdot 10^{-2} m )
B . ( 10^{-15} mathrm{m} )
c. infinite
D. ( 10^{-10} mathrm{m} )
9
551The largest and the shortest distance of
the earth from the sun is ( r_{1} ) and ( r_{2} ). Its
distance from the sun when it is at
perpendicular to the major axis of the orbit drawn from the sun:
( mathbf{A} cdotleft(r_{1}+r_{2}right) / 4 )
B . ( left(r_{1}+r_{2}right) /left(r_{1}-r_{2}right) )
( mathbf{c} cdot 2 r_{1} r_{2} /left(r_{1}+r_{2}right) )
D. ( left(r_{1}+r_{2}right) / 3 )
11
552Time period depends on Gravitational constant (G),plank constant, (h) and speed of light (c), then ( mathrm{T} ) is proportional
to
( ^{mathrm{A}} cdot frac{G^{1 / 2} h^{1 / 2}}{C^{3 / 2}} )
B. ( frac{G^{1 / 2} h}{C^{5 / 2}} )
( ^{mathrm{C}} cdot frac{G h^{1 / 2}}{C^{5 / 2}} )
( ^{mathrm{D} cdot frac{G^{1 / 2} h^{1 / 2}}{C^{5 / 2}}} )
11
553If a new planet is discovered rotating around sun with the orbital radius
double that of the earth, then what will
be its time period? (in earth’s days)
A . 1032
B. 1023
( c cdot 1024 )
D. 1043
11
554A body of mass ( m ) is taken from earth’s surface to q a height equal to radius of earth. the change in potential will be
A . ( m g )
B. ( frac{1}{2} m g R )
c. ( 2 m g R )
D. ( frac{1}{4} m g R )
11
555A satellite is projected with a speed ( sqrt{frac{5}{6}} )
times of its escape speed from the earth’s surface. The initial speed of the
satellite is parallel to the surface of the earth. The maximum distance of the
satellite from the center of the earth will
be
A. ( 3 R )
в. ( 6 R )
( c .5 R )
D. None of these
11
556If two balls of some mass are dropped from the same height, would they fall down at the same time?11
557If the attractive force between two
bodies of mass ( M_{1} ) and ( M_{2} ) and
situated at a distance ( mathrm{R} ) is ( mathrm{F} ), then find
the force ( F^{prime} ) between them at distance
( (R+d) ) in terms of ( F )
11
558The Sl unit of the universal gravitational
constant ( G: )
( mathbf{A} cdot N m K g^{-2} )
B. ( N m^{2} K g^{-2} )
c. ( N m^{2} K g^{-1} )
D. ( N m K g^{-1} )
11
559Two blocks, one of iron(i) and the other
of wood(w) are dropped from a height at the same time. If the time taken by the
blocks to reach the ground is ( T_{i} ) and ( T_{w} ) respectively, then find the relation
between them?
A ( . T_{i}T_{w} )
D. ( T_{i}=frac{1}{2 T_{w}} )
11
560The earth and the moon are attracted to
each other by gravitational force.Does
the earth attract the moon with a force
the moon attracts the earth? Why?
9
561Kepler’s first law provides information about
A. areal velocity of a planet
B. Shape of the orbit of the planettet
c. Mass of the planet
D. Distance of the planet from the sun
11
562A small planet is revolving around a very massive star in a circular orbit of
radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to ( R^{-5 / 2}, ) then ( T ) would be proportional to
A ( cdot R^{3 / 2} )
B. ( R^{3 / 5} )
c. ( R^{7 / 2} )
D. ( R^{7 / 4} )
11
563If the distance of earth from the sun
reduces to one fourth of its present
value then the length of the year will become
A . ( 1 / 6 ) of present year
B. 1/8 of present year
c. ( 1 / 4 ) of present year
D. ( 1 / 2 ) of present year
11
564The weakest forces of interaction
among all classified forces are
A. electrostatic forces
B. gravitational forces
c. weak nuclear forces
D. electromagnetic forces
9
565If the change in the value of ( g ) at height
( h ) above earth surface is the same as
that at depth ( xleft(x quad text { or } quad h<R_{e}right), ) then
A ( cdot x=h^{2} )
в. ( x=h )
c. ( _{x}=frac{h}{2} )
D. ( x=2 h )
11
566Assume that life has existed on the
surface of the moon, without changing its present acceleration due to gravity
i.e., one sixth that on the surface of the
moon. If 5 kg weight of sugar is purchased on the Earth and the Moon,
how many cups of tea can be made out
of it on the Earth and the Moon
respectively? Note, From 100 g of sugar 10 cups of tea can be mode on the earth. ( left(g=10 mathrm{m} mathrm{s}^{-2}right) )
9
567The gravitational potential energy is the
A. work done in bringing an object from infinity to radius
( r )
B. work done in moving an object around the earth
C. work done by an object in attaining an object’s acceleration equal to ( 9.8 m / s^{2} )
D. work done in moving an object between two points horizontally
11
568A person sitting in a chair in a satellite
feels weightless because
A. the earth does not attract the object in a satellite.
B. the normal force by the chair on the parson balance the earht’s attraction.
C. the normal force is zero.
D. the person is satellite is not accelerated.
11
569The mass of the moon is ( frac{1}{81} ) of the earth
but the gravitational pull is ( frac{1}{6} ) of the
earth. It is due to the fact that
A the radius of earth is ( frac{9}{sqrt{6}} ) of the moon
B. The radius of moon is ( frac{81}{6} ) of the eartt
c. Moon is the satellite of the earth
D. None of the above
11
570Assertion
If infinity is taken as reference, the
gravitational potential is negative everywhere on the surface of earth.
Reason

Every body on its surface is bound to
gravitational attraction of earth.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

11
571At the centre of the earth, the value of ( g )
becomes
A . zero
B. unity
c. infinity
D. none of these
11
572Where will it be profitable to purchase one kilogram sugar?
A. At poles
B. At equator
C . At ( 45^{circ} ) latitude
D. At ( 40^{circ} ) latitude
11
573If the gravitational force of earth suddenly disappears, then which of the following is correct?
A. weight of the body is zero
B. mass of the body is zero
c. both mass and weight become zero
D. neither the weight nor the mass is zero
11
574The value of acceleration due to gravity at height ( h ) from earth surface will
become half its value on the surface if
( (R=text { radius of earth }) )
( mathbf{A} cdot h=R )
в. ( h=2 R )
c. ( h=(sqrt{2}-1) R )
D. ( h=(sqrt{2}+1) R )
11
575A mass ( M ) is split into two parts ( m ) and
( (M-m), ) which are, then separated by
a certain distance. The ratio ( boldsymbol{m} / boldsymbol{M} ) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1
11
576Assertion
A balloon filled with hydrogen will fall with acceleration ( frac{boldsymbol{g}}{boldsymbol{6}} ) on the moon.
Reason
Moon has no atmosphere.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
9
577A capillary tube is immersed vertically
in water and the height of the water
column is ( x ). When this arrangement is
taken into a mine of depth ( d ), the height
of the water column is ( y . ) If ( R ) is the radius of the earth, the ratio ( frac{x}{y} ) is :
A ( cdotleft(1-frac{d}{R}right) )
B ( cdotleft(1-frac{2 d}{R}right) )
c. ( left(frac{R-d}{R+d}right) )
D. ( left(frac{R+d}{R-d}right) )
11
578How much faster than its normal rate
should the earth rotate about its axis so
that the weight of the body at the equator becomes zero? (Radius of the
earth ( =6.4 times 10^{6} m ) and ( g=9.8 m / s^{2} )
A. Nearly 17 times
B. Nearly 12 times
c. Nearly 10 times
D. Nearly 14 times
11
579Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of ( 200 mathrm{Km} ), the height of the other satellite is (Radius of the earth is ( R=6400 mathrm{Km} )
A. ( 8450 K m )
в. 845 Кт
c. ( 84.5 K m )
D. ( 84500 K m )
11
580A planet has twice the mass of earth
and of identical size. What will be the
height above the surface of the planet where its acceleration due to gravity
reduces by ( 36 % ) of its value on its surface?
11
581A satellite of mass ( 1000 k g ) is supposed
to orbit the earth at a height of ( 2000 k m ) above the earth’s surface. Find its speed
in the orbit.
11
582The diameters of two planets are in ratio ( 4: 1 . ) Their mean densities have
ratio ( 1: 2 . ) The ratio of ‘g’ on the planets
will be:
A .1: 2
B. 1: 4
c. 2: 1
D. 4: 1
11
583Two particles of masses ( 1.0 mathrm{kg} ) and ( 2.0 mathrm{kg} ) are placed at a separation of
( 50 mathrm{cm} . ) Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles.
11
584If the area swept by the line joining the sun and the earth from Feb 1 to Feb 7 is
A, then the area swept by the radius vector from Feb 8 to Feb 28 is
( A cdot A )
B. 2A
( c cdot 3 A )
D. ( 4 A )
11
585Supposing the earth suddenly contracts to half of its radius, what will be the
length of the day?
A. 12 hours
B. 8 hours
c. 6 hours
D. No change
11
586The value of G does not depend on
A. nature of the interacting bodies
B. size of the interacting bodies
c. mass of the interacting bodies
D. all the above
11
587A simple pendulum is taken to ( 64 K m ) above the earth’s surface. It’s time
period will :
A. increase by ( 1 % )
B. decrease by 1%
c. increase by 2%
D. decrease by 2%
11
588If suddenly the gravitational force of attraction between earth and satellite
revolving around it becomes zero, then the satellite will
A. continue to move in its orbit with same velocity
B. Move tangential to the original orbit with the same velocity
c. Becomes sationary in its orbit
D. Move towards the earth
9
589Two point masses each equal to ( 1 k g ) attract one another with a force of
( 10^{-9} k g w t . ) Find the distance between
the two point masses. Take: ( g= )
( 9.8 m / s^{2} )
( A cdot 8 c m )
B. ( 0.8 mathrm{cm} )
c. ( 80 mathrm{cm} )
D. ( 0.08 mathrm{cm} )
11
590Six particles each of mass ( m ) are placed
at the corners of a regular hexagon of
edge length ( a ). If a point mass ( m_{0} ) is
placed at the centre of the hexagon, then the net gravitational force on the
point mass ( boldsymbol{m}_{0} ) is :
A ( cdot frac{6 G m^{2}}{a^{2}} )
в. ( frac{6 G m m_{0}}{a^{2}} )
c. zero
D. none of these
11
591The gravitational force is a
A. contact force
B. action at a distance force
C. non contact force
D. both (B) and (C)
9
592Gravitational force between two bodies
is 1 newton.If the distance between them
twice, what will be the force?
11
593is the force of attraction
between any two bodies in the universe.
A. Gravitation
B. Polarityyy
c. Induction
D. Joule
9
594If ( R=r ) adius of the earth and ( g= ) acceleration due to gravity on the
surface of the earth, the acceleration
due to gravity at a distance (r>R) from the centre of the earth is proportional to
( A )
в. ( r^{2} )
( c cdot r^{-2} )
D. ( r^{-1} )
11
595Let ( V ) and ( E ) denote the gravitational
potential and gravitational field at a point. It is possible to have
A ( . V=0 ) and ( E=0 )
B. ( V=0 ) and ( E neq 0 )
c. ( V neq 0 ) and ( E=0 )
D. All of the above
11
596Statement 1: Geostationary satellites may be setup in equatorial plane in orbits of any radius more than earth’s

Statement 2: Geostationary satellites have period of revolution of 24 hrs.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True

11
597gravity ( g ) with distance ( d ) trom centre of
the earth is best represented by ( (boldsymbol{R}= )
( A )
( B )
( c )
( D )
11
598If ( ^{prime} R^{prime} ) is the radius of the earth, then the
height at which the weight of a body becomes ( frac{1}{4} ) of its weight on the surface of the earth is:
A ( .2 . R )
в. ( R )
c. ( frac{3 R}{8} )
D. ( frac{R}{4} )
11
599Newton’s law of gravitation holds good
for
A. only small bodies
B. only terrestrial bodies
c. only big bodies
D. all types of bodies
11
600The acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth,
is ( times 10^{-1} ) times the acceleration due to gravity on the surface of the earth.
A. 5
B. 3
( c cdot 0.5 )
D. 50
11
601If we assume only gravitational attraction between proton and electron in hydrogen atom and Bohr’s quantization rule to be followed, then the expression for the ground state energy of the atom will be the mass of proton is ( mathrm{M} ) and that of the electron is
( m): )
( ^{mathrm{A}} cdot frac{G^{2} M^{2} m^{2}}{h^{2}} )
( ^{text {В }} cdot frac{2 pi^{2} G^{2} M^{2} m^{3}}{h^{2}} )
c. ( frac{2 pi^{2} G M^{2} m^{3}}{h^{2}} )
D. None of these
11
602A force which produces an acceleration in a body equal to acceleration due to
gravity on earth, when the body has a unit mass is called
A. Gravitational unit of force
B. Gravity force
( c . ) Both
D. None
9
603The distance between two planets of
masses ( mathrm{M} ) and ( 4 mathrm{M} ) is ‘a’ what is the
gravitational potential at a point on a line joining them of which the gravitational intensity is zero?
( mathbf{A} cdot-frac{9 G M}{r} )
B. ( -frac{5 G M}{a} )
( mathbf{c} cdot-frac{3 G M}{a} )
D. ( -frac{7 G M}{a} )
11
604The condition for a uniform spherical mass ( m ) of radius ( r ) to be a black hole is
( :[G=text { gravitational constant and } g= )
acceleration due to gravity].
( ^{mathrm{A}}left(frac{2 G m}{r}right)^{1 / 2} leq c )
( ^{mathrm{B}}left(frac{2 g m}{r}right)^{1 / 2}=c )
( left(frac{2 G m}{r}right)^{1 / 2} geq c )
( ^{mathrm{D}}left(frac{g m}{r}right)^{1 / 2} geq c )
11
605S.I. Unit of universal gravitational
constant ( G ) is-
( ^{mathbf{A}} cdot frac{N m^{2}}{K g} )
в. ( frac{N m^{2}}{K g^{2}} )
c. ( frac{N m}{K g^{2}} )
D. ( frac{N m}{K g} )
11
606The rotation of the Earth having radius
( R ) about its axis speeds upto a value
such that a man at latitude angle ( 60^{circ} )
feels weightless. The duration of the day in such case will be.
A ( cdot 8 pi sqrt{frac{R}{g}} )
в. ( 8 pi sqrt{frac{g}{R}} )
( ^{c} cdot pi sqrt{frac{R}{g}} )
D. ( 4 pi sqrt{frac{g}{R}} )
11
607A remote-sensing satellite of earth revolves in a circular orbit at a height of
( 0.25 times 10^{5} mathrm{m} ) above the surface of earth
If earth’s radius is ( 6.38 times 10^{6} mathrm{m} ) and
( boldsymbol{g}=mathbf{9 . 8} quad boldsymbol{m} boldsymbol{s}^{-2}, ) then the orbital speed
of the satellite is
A ( .6 .67 mathrm{Kms}^{1} )
B. ( 7.92 mathrm{Kms}^{1} )
c. ( 8.56 mathrm{Kms}^{1} )
D. ( 9.13 mathrm{Kms}^{1} )
11
608Two satellites ( A ) and ( B ) go round the planet ( boldsymbol{P} ) in circular orbits having radii ( 4 R ) and ( R ) respectively. If the speed of
the satellite ( A ) is ( 3 v, ) then the speed of
satellite ( boldsymbol{B} ) will be
A . ( 6 v )
в. ( 12 v )
c. ( frac{3 v}{2} )
D. ( frac{4 v}{3} )
11
609At what height in km over the earth’s pole the free fall acceleration decreases
by one percent? (Assume the radius of
the earth to be ( 6400 mathrm{km} ) )
A .32
B. 64
c. 80
D. 1.253
11
610In order to shift a body of mass ( mathrm{m} ) from a circular orbit of radius ( 3 R ) to a higher orbit of radius ( 5 R ) around the earth, the
work done is?
( ^{A} cdot frac{3 G M m}{5 R} )
в. ( frac{G M m}{2 R} )
c. ( frac{2}{15} frac{G M m}{R} )
D. ( frac{G M m}{5 R} )
11
611At what depth (in terms of the radius of earth) the acceleration due to gravity will be ( frac{2 g}{5} ? )11
612Mass of the earth is:
A ( cdot frac{4}{3} pi R^{3}(A-B R) )
B ( cdot 4 pi R^{3}(A-B R) )
( ^{mathbf{C}} cdot frac{4}{3} pi R^{3}left(A-frac{3}{4} B Rright) )
D ( cdot 4 pi R^{3}left(A-frac{3}{4} B Rright) )
11
613A stone is released from the top of a
tower of height ( 19.6 mathrm{m} ). Calculate its
final velocityjust before touching the ground.
11
614Let ‘gh’ and ‘g ( _{d} ) ‘ be the acceleration due
to gravity at height ‘h’ above the earth’s
surface and at depth ‘ ( d ) below the
earth’s surface respectively. IF ( boldsymbol{g}_{boldsymbol{h}}=boldsymbol{g}_{boldsymbol{d}} )
then the relation between ‘h’ and ‘ ( d ) is
( mathbf{A} cdot d=h )
B. ( d=frac{h}{2} )
( c cdot d=frac{h}{4} )
D. ( d=2 h )
11
615A person on the surface of the moon:
A. Does not feel the effect of earth’s gravity because the gravity due to moon is such stronger.
B. Does not feel the effect of earth’s gravity.
C. Does not feel the effect of earth’s gravity and moon gravity he is freely towards the earth.
D. Feels only the combined effect of earth’s and moon gravity which are comparable in magnet
9
616Two bodies, each of mass ( mathrm{M} ), are kept
fixed with a separation 2 L. A particle of mass ( m ) is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are).
A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is ( 4 sqrt{frac{G M}{L}} )
B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is ( 2 sqrt{frac{G M}{L}} )
C. The minimum initial velocity of the mass ( m ) to escape the gravitational field of the two bodies is ( sqrt{frac{2 G M}{L}} )
D. The energy of the mass m remains constant
11
617The unit of ( frac{G}{g} ) is:
A. kg/m
в. ( k g / m^{2} )
( mathbf{c} cdot m^{2} / k g )
D. m/kg
11
618Which of the following units can be
used to express G?
( A cdot N K g^{-2} )
B. ( mathrm{Nm}^{-2} mathrm{Kg}^{2} )
( mathrm{C} cdot mathrm{Nm}^{2} mathrm{Kg}^{-2} )
D. ( mathrm{Nm}^{-2} mathrm{Kg}^{-3} )
11
619If the earth shrinks to half of its radius
without changing its mass, the duration of the day will be
A. 48 hours
B. 24 hours
c. 12 hours
D. 6 hours
11
620A small body of super dense material, with mass equal to half of that of earth
but whose size is very small compared
to that of earth, starts from rest at the
height h<
( A cdot sqrt{frac{2 h}{q}} )
в. ( sqrt{frac{4 h}{3 g}} )
c. ( sqrt{frac{2 h}{3 g}} )
D. ( sqrt{frac{h}{g}} )
11
621Which of the following statements regarding the gravitational attraction between man and the earth are correct?
1. The man and the earth pull each other with the same force
2. The earth pulls the man with more
force than the man pulling the earth
3. The acceleration of the man due to
the earth’s pull is more than that of the
earth due to the man’s pull
4. The accelerations of the man and the
earth are the same
( A cdot 2 ) and 3
B. 1 and 4
c. 1 and 3
D. 2 and 4
11
622If the acceleration due to gravity, ( g ), is ( 10 m / s^{2} ) at the surface of the earth
(radius ( 6400 k m ) ), then at a height of
1600 km the value of ( g ) will be? ( operatorname{lin} m / s^{2} )
A . 4
B. 5
( c .7 .5 )
D. 2.5
11
623The time period of a second’s pendulum inside a satellite will be
A . zero
B. ( 1 mathrm{sec} )
( c cdot 2 sec )
D. infinite
11
624No part of india is situated on the
equator .Is it possible to have a
geostationary satellite which always
remains over New Delhi?
11
625Assertion
An astronaut experience weightlessness in a space satellite
Reason

When a body falls freely it does not experience gravity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

11
626A satellite of mass ( m ) is orbiting around the earth at a height ( h ) above the
surface of the earth. Mass of the earth is
( M ) and its radius is ( R ). The angular
momentum of the satellite is
independent of :
A .
в. ( M )
( c cdot h )
D. None of these
11
627An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown
in the figure. The water which comes out from the hole at the instant when
hole is at height H above the ground, strikes the ground at a distance of ( x ) from P.
11
628A mass ( mathrm{M} ) is lowered with the help of a string by a distancex at a constant
acceleration ( frac{mathrm{g}}{2} . ) The magnitude of work doneby the string will be:
( ^{mathbf{A}} cdot frac{M g}{2} k )
B – ( frac{1}{2} M g x^{2} )
( mathbf{c} cdot frac{1}{2} M g x )
D. ( M g x^{2} )
11
629An ice cube of size ( a=10 mathrm{cm} ) is
floating in a tank (base ( =50 mathrm{cm} times )
50cm ) partially filled with water. The
change in gravitational potential energy, when ice completely melts is [Density of ice is ( 900 k g m^{-3} ) and ( g=10 m s^{-2} )
A. ( -0.0455 J )
в. ( -0.016 J )
c. ( -0.24 J )
D. ( -0.072 J )
11
630Suppose a new planet is discovered between Uranus and Neptune. Its time period would be
A. less than that of Neptune.
B. more than that of Neptune.
c. equal to that of Neptune or Uranus.
D. less than that of Uranus
11
631The weight of an object at the centre of
the earth of radius ( R ) is
A. Zero
B. Infinite
C . ( R ) times the weight at the surface of the earth.
D. ( 1 / R^{2} ) times the weight at surface of the earth.
11
632The acceleration of free fall for object moving near the surface of Earth is:
A ( cdot 9.81 m s^{-2} )
B. ( 9.31 m s^{-2} )
c. ( 8.81 m s^{-2} )
D. ( 10.81 m s^{-2} )
11
633Two block of mass ( m_{1} ) and ( m_{2} ) are kept
a part d from each other. What happen to
the magnitude of the force on ( m_{1} ) if the
mass of ( m_{2} ) is doubled?
B. It is doubleo
c. It remain the same
D. It is halved
E. It is quartered
11
634Compare the acceleration due to gravity on the surface of a planet, whose mass
and diameter are double that of the
earth, with the acceleration due to
gravity on the surface of the earth.
A . 1: 2
B . 2: 1
c. 3: 4
D. 4: 1
11
635If we consider the gravitational force ( F )
between two objects of masses ( m_{1} ) and
( m_{2} ) respectively, separated by a distance ( R, ) and we double the distance
between them, what is the new magnitude of the gravitational force between them?
( A cdot F / 4 )
B. F/2
( c cdot F )
D. 2F
E. 4
11
636Acceleration due to gravity of a body
during free fall does not depend upon
the:
A. mass of earth
B. mass of body
c. universal gravitational constant
11
637Taking the gravitational potential at a
point infinte distance away as zero, the gravitational potential at a point ( boldsymbol{A} ) is
-5 unit. If the gravitational potential at a point infinite distance away is taken as +10 units, the potential at a point ( A )
is
A. – 5 unit
B . +5 unit
c. +10 unit
D. +15 unit
11
638A planet is moving in an elliptical path around the sun as shown in
figure.Speed of planet in position ( P ) and
( mathrm{Q} ) are ( boldsymbol{v}_{1} ) and ( boldsymbol{v}_{2} ) respectively with ( boldsymbol{S} boldsymbol{P}= )
( r_{1} ) and ( S Q=r_{2} ) then ( v_{1} / v_{2} ) is equal to
then
A ( cdot frac{r_{1}}{r_{2}} )
в. ( frac{r_{2}}{r_{1}} )
c. consonant
D.
11
639A 10 kg satellite completes one revolution around the earth at a height of ( 100 mathrm{km} ) in 108 minutes. The work
done by the gravitational force of earth will be?
A . ( 108 times 100 times 10 ) J
в. ( frac{108 times 10}{100} )
c. 0 J
D. ( frac{100 times 10}{108} )
11
640Fill up the blank with suitable words. Value of universal gravitational
constant ( G= )
11
orbiting some star. The planet is closer to the star as it moves from point 1 to
point 2 than it is when it moves from
point 3 to point 4 in its orbit. The dotted
ine shows the orbital path.
If the time it takes the planet to get from point 1 to point 2 is equal to the time it takes the planet to get from point 3 to point 4 then which of the following statements is true, according to Kepler’s laws of planetary motion?
A. The average speed as the planet travels from 1 to 2 is the same as when it travels from 3 to 4
B. Area 1 in the diagram is equal to Area 2
C. Area 1 in the diagram is smaller than Area 2
D. The planet moves further from 3 to 4 from 1 to 2
E. The average speed as the planet moves from 3 to 4 is greater than when the planet moves from 1 to
11
642Take the mean distance of the moon
and the sun from the earth to be ( 0.4 times )
( 10^{6} k m ) and ( 150 times 10^{6} k m ) respectively.
Their masses are ( 8 times 10^{22} k g ) and ( 2 times )
( 10^{30} k g ) respectively. The radius of the
earth is ( 6400 mathrm{km} ). Let ( Delta F_{1} ) be the difference in the forces exerted by the
moon at the nearest and farthest points
on the earth and ( Delta F_{2} ) be the difference
in the force exerted by the sun at the nearest and farthest points o the earth. Then, the number closest to ( frac{Delta F_{1}}{Delta F_{2}} ) is :
A .2
B. ( 10^{-2} )
( c .0 .6 )
D.
11
643ENERGY OF AN ORBITING SATELLITE
A comet orbits the sun in a highly elliptical orbit. Which of the following quantities remains constant throughout its orbit?
(i) Linear speed
(ii) Angular speed (iii) Angular momentum (iv) Kinetic energy
(v) Potential energy (vi)Total energy
( A cdot(i),(text { ii) },( text { iii) } )
B. (iii), (iv), (v)
c. (iii) and (vi)
D. (ii), (iii) and (vi)
11
644A high jumper can jump ( 2.0 mathrm{m} ) on earth,
With the same effort how high will he be
able to jump on a planet whose density is one-third and radius one-fourth those
of the earth?
( A cdot 4 m )
B. 8 m
( c cdot 18 m )
D. 24 m
11
645If the acceleration due to gravity g at the earth’s surface is ( 9.8 m s^{-2} ) and
mass of the earth is 80 times that of
moon, radius of earth 4 times that of
the moon, the value of ( g ) at the moon’s surface will be approximately equal to?
( mathbf{A} cdot 4 m s^{-2} )
В. ( 1.96 m s^{-2} )
( mathrm{c} cdot 27 mathrm{ms}^{-2} )
D. ( 16 m s^{-2} )
11
646A remote – sensing satellite of earth revolves in a circular orbit at a height of
( 0.25 times 10^{6} mathrm{m} ) above the surface of earth
If earth’s radius is ( 6.38 times 10^{6} m ) and
( g=9.8 m s^{-2}, ) then the orbital speed of
the satellite is:
( mathbf{A} cdot 6.67 k m s^{-1} )
B . ( 7.76 mathrm{km} mathrm{s}^{-1} )
c. ( 8.56 k m s^{-1} )
D. ( 9.13 mathrm{km} mathrm{s}^{-1} )
11
647An artificial satellite moving in a
circular orbit around the earth has a
total (kinetic ( + ) potential ) energy ( frac{boldsymbol{E}_{0}}{boldsymbol{4}} )
Its potential energy is
A ( cdot frac{E_{0}}{4} )
в. ( frac{E_{0}}{2} )
c. ( frac{E_{0}}{8} )
D. ( E_{0} )
11
648Two spherical bodies of mass ( mathrm{M} ) and ( 5 mathrm{M} ) and radii R and ( 2 mathrm{R} ) respectively are released in free space with initial
separation between their centres equal to 12R. If they attract each other due to gravitational force only. then the
distance covered by the smaller body just before collision is
A . 1.5 R
в. 2.5
c. 4.5 R
D. 7.5R
11
649The height at which the acceleration due to gravity becomes ( g / 9 ) (where ( g= ) the acceleration due to gravity on the
surface of the earth) in terms of ( R ), the
A. ( R / 2 )
в. ( sqrt{2} R )
( c .2 R )
D. ( frac{R}{sqrt{2}} )
11
650For a satellite to be geostationary, which of the following are essential conditions?
This question has multiple correct options
A. It mu always be stationed above the equator.
B. It must rotate from west to east
c. It must be about ( 36,000 mathrm{km} ) above the earth.
D. Its orbit must be circular, and not elliptical
11
651Two projectiles, one fired from the surface of the earth with speed ( 5 m / s ) and the other fired from the surface of a
planet with initial speed ( 3 m / s, ) trace identical trajectories. Neglecting friction effect the value of acceleration
due to gravity on the planet is:
A. ( 5.9 mathrm{m} / mathrm{s}^{2} )
в. ( 3.5 mathrm{m} / mathrm{s}^{2} )
( mathbf{c} cdot 16.3 mathrm{m} / mathrm{s}^{2} )
D. ( 8.5 mathrm{m} / mathrm{s}^{2} )
11
652Assume that the earth moves around
the sun in a circular orbit of radius ( mathrm{R} )
and there exists a planet which also
moves around the sun in circular orbit
with an angular speed twice as large as
that of the earth. The radius of the orbit
of the planet is
A ( cdot frac{-2}{3} R )
B. ( frac{2}{3} R )
c. ( frac{-1}{3} R )
D. ( frac{R}{sqrt{2}} )
11
653A mass ( M ) is split into two parts ( m ) and ( (M-m), ) which are then separated by
a certain distance. What ratio ( (boldsymbol{m} / boldsymbol{M}) )
maximizes the gravitational force
between the parts.
11
654The distance between earth and moon
is about ( 3.8 times 10^{5} mathrm{km} . ) At what points
will the net gravitational force of earthmoon system be zero? [Given the mass
of the earth is 81 times the moon’s
mass]. (Hint: Assume a body of unit
mass at the null point)
11
655Assertion
It takes more fuel for a spacecraft to
travel from the earth to the Moon than
for the return trip.
Reason
The point of zero gravitational field
intensity due to the earth and the Moon
is Iying nearer to the Moon, i.e., in the
diagram shown, for ( r )
( r_{0}, E_{g} ) is towards the Moon’s centre, and
( operatorname{at} r=r_{0}, E_{g} ) is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct
11
656A ball of mass ( m ) is fired vertically upwards from the surface of the earth
with velocity ( n nu_{e}, ) where ( nu_{e} ) is the
escape velocity and ( n>1 . ) To what height will the ball rise? Neglecting air resistance, take radius of the earth as
( boldsymbol{R} )
A ( cdot frac{R}{n^{2}} )
в. ( frac{R}{left(1-n^{2}right)} )
c. ( frac{R n^{2}}{left(1-n^{2}right)} )
D. ( R n^{2} )
11
657Consider two satellites ( A ) and ( B ) of equal
mass ( mathrm{m}, ) moving in the same circular
orbit about the earth, but in the
opposite sense as shown in Figure. The orbital radius is ( r ). The satellites
undergo a collision which is perfectly
inelastic. For this situation, mark out
the correct statement(s). [Take mass of
earth as ( mathrm{M}] )
(6)
A. The satellites starts falling towards center of the earth.
B. The total energy of the two satellites plus earth system just after collision is ( -2(G M m) / r )
C. The total energy of two satellites plus earth system just after collision is ( -(G M m) / 2 r )
D. The combined mass(two satellites) will fall towards the earth just after collision.
11
658A particle falling under gravity
describes ( 80 f t ) in a certain sec. How
long does it take to describe next ( 112 f t )
( ?left[boldsymbol{g}=boldsymbol{3} 2 boldsymbol{f} boldsymbol{t} boldsymbol{s}^{-2}right] )
( mathbf{A} cdot 1 s )
B . ( 2 s )
c. ( 3 s )
D. ( 4 s )
11
659Assertion
The smaller the orbit of a planet around
the Sun, the shorter is the time it takes
to complete.
Reason
According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from Sun.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct
11
660Three particles of identical masses ( boldsymbol{m} )
are kept at the vertices of an equilateral triangle of each side length ‘a’. Find the gravitational force of attraction on any one of the particles.
11
661The maximum vertical distance
through which a full dressed astronaut canjump on the earth is ( 0.5 mathrm{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 mathrm{m} )
B. 3 m
( c cdot 6 m )
D. 7.5 ( m )
9
662Near the earth’s surface time period of a satellite is 1.4 hrs. Find its time period
if it is at the distance ( ^{prime} 4 R^{prime} ) from the
centre of the earth.
A . 32 hrs
B. ( left(frac{1}{8 sqrt{2}}right) ) hrs
c. ( 8 sqrt{2} hbar r s )
D. 16 hrs
11
663The radius in kilometers to which the
present radius of the earth ( (boldsymbol{R}= )
( 6400 k m) ) is to be compressed so that
the escape velocity is increased to 10 times is :
A. 6.4
B. 64
( c cdot 640 )
D. 4800
11
664A ball of mass ( mathrm{m} ) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If ( g ) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is
( mathbf{A} cdot sqrt{2 m^{2} g h} )
в. ( sqrt{4 m^{2} g h} )
( mathbf{c} cdot sqrt{8 m^{2} g h} )
D. ( 4 sqrt{m^{2} g h} )
11
665The value of ( ^{prime} g^{prime} ) will be ( 1 % ) of its value at the surface of the earth at a height of
( left(R_{e}=6400 k mright) )
( A cdot 6400 mathrm{km} )
B. 57600 km
c. ( 12560 mathrm{km} )
D. 64000 km
11
666A planet is moving around the Sun in a
circular orbit of circumference ( C . ) The
work done on the planet by the gravitational force ( F ) of the Sun is ( k F C )
then the value of ( k ) is
11
667Two bodies of masses ( m_{1} ) and ( m_{2} ) are
placed at distance X from each other.
IfX is kept constant and the masses of
the two bodies are increased to ( 2 m_{1} )
and ( 2 m_{2}, ) then the value of gravitational force between them will become
A. 4 times
B. 2 times
c. 8 times
D. ( 1 / 4 ) times
11
668A mass ( mathrm{m} ) is suspended form a sensitive spring balance kept in a satellite. The reading of the balance is
( W_{1} ) when the satellite is in an orbit of
radius ( mathrm{R} ) and is ( W_{2} ) when it is in an orbit
of radius ( 2 mathrm{R} ). Then
A. ( W_{1}>W_{2} )
в. ( W_{1}<W_{2} )
c. ( W_{1}=W_{2} )
D. cannot be predicted
11
669Two spherical lumps of clay attract each other with some amount of
gravitational force, as explained by Newton’s law of universal gravitation. If add clay to one lump and to the other so that the mass of one is 5 times as much
as before and the mass of the other is 3
times as much as before, and I move the lumps (still spherical) so that their centers are now 4 times as far apart as
before, how does the new gravitational force between them compare?
A. The new force is slightly smaller.
B. The new force is slightly greater.
c. The new force is more than 3 times as great
D. The new force is less than one-third as greatt
E. We cannot answer this question without knowing the universal gravitational constant
11
670Assertion
In a free fall, weight of a body becomes
effectively zero.
Reason
Acceleration due to gravity acting on a body having free fall is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
671A body weighs ( 160 mathrm{N} ) on the earth. Find
its weight on the other planet whose:
(a) mass is ( frac{1}{4} ) times the mass of earth and radius ( frac{1}{3} ) times that of the earth.
(b) mass is ( frac{5}{2} ) times the mass of earth and radius ( frac{4}{5} ) times that of the earth.
11
672A moon of Saturn has a nearly circular orbit of radius ( R ) and an orbit period of ( T ). Which of the following expressions gives the mass of Saturn?
( ^{A} cdot frac{2 pi R}{T} )
в. ( frac{4 pi^{2} R}{T} )
( ^{mathbf{c}} cdot frac{2 pi R^{3}}{left(G T^{2}right)} )
D. ( frac{4 pi^{2} R^{2}}{left(G T^{2}right)} )
E ( cdot frac{4 pi^{2} R^{3}}{left(G T^{2}right)} )
11
673Gravity is what makes objects orbit around other objects, and gravity is a reflection of an object’s mass. So why
doesn’ the mass of the objects appear in Kepler’s third law??
11
674Two spherical bodies the mass ( M ) and ( mathbf{5} M boldsymbol{m} ) and radii ( boldsymbol{R} ) and ( mathbf{2} boldsymbol{R} ) respectively
are released in free space with initial
separation between their centres equal
to ( 12 R ) If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is:
( mathbf{A} cdot 2.5 R )
B. ( 4.5 R )
c. ( 7.5 R )
D. ( 1.5 R )
11
675A satellite moves in a circular orbit
around the earth at height ( boldsymbol{R} / 2 ) from
earth’s surface where ( R_{e} ) is the radius
of the earth. Calculate its period of
revolution. Given ( boldsymbol{R}_{e}=mathbf{6 . 3 8} times mathbf{1 0}^{mathbf{6}} mathbf{m} )
11
676A planet revolves about the sun in elliptical orbit. The arial velocity ( left(frac{boldsymbol{d} boldsymbol{A}}{boldsymbol{d} boldsymbol{t}}right) )
of the planet is ( 4.0 times 10^{16} m^{2} / s . ) The
least distance between planet and the sun is ( 2 times 10^{12} mathrm{m} . ) Then the maximum
speed of the planet in ( mathrm{km} / mathrm{s} ) is
( A cdot 10 )
B. 20
( c cdot 40 )
D. none of these
11
677Two particles of masses ( 4 k g ) and ( 6 k g )
are at rest separated by 20 m. If they
move towards each other under mutual
force of attraction, the position of the point where they meet is
( mathbf{A} cdot 12 m ) from ( 4 k g ) body
B. ( 12 mathrm{m} ) from ( 6 mathrm{kg} ) body
c. ( 8 m ) from 4 kg body
D. ( 10 m ) from ( 4 k g ) body
11
678An artificial satellite moves in a
circular orbit around the earth. Total
energy of the satellite is given by ( boldsymbol{E} ). The
potential energy of the satellite is:
A . ( -2 E )
в. ( 2 E )
c. ( frac{2 E}{3} )
D. ( -frac{2 E}{3} )
11
679The horizontal component of the weight of a body of mass ( m ) is
A . ( m g )
B. ( frac{mathrm{mg}}{2} )
c. 0
D. Infinity
9
680Escape velocity from earth is 11.2km/sec. Another planet of same mass has radius ( frac{1}{4} ) times that of earth. What is the escape velocity from this
planet?
A. ( 11.2 k m / )sec
в. ( 44.8 k m / )sec
c. ( 22.4 k m / )sec
D. ( 5.6 k m / )sec
11
681A satellite moves around the earth in a
circular orbit with speed ( V ). If ( m ) is
mass of the satellite then its total
energy is
A ( cdot frac{1}{2} m V^{2} )
в. ( m V^{2} )
c. ( -frac{1}{2} m V^{2} )
D. ( frac{3}{2} m V^{2} )
11
682Two particles of equal mass go around
a circle of radius ( R ) under the action of
their mutual gravitational attraction.The speed of each particle is
( ^{mathbf{A}} cdot_{v}=frac{1}{2 R} sqrt{left(frac{1}{G m}right)} )
в. ( v=sqrt{left(frac{G m}{2 R}right)} )
( ^{mathrm{c}} v=sqrt{left(frac{G m}{R}right)} )
D. ( v=sqrt{left(frac{4 G m}{R}right)} )
11
683The ratio of mean distances of three
planets from the sun are ( 0.5,1,1.5, ) then the square of time periods are in the ratio of:
A. 1: 4: 9
B. 1: 9: 4
c. 1: 8: 27
D. 2: 1: 3
11
684What will be change in value of gravitational acceleration with increase in ( r ) from the center of the earth?
A. Decreases continuously
B. Increases continuously
C. Initially increases then decreases
D. Initially decreases then increases
11
685A particle is dropped on Earth from
height ( mathbf{R}(text { radius of Earth }) ) and it
bounces back to a height ( mathbf{R} / mathbf{2} )
coefficient of restitution for collision is
(ignore air resistance and rotation of Earth)
( A cdot frac{2}{3} )
B. ( sqrt{frac{2}{3}} )
( c cdot sqrt{frac{1}{3}} )
D. ( sqrt{frac{1}{2}} )
9
686The radius of the nearly circular orbit of mercury is ( 5.8 times 10^{10} m ) and its orbital
period is 88 days. If a hypothetical planet has an orbital period of 55 days, what is the radius of its circular orbit?
11
687Sl unit of ( G ) is ( N m^{2} k g^{-2} ) Which of the following can also be used as the Sl unit of G?
A ( cdot m^{3} k g^{-1} s^{-2} )
B . ( m^{2} k g^{-2} s^{-1} )
c. ( m k g^{-1} s^{-1} )
D. ( m^{3} k g^{-3} s^{-2} )
11
688Suppose(God forbid) due to some
reason, the earth expands to make its volume eight-fold. What you expect your
weight to be?
A. Two-fold
B. One-half
c. one-fourth
D. Unaffected
11
689A spaceship is released in a circular orbit near the Earth’s surface. How
much additional velocity will have to be
given to the spaceship in order to escape out of this orbit?
( begin{array}{ll}text { A. } 3.28 & text { m/s }end{array} )
В. ( 3.28 times 10^{3} mathrm{m} / mathrm{s} )
C ( .3 .28 times 10^{7} mathrm{m} / mathrm{s} )
D. ( 3.28 times 10^{-3} mathrm{m} / mathrm{s} )
11
690If the radius of a planet is doubled keeping density constant, what will be the value of escape velocity
A. Escape velocity remains same
B. Escape velocity doubles
c. Escape velocity becomes halved
D. Escape velocity becomes one fourth
11
691Assuming the earth to be a uniform
sphere of radius ( 6400 mathrm{km} ) and density ( 5.5 mathrm{g} / mathrm{c} . mathrm{c}, ) find the value of ( mathrm{g} ) on its
surface. ( G=6.66 times 10^{-11} N m^{2} k g^{-2} )
( mathbf{A} cdot=3.82 m s^{-2} )
В. ( =9.82 m s^{-2} )
( mathbf{c} .=19.82 m s^{-2} )
( mathrm{D} cdot=2 m s^{-2} )
11
692Assertion
When the distance between two bodies
is doubled and also the mass of each
body is doubled, the gravitational force between them remains the same
Reason
According to Newton’s law of gravitation, force is directly
proportional to mass of the bodies and
inversely proportional to square of the distance between them
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
693One kilogramme force is the force due to gravity on a mass of
A . ( 1 g )
B. ( 10 g )
( c .100 g )
D. ( 1000 g )
9
694Suppose, the acceleration due ot gravity
at the earth’s surface is ( 10 m s^{-2} ) and at
the surface of Mars it is ( 4.0 m s^{-2} . A 60 )
kg passenger goes from the Earth to the
Mars in a spaceship moving with a
constant velocity. Neglect all other
objects in the sky. Which part of figure
bests represents the weight (net
gravitational force) of the passenger as
a function of time?
( mathbf{A} cdot A )
B. ( B )
( c cdot C )
( D . D )
11
695Why will a sheet of paper fall slower
than one that is crumpled into a ball?
11
696A body weight ( 72 N ) on the surface of
the earth. What is the gravitational force acting on it due to the earth at a height equal to half the radius of the earth from the surface?
A. ( 16 N )
в. 32 N
c. ( 8 N )
D. ( 48 N )
11
697Assertion
The value of acceleration due to gravity
does not depend upon mass of the body
Reason
Acceleration due to gravity is a constant quantity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
698If you have to purchase 100 kg weight of gold, which place would you prefer-the
Earth or the Moon?

Similarly, if you have to sell gold, which place you prefer – The earth or the moon? Explain.
A. earth, moon
B. moon, moon
c. earth, earth
D. moon, earth

9
699The acceleration due to gravity ( g ) and mean density of earth ( rho ) are related by
which of the following relations? ( [G= ) gravitational constant and ( mathrm{R}= ) radius of earth].
A ( cdot rho=frac{4 pi g R^{2}}{3 G} )
В ( cdot rho=frac{4 pi g R^{3}}{3 G} )
( mathbf{c} cdot rho=frac{3 G}{4 pi g R} )
D. ( rho=frac{3 G}{4 pi g R^{3}} )
11
700Imagine a planet having the same density as that of the earth but radius
is three times the radius of the earth. If
acceleration due to gravity on the surface of the earth is ( g ) and that on the said planet is ( g^{prime} ), then
A ( cdot g^{prime}=frac{g}{9} )
B . ( g^{prime}=9 g )
c. ( g^{prime}=frac{g}{27} )
D. ( g^{prime}=3 g )
11
701The height from earth’s surface at
which acceleration due to gravity becomes ( frac{g}{4} ) is (where ( g ) is acceleration due to gravity on the surface of earth and ( R ) is radius of earth)
A ( cdot sqrt{2} R )
в. ( R )
c. ( frac{R}{sqrt{2}} )
D. 2R
11
702Nikhil calculates the change in gravitational potential energy at a height of ( 5 mathrm{km} ) from the surface of earth using the equation ( U=-G M m / r ) and Varun calculates this energy using the formula ( U= ) mgh. The energies
calculated have different numerical
values.
A . True
B. False
11
703If density of earth increases 4 times and its radius becomes half of what it is, our
weight will:
A. be 4 times its present value
B. be doubled
c. remain same
D. be halved
11
704The height at which the acceleration due to gravity becomes ( frac{mathbf{g}}{mathbf{g}} ) (where ( mathbf{g}= )
the acceleration due to gravity on the surface of the earth) in terms of ( mathbf{R} ), the
A . 2 R
B. ( frac{mathrm{R}}{sqrt{2}} )
c. ( mathrm{R} / 2 )
D. ( sqrt{2} mathrm{R} )
11
705The weight of a boy on the surface of moon is ( 300 N . ) The weight of this boy on
the surface of earth is:
( mathbf{A} cdot 300 N )
в. ( 5 N )
( c .50 N )
D. ( 1800 N )
9
706Value of g is:
A. maximum at poles
B. maximum at equator
C . same everywhere
D. minimum at poles
11
707Two solid spheres of same size of a
certain metal are placed in contact with
each other. Prove that the gravitiational
force acting between them is directly
proportional to the fourth power of their
11
708Rain drops are falling with a constant speed by the time they reach the ground
because.
A. Rain drops originate in outer space where the gravitational forces are negligible
B. The force due to air resistance increases with the speed of the rain drops until it balances the gravitational force
C. Rain drops are two light and hence not affected by acceleration due to gravity
D. The force due to air resistance is constant and
balances the gravitational force
11
709ACCELERATION DUE TO GRAVITY OF THE
EARTH

Radius of earth is ( 6400 mathrm{km} ) and that of
mars is ( 3200 mathrm{km} ). Mass of mars is 0.1
that of earth’s mass. Then the acceleration due to gravity on mars is nearly.
A ( cdot 1 mathrm{m} / mathrm{s}^{2} )
B ( .2 .5 m / s^{2} )
c. ( 4 m / s^{2} )
D. ( 5 m / s^{2} )

11
710A planet of mass ( 3 times 10^{29} mathrm{gm} ) moves
around a star with a constant speed of
( 2 times 10^{8} m s^{-1} ) in a circle of radii ( 1.5 times )
( 10^{12} mathrm{m} . ) The gravitational force exerted
on the planet by the star is
A ( .6 .67 times 10^{22} ) dyne
B . ( 6.67 times 10^{26} ) N
c. ( 8 times 10^{26} mathrm{N} )
D. ( 8 times 10^{27} ) dyne
11
711What is gravitational potential energy?
Explain with the help of an example.
11
712A particle when thrown. moves such that it passes from same height at 2
and ( 10 s, ) the height is:
( mathbf{A} cdot g )
в. ( 2 g )
c. ( 5 g )
D. ( 10 g )
11
713The escape velocity on a planet is ( boldsymbol{v} . ) If the radius of the planet contracts to ( frac{1}{4} ) of present value without any change in its mass, the escape velocity will be
A. halved
B. doubled
D. becomes one fourth
11
714The escape velocity from the earth is 11
( mathrm{km} s^{-1} . ) The escape velocity from a planet having twice the mass and twice
A . ( (11 times sqrt{12}) k m s^{-1} )
B. ( 11 k m s^{-1} )
c. ( frac{11}{2} k m s^{-1} )
D. ( (11 times sqrt{2}) k m s^{-1} )
11
715At a place, the value of ‘g’ is less by ( 1 % ) than its value on the surface of the Earth (Radius of Earth, ( boldsymbol{R}=mathbf{6 4 0 0 k m} ) ).
The place is:
A. ( 64 mathrm{km} ) below the surface of the earth
B. ( 64 mathrm{km} ) above the surface of the earth
c. ( 30 mathrm{km} ) above the surface of the earth
D. 32 km below the surface of the earth
11
716A mass of ( M ) at rest is broken into two
pieces having masses ( m ) and ( (M-m) )
The two masses are then separated by a distance. The gravitational force between them will be the maximum
when the ratio of the masses ( [m: )
( (M-m)] ) of the two parts is:
A . 1: 1
B. 1: 2
( c cdot 1: 3 )
D. 1: 4
11
717Find out the correct relation for the
dependance of change in acceleration due to gravity on the angle at the latitude due to rotation of earth?
A ( . d g propto cos phi )
B. ( d g propto cos ^{2} phi )
c. ( d g propto cos ^{3 / 2} phi )
D. ( d g propto frac{1}{cos phi} )
11
718A remote sensing satellite is revolving in an orbit of radius x over the equator
of earth. If the area on each surface in
which satellite can not send message is ( operatorname{given} operatorname{as}left(1-frac{sqrt{x^{2}-R^{2}}}{x}right) s pi R^{2} . ) Find ( s )
11
719The masses and radii of the earth and
the Moon are ( M_{1}, R_{1} ) and ( M_{2}, R_{2} )
respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is?
A ( cdot sqrt{frac{2 Gleft(M_{1}+M_{2}right)}{d}} )
B. ( sqrt{frac{4 Gleft(M_{1}+M_{2}right)}{d}} )
c. ( sqrt{frac{4 G M_{1} M_{2}}{d}} )
D. ( sqrt{frac{Gleft(M_{1}+M_{2}right)}{d}} )
11
720A ball is dropped from a satellite revolving around the earth at height of 120km. The ball will
A. Continue to move with same speed along a straight line tangentially to the satellite at that time
B. Continue to move with same speed along the original orbit of satellite
c. Fall down to earth gradually
D. Go far away in space
11
721whose hemispherical base is of
diameter ( 0.20 mathrm{m} . ) The height of the flask
is ( 0.25 mathrm{m} ). The flask is filled to the brim
with 2.5 litres ( left(1 text { litre }=10^{-3} m^{3}right) ) of
water and sealed with a glass lid.
What is the approximate magnitude of
the total vertical force exerted by the
water on the curved surface of the
flask? (Take the acceleration due to
gravity, ( g, ) to be ( 10 m s^{-2} ) ).
( A cdot O N )
B. 78.5
c. 53.5 N
D. 25.0
11
722The gravitational force between two
objects in ( 200 N ) How should the distance between these objects be changed so that force between them becomes ( 50 N ? )
11
723For the moon to cease to remain the
earth’s satellite its orbital velocity has to increase by a factor of
( A cdot 2 )
B. ( sqrt{2} )
( c cdot 1 sqrt{2} )
D. ( sqrt{3} )
11
724How the value of ( g ) varies with height.11
725Variation in the Acceleration Due to
Gravity:
Inside the earth: ( g=g_{0} frac{x}{R_{0}}(x ) is
distance from the centre of the earth).
11
726The attached figure shows a planet
revolving a star. It was recorded that the
planet takes 50 days to travel from ( T ) to
U. Which other two observations could
be 50 days apart?
A. ( mathrm{V} ) and ( mathrm{W} )
B. Wand Y
c. ( x ) and ( Y )
D. ( x ) and ( z )
E. ( Y ) and
11
727Three planets of same density and with
radii ( mathbf{R}_{1}, mathbf{R}_{2} ) and ( mathbf{R}_{3}, ) such that ( mathbf{R}_{1}= )
( 2 mathrm{R}_{2}=3 mathrm{R}_{3}, ) have gravitation fields on
the surfaces ( mathrm{E}_{1}, mathrm{E}_{2}, mathrm{E}_{3} ) and escape velocities ( mathbf{v}_{mathbf{1}}, mathbf{v}_{mathbf{2}}, mathbf{v}_{mathbf{3}} ) respectively, Then
This question has multiple correct options
A ( cdot frac{mathrm{E}_{1}}{mathrm{E}_{2}}=frac{1}{2} )
в. ( frac{mathrm{E}_{1}}{mathrm{E}_{3}}=3 )
c. ( frac{v_{1}}{v_{2}}=2 )
D. ( frac{v_{1}}{v_{3}}=frac{1}{3} )
11
728An astronaut whose mass is ( 84 k g ) on earth will have a mass of approximately
14 ( k g ) on the moon
A. True
B. False
9
729Escape velocity for a projectile at
earth’s surface is ( v_{e} . ) A body is projected form earth’s surface with velocity ( 2_{v_{e}} )
The velocity of the body when it is at infinite distance from the centre of
the earth is
A ( cdot v_{e} )
B. ( 2 v_{e} )
( c cdot sqrt{2 v} )
D. ( sqrt{3} v_{e} )
11
730If ( F ) is the force between two bodies of
masses ( m_{1} ) and ( m_{2} ) at certain
separation. Find the force between ( sqrt{2} m_{1} ) and ( sqrt{3} m_{2} ) at same separation.
11
731The orbital radius of moon around the
earth is ( 3.8 times 10^{8} ) meter and its time
period is 27.3 days. The centripetal acceleration of moon will be
A. ( -2.4 times 10^{-3} mathrm{m} / mathrm{s}^{2} )
B. ( 11.2 m / s^{2} )
c. ( 2.7 times 10^{-3} mathrm{m} / mathrm{s}^{2} )
D. ( 9.8 m / s^{2} )
11
732Average distance of the earth from the
sun is ( L_{1} . ) If one year of the earth ( =D )
days, one year of another planet whose
average distance from the sun is ( L_{2} ) will
be
( ^{mathrm{A}} cdot_{D}left(frac{L_{2}}{L_{1}}right)^{1 / 2} ) days
B. ( quad Dleft(frac{L_{2}}{L_{1}}right)^{3 / 2} ) days
( ^{mathbf{C}} cdot_{D}left(frac{L_{2}}{L_{1}}right)^{2 / 3} ) days
D. ( Dleft(frac{L_{L}}{L_{1}}right) ) days
11
733A body suspended from a spring balance is placed in a satellite. Reading
in balance is ( W_{1} ) when the satellite
in balance is ( W_{2} ) when the satellite
moves in an or bit of radius ( 2 R ). Then.
A. ( W_{1}=W_{2} )
в. ( W_{1}>W_{2} )
( mathbf{c} cdot W_{1}<W_{2} )
D. ( W_{1}=2 W_{2} )
11
734What is meant by torque due to gravity?11
735The time period of a geo-stationary satellite in its orbit is
A . 12 hrs
B. 24 hrs
c. 365 days
D. none of these
11
736If a Parrot starts flying upwards with an
acceleration in an air tight cage, then the boy will feel the weight of the cage:
A. Unchanged
B. Reduced
c. Increased
D. Nothing can be said
11
737In CGS, the gravitational unit of force is
A. ( k g f )
B. ( N )
( mathrm{c} cdot g f )
D. dyne
9
738Consider two spherical planets of same average density, Planet 2 is 8 limes as massive as planet 1. The ratio ot the
acceleration due to gravity on the second planet to that on the first is.
( A )
B. 2
( c cdot 4 )
D. 8
11
739If the radius of the earth is reduced to
half of its present value, with no change in the mass, how will the acceleration
due to gravity, be affected?
11
740Consider a satellite going round the
earth in a circular orbit. Which of the
following statements is wrong?
A. It is a freely falling body
B. It is a moving with constant speed.
c. It is acted upon by a force directed away from the centre of the earth which counter- balances the gravitational pull.
D. Its angular momentum remains constant
11
741A thin rod length L is bent to form a circle. Its mass is M. What force will act
on the mass ( mathrm{m} ) placed at the center of the circle?
A ( cdot frac{4 pi^{2} G M m}{L^{2}} )
B. ( frac{G M m}{4 pi^{2} L^{2}} )
c. ( frac{2 pi G M m}{L^{2}} )
D. zero
11
742The orbital speed ( v ) of each moon, such that they maintain the triangular configuration is:
A ( cdot sqrt{frac{G M}{R^{2}}+frac{G m}{sqrt{3} R}} )
B. ( sqrt{frac{G M}{R}+frac{G m}{sqrt{3} R}} )
( ^{mathrm{c}} cdot sqrt{frac{G M^{2}}{R}+frac{G m}{sqrt{3} R}} )
D. ( sqrt{frac{G M}{R}+frac{G m^{2}}{3 R}} )
11
743Velocity of the planet is minimum at
A ( . C )
в. ( D )
( c . A )
( D )
11
744An astronaut, inside an earth satellite,
experiences weightlessness because
This question has multiple correct options
A. no external force is acting on him
B. he is falling freely
C. no reaction is exerted by the floor of the satellite
D. he is far away from the earth’s surface
11
745Calculate the value of the acceleration
due to gravity at a place ( 3,200 k m )
above the surface of the earth.
11
746the value of ( g ) at the surface of the earth
is ( 9.8 m / s^{2} . ) then the value of ( g ) at the place ( 480 k m ) above the surface of the
earth will be nearly? (Radius of the earth is ( 6400 k m )
11
747The gravitational potential is a
A. scalar
B. vector
C. scalar based on the mass of the particle
D. scalar or vector depending on the situation
11
748The escape velocity of a projectile from the earth’s surface is approximately.
A. ( 7 mathrm{km} / mathrm{s} )
В. ( 112 mathrm{km} / mathrm{s} )
c. ( 11.2 mathrm{km} / mathrm{s} )
D. ( 1.1 mathrm{km} / mathrm{s} )
11
749A body is taken to a height of ( n R ) from the surface of the earth. The ratio of the acceleration due to gravity on the
surface to that at the altitude is
A ( cdot(n+1)^{2} )
B ( cdot(n+1)^{-2} )
c. ( (n+1)^{-1} )
D. ( (n+1) )
11
750How much would a W kg man weigh on the moon in terms of gravitational
units?
A ( cdot frac{W}{6} ) kg-wt
B. 6W kg-wt
c. w kg-wt
D. zero
9
751Suppose the acceleration due to gravity
at the earth’s surface is ( 10 mathrm{m} / mathrm{s}^{2} ) and at
the surface of mars it is ( 4.0 mathrm{m} / mathrm{s}^{2} . ) A
( 60 mathrm{kg} ) passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other
object in the sky. Which part of the
figure best represent the weight (net gravitational force) of the passenger as a function of time?
( A cdot A )
В. ( B )
( D )
11
752Two planets revolves around the sun
with frequencies ( N_{1} ) and ( N_{2} ) revolutions
per year. If their average radii (orbital)
be ( R_{1} ) and ( R_{2} ) respectively, then ( R_{1} / R_{2} )
is equal to:
A ( cdotleft(N_{1} / N_{2}right)^{2 / 3} )
a
B . ( left(N_{1} / N_{2}right)^{3 / 2} )
C ( cdotleft(N_{2} / N_{1}right)^{2 / 3} )
D. ( left(N_{2} / N_{1}right)^{3 / 2} )
11
753The value of ‘g’ at the depth from the ground goes on
A. increasing
B. fluctuating
c. decreasing
D. varying
11
754If the density of the earth is doubled to that of its original value, the radius
remaining the same, what will be the change in acceleration due to gravity?
11
755At which height from the earth’s surface, acceleration due to gravity is
decreased by ( 75 % ) of its value at earth’s
surface.
11
756Two spherical bodies of mass ( M ) and
( 5 M ) and radii ( R ) and ( 2 R ) respectively are
released in free space with initial separation between their centres equal
to ( 12 R ) If they attract each other due to
gravitational force only, then the distance covered by the smaller body just before collision is
A . ( 2.5 R )
в. ( 4.5 R )
( c .7 .5 R )
D. ( 1.5 R )
11
757A semicircular wire.has a length L and mass M.A particle of mass m is placed at the center of the circle. Find the
gravitational attraction on the particle
due to the wire.
11
758Kepler’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
11
759Weight of a body of mass m decreases
by ( 1 % ) when it is raised to height ( h ) above the Earth’s surface. If the body is taken to a depth h in a mine, then its weight will:
A. Decreases by ( 0.5 % )
B. Decreases by ( 2 % )
c. Increases by ( 0.5 % )
D. Increase by ( 1 % )
11
760Imagine 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 stars is proportion to ( R_{1} / 2, ) there ( T^{2} ) is proportional to.
A ( cdot R^{2} )
B . ( R^{1 / 2} )
c. ( R^{-1 / 2} )
D. ( R^{1} / 3 )
11
761The percentage change in the acceleration of the earth towards the
sun from a total eclipse of the sun to the
point where the moon is on a side of earth directly opposite to the sun is:
( r_{1} ) is the distance of earth from sun, ( r_{2} )
is the distance of earth from moon
A ( cdot frac{M_{s}}{M_{m}} frac{r_{2}}{r_{1}} times 100 )
B. ( frac{M_{s}}{M_{m}}left(frac{r_{2}}{r_{1}}right)^{2} times 100 )
( ^{mathbf{C}} 2left(frac{r_{1}}{r_{2}}right)^{2} frac{M_{m}}{M_{s}} times 100 )
( ^{mathrm{D}}left(frac{r_{1}}{r_{2}}right)^{2} frac{M_{s}}{M_{m}} times 100 )
11
762If the inertial mass ( m_{i} ) of the bob of a
simple pendulum of length ( ; l^{prime} ) is not
equal to the gravitational mass ( m_{g} ) then its time period is:
( ^{mathrm{A}} cdot_{T}=2 pi sqrt{frac{m_{i} l}{m_{g} cdot g}} )
В ( cdot T=2 pi sqrt{frac{m_{g} cdot l}{m_{i cdot g}}} )
( ^{mathbf{c}} cdot_{T}=2 pi sqrt{frac{l}{g}} )
( ^{mathrm{D}} cdot_{T}=2 pi sqrt{frac{left(m_{i}+m_{g}right)}{left(m_{i}-m_{g}right)} cdot frac{l}{g}} )
11
763Two planets, ( A ) and ( B ), orbit a star. Planet A moves in an elliptical orbit whose semi major axis has length a. Planet B moves in an elliptical orbit whose semi major axis has a length of 9a. If planet ( A ) orbits with a period ( T, ) what is the period
of planet Bs orbit?
A. 7297
в. 27 T
( c cdot 3 T )
D. ( T / 3 )
E. т/27
11
764A body weighs ( 36 k g ) on the surface of the Earth. How much would it weights
on the surface of a planet,whose mass is ( frac{1}{9} ) and radius ( frac{1}{3} ) of that of earth?
11
765Mass of the earth is 81 times the mass
of the moon and distance between the
earth and moon is 60 times the radius
of the earth. If ( R ) is radius of the earth,
then the distance between moon and
the point on the line joining the moon and the earth where the gravitation force becomes zero is
A. 30R
в. 15R
( c cdot 6 R )
D. 5R
11
766A particle of mass ( M ) is placed at the centre of a uniform spherical shell of mass ( 2 M ) and radius The gravitational potential on the surface of the shell is:
A. ( -frac{G M}{R} )
в. ( -frac{3 G M}{R} )
c. ( -frac{2 G M}{R} )
D. zero
11
767Two identical particles of mass ( 1 mathrm{kg} ) experience a gravitational force of 10N between them . The distance between
them is r. If the same setup is put in water (refractive index ( =1.5 ) ), how will
their gravitational force change
A. The gravitational force will reduce to 1 N
B. The gravitational force remains constant
c. The gravitational force becomes ( 20 / 3 mathrm{N} )
D. The gravitational force becomes 15 N
11
768The radii of two planets are respectively
( R_{1} ) and ( R_{2} ) and their densities are
respectively ( rho_{1} ) and ( rho_{2} . ) The ratio of the
accelerations due to gravity at their
surfaces is
A ( cdot g_{1}: g_{2}=frac{rho_{1}}{R_{1}^{2}}: frac{rho_{2}}{R_{2}^{2}} )
( mathbf{B} cdot g_{1}: g_{2}=R_{1} R_{2}: rho_{1} rho_{2} )
( mathbf{c} cdot g_{1}: g_{2}=R_{1} rho_{1}: R_{2} rho_{1} )
( mathbf{D} cdot g_{1}: g_{2}=R_{1} rho_{1}: R_{2} rho_{2} )
11
769The acceleration due to gravity at the
poles and the equator is ( g_{p} ) and ( g_{e} ) respectively. If the earth is a sphere of
with angular speed ( omega, ) then ( g_{p}-g_{e} ) is
then given by
( ^{mathrm{A}} cdot frac{omega^{2}}{R_{E}} )
B. ( frac{omega^{2}}{R_{E}^{2}} )
c. ( omega^{2} R_{E}^{2} )
D. ( omega^{2} R_{E} )
11
770Consider earth to be a homogeneous
sphere. Scientist ( boldsymbol{A} ) goes deep down in a
mine and scientist ( B ) goes high up in a
balloon. The gravitational field measured by
A. ( A ) goes on decreasing and that by ( B ) goes on increasing
B. ( B ) goes on decreasing and that by ( A ) goes on increasing
c. Each decreases at the same rate
D. Each decreases at different
11
771A particle of mass ( mathrm{M} ) is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the
centre will be :
( A cdot frac{G M}{a} )
B. ( frac{2 G M}{a} )
( mathrm{c} cdot frac{3 G M}{a} )
D. ( frac{4 G M}{a} )
11
772Find the height from the earth’s surface where ( g ) will be ( 25 % ) of its value on the
surface of earth ( (mathrm{R}=mathbf{6 4 0 0} mathrm{km}) . ) (b) Find
the percentage increase in the value of ( mathrm{g} ) at a depth h from the surface of earth.
11
773Average density of the earth
A. does not depend on g
B. is a complex function of ( g )
C. is directly proportional to ( g )
D. is inversely proportional to g
11
774Assertion
Kepler’s second law can be understood by conservation of angular momentum principle.
Reason
Kepler’s second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as ( (boldsymbol{d A} / boldsymbol{d t})=left(boldsymbol{r}^{2} boldsymbol{omega}right) / 2 )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct
11
775If a planet of given density were made larger, its force of attraction for an object on its surface would increase
because of the greater distance from the object to the centre of the planet. Which effect predominates?
11
776If ( W_{1}, W_{2} ) and ( W_{3} ) represent the work
done in moving a particle from ( boldsymbol{A} ) to ( boldsymbol{B} )
along three different paths 1,2 and 3
respectively (as shown) in a
gravitational field of point mass ( boldsymbol{m} )
then find the correct relation between
( W_{1}, W_{2} ) and ( W_{3} )
A ( . W_{1}=W_{2}=W_{3} )
B. ( W_{1}>W_{2}>W_{3} )
( mathbf{c} cdot W_{1}<W_{2}W_{1}>W_{3} )
11
777Which of the following doesn’t show that
air has pressure?
A. Ball falling to the ground
B. Flying a kite
c. Riding a bicycle against the wind
D. none of these
11
778Given that ( T ) stands for time period and stands for the length of simple pendulum. If ( g ) is the acceleration due to gravity, then which of the following
statements about the relation ( boldsymbol{T}^{2}= )
( (l / g) ) is correct?
A. It is correct both dimensionally as well as numerically y
B. It is neither dimensionally correct nor numerically.
c. It is dimensionally correct but not numerically.
D. It is numerically correct but not dimensionally.
11
779The gravitational force with which the
earth attracts the moon:
A. is less than the force with which the moon attracts the earth
( mathbf{B} ). is equal to the force with which the moon attracts the earth
c. is greater than the force with which the moon attracts the earth
D. varies with the phases of the moon
9
780Escape velocity of a particle depends on
its mass
( mathbf{A} cdot m^{2} )
в. ( m )
( mathrm{c} cdot m^{0} )
D. ( m^{-1} )
11
781The earth ( left(operatorname{mas} s=6 times 10^{24} k gright) ) revolves
around the sun with an angular velocity
of ( 2 times 10^{-7} ) radian/sec in a circular
orbit of radius ( 1.5 times 10^{8} k m . ) The force
exerted by the sun, on the earth is :-
A ( cdot 6 times 10^{19} N )
B . ( 18 times 10^{25} N )
c. ( 36 times 10^{21} N )
D. ( 27 times 10^{39} N )
11
782Assertion
A planet moves faster, when it is closer
to the sun in its orbit and vice versa
Reason
Orbital velocity for an orbiting planet is
constant
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
783Two point object of masses ( 10^{4} k g, 10^{6} k g ) are ( 1.2 times 10^{3} m ) apart.
Find distance of point from smaller mass at which the net gravitational force due to them will be zero(in m)
A . 109
B. 1100
( c cdot 11 )
D. 99
9
784A satellite is in a circular orbit around a planet, Its period of revolution is ( mathrm{T} ), radius of the orbit is ( R ), orbital velocity ( V )
and acceleration ‘a’, then:
A ( cdot V=a t ) and ( a=frac{V^{2}}{R} )
B. ( V=frac{2 pi R}{T} ) and ( V=a T )
c. ( V=frac{2 pi R}{T} ) and ( a=frac{V^{2}}{R} )
D. ( V=frac{1}{2} a T^{2} )
11
785The speed of the earth is highest when
it is
A. Farthest from the sun
B. Nearest to the sun
c. Passing through the month of September
D. None of the above
11
786Assertion
Many great rivers flow towards the equator. The sediments that they carry
increase the time of rotation of the
Reason
The angular momentum of the earth about its rotation axis is conserved.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
787What is the value of acceleration due to
gravity at height equal to half the
radius of earth from surface of earth.
[take ( left.g=10 m / s^{2} text { at earth surface }right] )
11
788The value of ( g ) near the earth’s surface is
A ( cdot 8.9 m / s^{2} )
в. ( 8.9 m / s )
( mathrm{c} cdot 9.8 mathrm{m} / mathrm{s}^{2} )
D. ( 9.8 m / s )
11
789A body weighs ( 60 mathrm{kg} ) on the earth’s surface. What would be its weight at the centre of the earth?
A. 60 kg-wt
B. 6 kg-wt
c. ( 60 times 9.8 mathrm{kg} ) -wt
D. zero
11
790If a ball is projected with a velocity equal to ( 1 / 4 ) th of the escape velocity from the surface of the earth. the height it will attain is ( _{-} ).
A ( cdot frac{R}{4} )
в. ( frac{R}{32} )
c. ( 4 R )
D. ( frac{R}{16} )
11
791The angular speed of rotation of earth about its axis at which the weight of man standing on the equator becomes half of its weight at the poles is given by:
B. ( 8.75 times 10^{-4} )rads( ^{-1} )
c. ( 1.23 times 10^{-2} mathrm{rads}^{-1} )
D. ( 7.65 times 10^{-7} )rads( ^{-1} )
11
792To overcome the effect weightlessness
in an artificial satellite
A. the satellite is rotated around its axis with
compartment of astronaut at the centre of the satellite.
B. the satellite is shaped like wheel.
C. the satellite is rotated around and around till weightlessness disappears.
D. the compartment of astronaut is kept on the periphery of rotating wheel like satellite.
11
793State whether true or false.
As the distance of the planet from the sun increases, the period of revolution decreases.
A. True
B. False
11
794A satellite S is moving in an elliptical orbit around the earth. The mass of the
satellite is very small compared to the
mass of the earth
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
11
795Gravitational acceleration on the
surface of a planet is ( frac{sqrt{mathbf{6}}}{11} ) g, where ( g ) is the gravitational acceleration on the surface of the earth. The average mass density of the planet is ( frac{2}{3} ) times that of
the Earth. If the escape speed on the surface of the earth is taken to be 11
( k m s^{-1}, ) the escape speed on the surface
of the planet is ( k m s^{-1} ) will be?
11
796The depth at which the value of ( g )
becomes ( 25 % ) of that at the surface of
the earth is (in ( mathrm{Km} ) )
( A cdot 4800 )
B. 2400
c. 3600
D. 1200
11
797The distance of Neptune and Saturn
from the sun are nearly ( 10^{13} mathrm{m} ) and ( 10^{12} ) ( mathrm{m} ) respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of
A . 10
в. 100
c. ( 10 sqrt{10} )
D. 1000
11
798Two spheres each of mass ( 10^{5} k g ) and
radius ( 10 m ) are kept in constant. Find the force of gravitational acting between them.
( mathbf{A} cdot 10^{-3} N )
В ( cdot 6.67 times 10^{-3} N )
c. ( 6.67 times 10^{-11} N )
D. ( 10^{-11} N )
11
799The moon’s radius is ( frac{1}{4} ) that of the earth and its mass is ( frac{1}{80} ) times 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
A. ( frac{g}{4} )
в. ( frac{g}{5} )
c. ( frac{g}{6} )
D. ( frac{g}{8} )
11
800Kepler’s second law is a consequence of
A. conservation of energy
B. conservation of linear momentum
C. conservation of angular momentum
D. conservation of mass
11
801If the radius of the Earth were increased
by a factor of 2 and its mass remained
the same, then the acceleration due to
gravity on the Earth would
A. reduce by factor 4
B. reduce by factor 2
c. not change
D. none of the above
11
802The value of acceleration due to gravity,
at earth surface is ( g ). Its value at the
centre of the earth, which we assume as
a.sphere of radius ( R ) and of uniform mass density, will be:
( mathbf{A} cdot 10 R m / s^{2} )
B. zero
c. ( 5 R m / s )
D. ( 20 R m / s^{2} )
11
803The gravitational force between two bodies is
A. repulsive at large distances
B. attractive at all places
c. attractive at short distances
D. repulsive at short distances
9
804Potential due to a point mass ( m ) at a distance ( r ) is ( V=-frac{G M}{r} )11
805The gravitational P.E. of a rocket of mass ( 100 mathrm{kg} ) at a distance of ( 10^{7} mathrm{m} ) from the earths centre is ( -4 times 10^{9} ) J.
The weight of the rocket at a distance of ( 10^{9} mathrm{m} ) from the centre of the earth is :
A ( cdot 4 times 10^{-2} mathrm{N} )
В. ( 4 times 10^{-9} mathrm{N} )
c. ( 4 times 10^{-6} mathrm{N} )
D. ( 4 times 10^{-3} mathrm{N} )
11
806If the distance between the earth and
sun were to be doubled from its present value, the number of days in a year
would be :
A . 64.5
в. 1032
( c cdot 182.5 )
D. 730
11
807An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The
time taken by this satellite in completing one revolution will be
A. 2 lunar months
B ( cdot 2^{-2 / 3} ) lunar months
( mathrm{c} cdot 2^{-3 / 2} ) lunar months
D. ( 1 / 2 ) lunar months
11
808The escape velocity for the earth is ( v_{e} )
The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is :
A. ( 36 v_{e} )
B. ( 12 v_{e} )
( c cdot 6 v_{e} )
D. ( 20 v_{c} )
11
809Average density of the earth
A. does not depend on ( g )
B. is a complex function of ( g )
C. is directly proportional to ( g )
D. is inversely proportional to ( g )
11
810The magnitude of acceleration due to
gravity decreases
A. as the height from the surface of the earth increases
B. as the depth from the surface of the earth increases
C. as one moves from the pole of the earth to its equator
D. All the above
11
811If the distance between the Sun and
Earth is increased by three times then attraction between two will:
A. decreases by ( 11 % )
B. decreases by 33%
c. decreases by 66%
D. decreases by 89%
11
812A point mass ( m_{0} ) is placed at a distance ( boldsymbol{R} )
( frac{n}{3} ) from the centre of a spherical shell of mass ( M ) and radius ( R ). The
gravitational force on the point mass
( boldsymbol{m}_{0} ) is:
( ^{mathrm{A}} cdot frac{9 G M m_{0}}{R^{2}} )
в. ( frac{G M m_{0}}{R^{2}} )
c. zero
D. ( frac{4 G M m_{0}}{R^{2}} )
11
813A body falls freely towards the earth
with:
A. uniform speed
B. uniform velocity
c. uniform acceleration
D. none of these
11
814If the mass of the earth is doubled and
the distance of the moon revolving around the earth is also doubled, then, find the new time period of revolution of moon. (Take the present time of
revolution as 28 days)
( A cdot 6 )
B. 36
( c .56 )
D. 112
11
815A satellite of mass ( 250 k g ) is orbiting the Earth a height of ( 500 k m ) 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 times 10^{24} ) kgradius of the
Earth ( =6400 mathrm{km} ; ) and ( mathrm{G}=6.67 mathrm{x} )
( 10^{-11} N m^{2} k g^{-2} )
11
816The square of its period of revolution around the sun is the cube of the mean distance of a
planet from the sun
A. Inversely proportional
B. Directly proportional
c. Not proportional
D. depend
11
817Newton said that an apple falls down from a tree because
A. Apple exerts a force of attraction on the earth
B. The earth exerts a force of attraction on the apple
c. Both are true
D. None of the options are correct
11
818A satellite has a kinetic energy ( X ) potential energy ( Y ) and total energy ( z ) in a given orbit. How are they related
A. ( Z=Y=-2 X )
в. ( Z=Y / 2=-X )
c. ( Z=2 Y=-2 X )
D. ( 2 Z=Y=-2 X )
( X )
11
819A mass ( M ) is split into two parts ( m ) and
( (M-m) ) which are then separated by a
certain distance. The ratio ( boldsymbol{m} / boldsymbol{M} ) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1
11
820The escape velocity on the earth is ( 11.2 k m / s . ) A planet has twice the radius of earth and same mean density as earth Then the escape velocity on planet in ( k m / s ) will be :
A . 5.6
B. 11.2
c. 22.4
D. 16.5
11
821If Earth is supposed to be a sphere of
radius ( R, ) if ( g_{30^{circ}} ) is value of acceleration
due to gravity at latitude of ( 30^{circ} ) and ( g ) at
the equator, the value of ( g-g_{30^{circ}} ) is
A ( cdot frac{1}{4} omega^{2} R )
в. ( frac{3}{4} omega^{2} R )
c. ( omega^{2} R )
D. ( frac{1}{2} omega^{2} R )
11
822The largest and the shortest distance of
the earth from the sun are ( r_{1} ) and ( r_{2} ). Its
distance from the sun when it is at
perpendicular to the major-axis of the orbit drawn from the sun is:
A ( cdot frac{r_{1}+r_{2}}{4} )
в. ( frac{r_{1}+r_{2}}{r_{1}-r_{2}} )
c. ( frac{2 r_{1} r_{2}}{r_{1}+r_{2}} )
D. ( frac{r_{1}+r_{2}}{3} )
11
823A hypothetical planet has density ( rho ) radius ( mathrm{R} ), and surface gravitational acceleration ( g ). If the radius of the
planet were doubled, but the planetary density stayed the same, find the acceleration due to gravity at the planet’s surface.
A ( .4 g )
в. ( 2 g )
( c . g )
D. ( g / 2 )
11
824Two objects have the same mass and are located near each other at a
distance (r). If the mass of one of the
objects is doubled and the mass of the other object is tripled, Find out the
change in gravitational attraction between them?
A. Decrease by ( 1 / 6 )
B. Decrease by ( 2 / 3 )
c. Increase by ( 3 / 2 )
D. Increase by 5
E. Increase by 6
11
825Motion of artificial satellite around the
A . Liquid fuel
B. Solar energy
c. Atomic energy
D. None of these
11
826Two satellites of identical masses orbit
the earth at different heights. The ratio of their distances from the centre of
earth is ( d: 1 ) and the ratio of the
acceleration due to gravity at those height is ( g: 1 . ) Then find the ratio of their orbital velocities.
A ( cdot sqrt{frac{g}{d}} )
B. ( sqrt{g d} )
( mathrm{c} cdot sqrt{g} )
D. ( sqrt{g} d )
11
827A student determined to test the law of
gravity for himself walks off a
skyscraper ( 320 m ) high with a stopwatch in hand and starts his free
fall (zero initial velocity). 5 seconds later, superman arrives at the scene
and dives off the roof to save the
student. what must be superman’s initial velocity in order that he catches the student just before reaching the ground? [assume that superman’s acceleration is that of a free-falling body, ( left.g=10 m / s^{2}right] )
B . ( 25.8 mathrm{ms}^{-1} )
c. ( 4.785 mathrm{ms}^{-1} )
D. Cannot be determined
11
828The ratio of the radii of two planets ( r_{1} )
and ( r_{2} ) is ( k . ) The ratio of acceleration due
to gravity on them is ( r . ) Then the ratio of the escape velocities from them, will be:
A. ( sqrt{frac{r}{k}} )
в. ( sqrt{frac{k}{r}} )
( c . k r )
D. ( sqrt{k s} )
11
829A satellite is to be placed in equatorial geostationary orbit around earth for communication. The height of such a satellite is
( left[M_{E}=6 times 10^{24} k g, R_{E}=6400 k m, T=right. )
A ( .3 .57 times 10^{5} m )
В. ( 3.57 times 10^{6} m )
c. ( 3.57 times 10^{7} m )
D. ( 3.57 times 10^{8} m )
11
830A saturn year is 29.5 times the earth
year. How far is saturn from the moon
( (M) ) if the earth is ( 1.5 times 10^{8} k m ) away
from the sun?
11
831How is the gravitational force of attraction between two bodies affected
if:
(i) Mass of both bodies is doubled
(ii) The distance between them is
halved.
11
832Two identical spheres of gold are in
contact with each other. The
gravitational attraction between them
is
A. Directly proportional to the square of the radius
B. Directly proportional to the cube of the radius
C. Directly proportional to the fourth power of the radius
D. Inversely proportional to the square of the radius
11
833A ball of mass ( mathrm{m} ) is thrown vertically upward from the ground and reaches a height h before momentarily coming to rest.If ( g ) is acceleration due to gravity,the impulse received by the ball due to gravity force during its flight is
( mathbf{A} cdot sqrt{2 m^{2} g h} )
в. ( sqrt{4 m^{2} g h} )
( mathbf{c} cdot sqrt{8 m^{2} g h} )
D. ( 4 sqrt{m^{2} g h} )
11
834A body weighs ( 72 N ) on the surface of
earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the
surface?
B. ( 28 N )
( c .16 N )
D. 32 N
11
835If ( R ) is the radius of the earth and ( g ) the
acceleration due to gravity on the earth’s surface, then mean density of the earth is:
A ( cdot frac{4 pi G}{3 g R} )
в. ( frac{3 pi R}{4 g G} )
c. ( frac{3 g}{4 pi R G} )
D. ( frac{r g}{12 R G} )
11
836Assertion
The smaller the orbit of a planet around
the Sun, the shorter is the time it takes
to complete.
Reason
According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from Sun.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
837The value of acceleration due to gravity on the surface of the earth depends on.
A. pressure
B. acceleration
c. gravitational force between an object and the earth
D. none of these
11
838A satellite of mass ‘m’, moving around
the earth in a circular orbit of radius ( boldsymbol{R} )
has angular momentum ( L ). The areal velocity of satellite is:
( mathbf{A} cdot L / 2 m )
в. ( L / m )
( mathbf{c} cdot 2 L / m )
D. ( 2 L / m_{e} )
11
839A man weighs ( 75 k g ) on the surface of the earth. His weight in a geostationary satellite is:
A . infinity
в. ( 150 k g )
c. zero
D. ( 75 / 2 k g )
11
840The mass of the earth is ( 6 times 10^{22} k g )
and that of the moon is ( 7.4 times 10^{22} ) kg. If
the distance between the earth and the
moon is ( 3.84 times 10^{5} k m, ) calculate the
force exerted by the earth on the moon. ( G=6.7 times 10^{-11} N m^{2} k g^{-2} )
11
841Assertion
If an object is projected from the earth’s surface with escape velocity, path of the
object will be parabola.
Reason
When object is projected with a velocity less than escape velocity from horizontal surface and greater than orbital velocity, path of the object will be ellipse.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
11
842Two spheres of radius ( r=0.5 mathrm{m} ) and mass
1 kg are placed in contact with each other, what will be the gravitational force between them:
A. ( 0 N ),since the spheres are touching each other and ( r=0 )
В. ( 6.67 times 10^{-11} N )
( mathbf{c} cdot 6.67 times 10^{-4} N )
D. ( 6.67 times 10^{-6} N )
11
843Earth is flattened at poles and bulging
at equator. This is due to
A. revolution of Earth around the Sun in an elliptical orbit
B. angular velocity of spinning about its axis is more at Equator
C . centrifugal force is more at Equator than poles
D. more centrifugal force at poles than Equator
11
844Renu is standing in a dining line ( 6.38 times 10^{4} k m ) from the centre of the
earth. The mass of the earth is ( 6 times )
( 10^{24} k g )
i) Find the acceleration due to gravity
ii) Will the value change after she
finishes her lunch?
11
845Two particles are placed at some distance and the magnitude of gravitational force between them is F. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the new value of gravitational force, in terms of ( F ) between them will be:
A ( cdot frac{F}{4} )
в. ( 4 F )
c. ( frac{F}{2} )
D.
11
846How does the force of gravitation between two objects change when the distance between them is reduced to
half?
( mathbf{A} cdot F^{prime}=4 F )
В . ( F^{prime}=8 F )
( mathbf{c} cdot F^{prime}=2 F )
D. ( F^{prime}=F )
11
847A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to
the mass of the earth.
A. The acceleration of S is always directed towards the centre of earth
B. The angular momentum of S about the centre of 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
11
848A rocket starts vertically upward with
speed ( v_{0} . ) Show that its speed ( v ) at height ( h ) is given by ( v_{0}^{2}-v^{2}=frac{2 g h}{1+frac{h}{R}} )
hence ( R ) is the radius of the Earth.
11
849Weight of a body on earth’s surface is ( W . ) At a depth half way to the centre of
the earth, it will be (assuming uniform density in earth).
( mathbf{A} cdot W )
в. ( W / 2 )
c. ( W / 4 )
D. ( W / 8 )
11
850Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object
A) so that only its gravitational potential energy changes. How many times does the height of object B change compared to the height change of object ( A, ) as result of the work done?
A. object B changes height four times as much as object
A changes height
B. Object B changes height sixteen times as much as object A changes height
c. object B changes height two times as much as object
A changes height
D. object B changes height less than two times as much as object A changes height (but not the same amount
E. object B changes height the same amount as object changes height
11
851If the mass of the earth increases by ( 80 % ) and radius of the earth increases
by ( 40 % ) then the percentage charge in acceleration due to gravity on the surface of radius of earth is (where ( g_{s}=frac{G M}{R^{2}}, M= ) mass of earth and ( R= ) radius of earth ( } ) )
A. zero
B . ( +8.16 % )
c. ( -8.16 % )
D. ( 160 % )
11
852The dependence of acceleration due to gravity g on the distance r from the centers of the earth assumed to be a
sphere of radius ( R ) of uniform density is as shown figure below.
The correct figure is
( (i) )
(ii)
(iii)
(iv)
( A cdot(i) )
B. (ii)
( c )
D. Güvüù
11
853Assertion : The acceleration due to
gravity on the moon is one-sixth that on
the earth.
Reason : The law of gravitation is the
same on both the moon and the earth.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false
11
854If the distance between two masses is
doubled, the gravitational attraction between them Is doubled
A . Is doubled
B. Becomes 4 times
c. Is reduced to half
D. Is reduced to a quarter
11
855In an earth satellite moving in a circular orbit, a piece of metal weighing ( 16 g ) (on the earth) is weighed by a spring balance while the metal is suspended in water. If the relative density of the
metal is ( 8, ) what weight will be
recorded?
A. ( -2 g )
B. zero
( c cdot 2 g )
D. 14 g
11
856Two planets are revolving around the
Earth with velocities ( v_{1}, v_{2} ) and in radii
( r_{1} ) and ( r_{2}left(r_{1}>r_{2}right) ) respectively. Then
A ( cdot v_{1}=v_{2} )
в. ( v_{1}>v_{2} )
c. ( v_{1}<v_{2} )
D. ( frac{v_{1}}{r_{1}}=frac{v_{2}}{r_{2}} )
11
857The gravitational force with which the
earth attracts the moon:
A. Is less than the force with which the moon attracts the earth
B. Is equal to the force with which the moon attracts the earth
c. Is greater than the force with which the moon attracts the earth
D. Varies with the phases of the moon
11
858One mega joule approximately equals
( A cdot 240 mathrm{kcal} )
B. 2400 kcal
c. 24 kcasl
D. 2.4 kcal
11
859Two balls, each of radius ( R ), equal mass
and density are placed in contact, than the force of gravitation between them is
proportional to
( ^{mathrm{A}} cdot F propto frac{1}{R^{2}} )
в. ( F propto R )
( c cdot F propto R^{4} )
D. ( F propto frac{1}{R} )
9
860The length of time a satellite takes to orbit the earth depends on its:
A. launch speed
B. mass
c. distance from the earth
D. weight
E. orbital direction
11
861G’ represents
I. Mutual conductance
II. Gibbs function
III. Gravitational constant
Which combination is correct?
A. Il and III only
B. I and III only
c. ॥ only
D. I, I land III
11
862While orbiting around the earth in a spaceship, an astronaut weight becomes
A. greater than their real weight
B. lesser than their real weight
c. zero
D. infinity
11
863Taking the earth to be a uniform sphere of radius ( 6400 mathrm{km} ) and the value of ( g ) at
the surface to be ( 10 mathrm{m} s^{-2} ), calculate the
energy needed to raise a satellite of
mass ( 2000 mathrm{kg} ) to a height of ( 800 mathrm{km} ) above the earth’s surface and to set it
into circular orbit at that altitude.
B. ( 8 times 10^{10} ) J.
( mathbf{c} cdot 9 times 10^{10} J )
D. ( 1.8 times 10^{10} ) J.
11
864A satellite moving in a circular path of radius ( r ) around earth has a time period
T. If its radius slightly increases by ( 4 % ) then percentage change in its time period is:
A . ( 1 % )
B. ( 6 % )
c. ( 3 % )
D. ( 9 % )
11
865The gravitational potential at height ( h ) above the earth’s surface is ( -5.12 times )
( 10^{7} mathrm{J} / mathrm{kg} ) and acceleration due to gravity
at this point is ( 6.4 m s^{-2} . ) If radius of the
earth is ( 6400 mathrm{km} ), the value of h is :
A. ( 1200 mathrm{km} )
B. 1600 km
c. ( 1800 mathrm{km} )
D. 2400 km
11
8661 kgf ( = )
( mathbf{A} cdot 9.8 N )
В. ( 98 N )
c. ( 980 N )
D. none of these
9
867The change in the gravitational
potential energy when a body of mass ( m )
is raised to a height ( n R ) above the
surface of the earth is (here ( R ) is the
A ( cdotleft(frac{n}{n+1}right) m g R )
B ( cdotleft(frac{n}{n-1}right) m g R )
c. ( n m g R )
D. ( frac{m g R}{n} )
11
868At some planet, ( g=1.96 m s^{-2} . ) If it is
safe to jump from a height of ( 2 m ) on earth, then the corresponding safe height on that planet is
( mathbf{A} cdot 2 m )
B. ( 5 m )
c. ( 10 m )
D. ( 20 m )
11
869When an object is thrown up from the surface of the earth, the force of gravity:
A. acts in the direction of the motion
B. acts in the opposite direction of the motion
c. remains constant as the body moves up
D. increases as the body moves up
11
870Two spherical balls of mass 10 kg each are placed ( 10 mathrm{cm} ) apart.Find the
gravitational force of attraction
between them.
11
871The moon revolves round the earth 13
times in one year. If the ratio of sunearth distance to earth-moon distance
is ( 392, ) then the ratio of masses of sun
and earth will be
A . 365
B. 356
c. ( 3.56 times 10^{5} )
D.
11
872A point mass ( mathrm{m} ) is placed inside a spherical shell of radius ( mathrm{R} ) and mass ( mathrm{M} )
at a distance ( R / 2 ) from the centre of the shell. The gravitational force exerted by the shell on the point mass is?
( ^{mathbf{A}} cdot frac{G M m}{R^{2}} )
В. ( -frac{G M m}{R^{2}} )
c. zero
D. ( _{4} frac{G M m}{R^{2}} )
11
873“Action at a distance” is revealed most
prominently in:
A. Magnetic force
B. Electric force
c. Gravitational force
D. All of them
11
874Two point objects of masses 1.5 g and 2.5 g respectively are at a distance of 16 ( mathrm{cm} ) apart, the centre of gravity is at a distance ( x ) from the object of mass 1.5 g where ( x ) is:
( A cdot 10 mathrm{cm} )
B. ( 6 mathrm{cm} )
( c cdot 13 mathrm{cm} )
D. 3 cm
9
875Sl unit of gravitational constant is:
A ( cdot N^{2} m^{2} k g^{2} )
в. ( N m k g^{2} )
c. ( N^{2} m k g^{-2} )
D. ( N m^{2} k g^{-2} )
11
876Universal Gravitational Constant is
measured by
A. Newton’s Experiment
B. Cavendish’s Experiment
c. Max’s Experiment
D. de Broglie’s Experiment
11
877Two celestial bodies are separated by
some distance. If the mass of any one of the point like bodies is doubled while
the mass of other is halved then how far
should they be taken so that the gravitational force between them becomes one-fourth?
11
878An artificial satellite revolves around
the earth in a circular orbit with a speed
v. If ( m ) is the mass of the satellite, its
total energy is :
A ( cdot frac{1}{2} m v^{2} )
B. ( -frac{1}{2} m v^{2} )
( mathrm{c} cdot-m v^{2} )
D. ( frac{3}{2} m v^{2} )
11
879State two essential features of a
geostationary satellite.
11
880A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth is ( 11 mathrm{kms}^{-1} ), the escape velocity from
the surface of the planet would be
A. ( 1.1 mathrm{km} / mathrm{s} )
в. ( 11 mathrm{km} / mathrm{s} )
c. ( 110 mathrm{km} / mathrm{s} )
D. ( 0.11 mathrm{km} / mathrm{s} )
11
881Imagine a new planet having the same density as that of Earth but 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^{prime} ), then:
A ( cdot g^{prime}=3 g )
B. ( g^{prime}=frac{g}{9} )
c. ( g^{prime}=9 g )
D. ( g^{prime}=27 g )
11
882The mass of earth is 80 times that of
moon and its diameter is double that of
moon. If the value of acceleration due to
gravity on earth is ( 9.8 m s^{-2} ) then the
value of acceleration due to gravity on
moon will be?
A ( cdot 0.98 mathrm{ms}^{-2} )
В. ( 0.49 mathrm{ms}^{-2} )
c. ( 9.8 mathrm{ms}^{-2} )
D. ( 4.9 mathrm{ms}^{-2} )
11
883The areal velocity of an object of mass ( mathrm{m}=2 mathrm{kg} ) revolving around another object
is given by ( 2 m^{2} / s, ) what is the angular momentum of the particle
A ( cdot 6 k g-m^{2} / s )
в. ( 8 k g-m^{2} / s )
c. ( 4 k g-m^{2} / s )
D. ( 2 k g-m^{2} / s )
11
884Read the assertion and reason carefully to mark the correct option out of the options given below:

Assertion : Radius of circular orbit of a
satellite is made two times, then it
areal velocity will also become two
times.

Reason: Areal velocity is given as ( frac{boldsymbol{d} boldsymbol{A}}{boldsymbol{d} boldsymbol{t}}=frac{boldsymbol{L}}{boldsymbol{2 m}}=frac{boldsymbol{m} boldsymbol{v} boldsymbol{r}}{boldsymbol{2} boldsymbol{m}} )
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true

11
885Weightlessness in the satellite is due to
A. zero gravitational acceleration
B. zero acceleration
c. zero mass
D. None of these
11
886The place where the value of ‘g’ is unaffected by the increase (or) decrease in the speed of rotation of the earth about its own axis is poles
A. True
B. False
11
887Two spheres each of mass ( 10^{5} mathrm{kg} ) and
radius ( 10 mathrm{m} ) are kept in contact. Find the force of gravitation acting between them?
11
888Two bodies of masses ( m ) and ( 4 m ) are
placed at a distance ( r . ) The
gravitational potential at a point on the line joining them where the gravitational field is zero is :
A . zero
B. ( -frac{4 mathrm{Gm}}{mathrm{r}} )
( c cdot-frac{6 G m}{r} )
D. ( -frac{9 mathrm{Gm}}{mathrm{r}} )
11
889Four similar particles of mass ( mathrm{m} ) are orbiting in a circle of radius ( r ) in the
same angular direction because of their
mutual gravitational attractive force.
Velocity of a particle is given by
( A )
B. ( sqrt{frac{G m}{r}} )
c. ( sqrt{frac{G m}{2}(1+2 sqrt{2})} )
( frac{1}{2}left[frac{G m}{r}left(frac{1+2 sqrt{2}}{2}right)right]^{frac{1}{2}} )
9
890A mass ( M ) is broken in two parts : ( m )
and (M- m). What would be the relation
between ( m ) and ( M ) so that the force of
gravitation between the two parts is maximum?
A. ( m M=2 )
в. ( m=frac{M}{2} )
( mathbf{c} cdot M=m^{2} )
D. none of these
11
891Imagine 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 the planet and the star is proportional to ( R^{-5 / 2}, ) then ( T^{2} ) is
proportional to:
( mathbf{A} cdot R^{3} )
B. ( R^{7 / 12} )
c. ( R^{3 / 2} )
D. ( R^{3.75} )
11
892What is difference between ( mathrm{Nm} ) & mN?11
893A satellite of mass ( m ) revolves around
the earth of radius ( R ) at a height ( x ) from its surface. If ( g ) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
A . ( sqrt{g x} )
в. ( sqrt{frac{g R}{R-x}} )
( ^{mathrm{c}} cdot sqrt{frac{g R^{2}}{R-x}} )
D. ( sqrt{frac{g R^{2}}{R+x}} )
11
894Weight’ of a body may have the following attributes. It is the gravitational force acting on a body at the earth’s surface
II. It is independent of the mass of the
body
III. The body is weightless during free fall
IV. It is different at different places on
earth’s surface.
A . I, Il and III only
B . I, III and IV only
c. I and III only
D. I, II, III and IV
11
895Assertion
A heavy object always falls faster than a light object when dropped from a height
Reason

Gravitational force is proportional to the
mass of an object.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect

11
896If ( mathrm{M} ) is the mass of the earth and ( mathrm{R} ) its
radius, the ratio of the gravitational acceleration and the gravitational constant is given by:
A ( cdot frac{R^{2}}{M} )
в. ( frac{M}{R^{2}} )
c. ( M R^{2} )
D. ( frac{M}{R} )
11
897Suppose universal gravitational constant starts of decrease, then This question has multiple correct options
A. Length of the day on the earth will increase
B. Length of the year will increase
D. Kinetic energy of the earth will decrease
11
898How much would a W kg man weigh on the moon in terms of gravitational
units?
A ( cdot frac{W}{6} ) kg wt
B. 6 W kg wt
c. w kg wt
D. zero
9
899The value of gravitational constant ( boldsymbol{G} ) in Meter-Kilogram-Second system is ( 6.67 times 10^{-11} N-m^{2} k g^{-2} . ) What will be
its value in centimetre gram
second system.
A. ( 6.67 times 10^{-5} )
В. ( 6.67 times 10^{-9} )
( mathbf{c} cdot 6.67 times 10^{-8} )
D. ( 6.67 times 10^{-13} )
9
900In the figure ( A B=B C, A C=C D ) and
( angle A C D=90^{circ} . ) If the radius of the circle
is “r” units then find the length of the
chord BC.
A ( cdot r sqrt{sqrt{2-1}} )
B ( cdot r sqrt{sqrt{3-1}} )
c. ( r sqrt{2-sqrt{2}} )
D. ( r sqrt{2-sqrt{3}} )
11
901A man covers 60 m distance in one
minute on the surface of earth. The
distance he will cover on the surface of moon in one minute is ( left(g_{m}=frac{g_{e}}{6}right) )
( A .60 m )
в. 60 Х 6 т
c. ( frac{60}{6} m )
D. ( sqrt{60} m )
11
902An object is dropped at the surface of
the earth from the height of ( 3600 mathrm{km} ) Calculate the ratio of the weight of the body at that height and on the surface of the earth.
A .1 .34
B . 2.44
( c .6 .25 )
D. 12.32
11
903Kepler’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
11
904India’s Mangalyan was sent to the Mars
by launching it into a transfer orbit EOM around the sun. It leaves the earth at ( mathrm{E} )
and meets Mars at M. If the semi-major
axis of Earth’s orbit is ( a_{e}=1.5 times )
( 10^{11} m, ) that of Mars’s orbit ( a_{m}= )
( 2.28 times 10^{11} m, ) taken Kepler’s laws, the
estimate of time of Mangalyan to reach
Mars from Earth to be close to
A. 500 days
B. 320 days
c. 260 days
D. 220 days
11
905The motion of a planet around sun in an
elliptical orbit is shown in the following
figure. Sun is situated on one focus. The
shaded areas are equal. If the planet
takes time ( t_{1} ) and ( t_{2} ) in moving from ( A ) to
B and from ( C ) to D respectively then
( mathbf{A} cdot t_{1}>t_{2} )
B . ( t_{1}<t_{2} )
c. ( t_{1}=t_{2} )
D. information incomplete
11
906Motion of artificial earth satellites
A . Liquid fuel
B. Solar batteries
C. Atomic energy
D. None of the above
11
907Minimum percentage increase in the kinetic energy of a satellite orbiting close to the surface of the earth so that
it will escape the earth’s gravitational pull is
A . 50%
B. 150%
c. ( 100 % )
D. 200%
9
908If the distance between the earth and
the sun is half its present value, the number of days in a year would have
been
A. 730
B. 182.5
( c cdot 129 )
D. 64.5
11
909At what height from the ground will be the value of ( g ) be the same as
that in ( 10 k m ) deep mine below the
surface of earth.
( A cdot 20 mathrm{km} )
B. 7.5 km
( c cdot 5 k m )
D. 2.5 km
11
910A particle of mass ( 1 mathrm{kg} ) is placed at a distance of ( 4 mathrm{m} ) from the centre and on
the axis of a uniform ring of mass ( 5 mathrm{kg} )
and radius 3m. The work done to
increase the distance of the particle from ( 4 mathrm{m} ) to ( sqrt{3} m ) is.
A ( cdot frac{G}{3} J )
в. ( frac{G}{4} J )
c. ( frac{G}{5} J )
D. ( frac{G}{6} J )
11
911A body weighs ( 60 mathrm{kg} ) on the earth’s surface. What would be its weight at the centre of the earth?
A. 60 kg-wt
B. 6 kg-wt
c. ( 60 times 9.8 mathrm{kg} ) -wt
D. zero
11
912State and explain Universal law of Gravitation. Give its vector form.11
913When a fruit falls from a tree,
A. only the earth attracts the fruit
B. both the earth and the fruit attract each other
C . only the fruit attracts the earth
D. they repel each other
9
914When a satellite falls to an orbit of
A . Decrease
B. Increase
c. Remains same
D. Nothing can be predicted
11
915If velocity of a satellite is half of escape velocity, then distance of the satellite from earth surface will be.
A. ( 6400 k m )
B. ( 12800 k m )
c. ( 6400 sqrt{2} k m )
D. ( frac{6400}{sqrt{2}} k m )
11
916Weightlessness experienced while orbiting the earth in a spaceship is the result of
A. Inertia
B. Accelaration
c. zero gravity
D. Centre of gravity
11
917What is the geometrical interpretation of infinity for gravitational field and gravitational potential?11
918Weightlessness experienced in a spaceship is due to
A. absence of of inertia.
B. absence of gravity
c. absence of accelerating force.
D. free fall of the spaceship
11
919State whether true or false.
The direction of acceleration due to
gravity is always vertically downward.
A. True
B. False
11
920A spherical uniform planet is rotating about its axis. The velocity of a point on
its equator is ( V ). Due to the rotation of
a planet about its axis the acceleration due to gravity ( g ) at equator is ( frac{1}{2} ) of ( g ) at
poles. The escape velocity of a particle
on the pole of a planet in terms of ( V ) is
A ( cdot V_{e}=2 V )
B. ( V_{e}=V )
( mathrm{c} cdot_{V_{e}}=frac{V}{2} )
D. ( V_{e}=sqrt{3} V )
11
921A planet of mass ( M ) moves around the
Sun along an ellipse so that its minimum distance from the Sun is
equal to ( r ) and the maximum distance
to
( R ) Making use of Kepler’s laws, find
its period of revolution around the Sun.
11
922The force acting on a mass of 1 g due to the gravitational pull on the earth is called 1 g wt. One ( g ) wt equals
A . ( 1 mathrm{N} )
B. 9.8N
c. 980 dyne
D. None of these
11
923Four particles having masses ( mathrm{m}, 2 mathrm{m}, 3 mathrm{m} ) and ( 4 mathrm{m} ) are placed at the four corners
of a square of edge a. Find gravitational force acting on a
particle of mass ( mathrm{m} ) place at the center.
11
924A hole is drilled along the earth’s diameter and a stone is dropped into it.
When the stone is at the centre of the
earth, it has.
A. Acceleration
B. Weight
c. Mass
D. Potential energy
11
925If the radius of the earth is increased
by three times, keeping the mass constant, then the weight of a body on the earth surface will be
as compared to its previous value
A . one third
B. one ninth
c. three times
D. nine times
11
926Three uniform spheres, each having mass ( mathrm{m} ) and radius ( mathrm{r}, ) are kept in such a way that each touches the other two.
The magnitude of the gravitational
force on any sphere due to the other two is?
A ( cdot frac{G m^{2}}{r^{2}} )
в. ( frac{G m^{2}}{4 r^{2}} )
c. ( sqrt{2} frac{G m^{2}}{4 r^{2}} )
D. ( sqrt{3} frac{G m^{2}}{4 r^{2}} )
11
927The energy required to remove a body of mass ‘m’ from earths surface is/are
equal to:
( mathbf{A} cdot-mathbf{G M m} / mathrm{R} )
в. ( mathrm{mgR} )
c. -mgR
D. none of these.
11
928The weight of a body at the centre of the earth is
A. zero
B. Equal to its mass
c. Maximum
D. Infinite
11
929The escape velocity for a rocket on the earth is ( 11.2 mathrm{km} / mathrm{sec} ). Its value on a planet where acceleration due to gravity
is twice that on the earth and the
diameter of the planet is twice that of the earth, will be (in ( k m / s e c ) ):
A . 11.2
B. 5.6
c. 22.4
D. 33.6
11
930A body is weighed by a spring balance
to be ( 1000 mathrm{N} ) at the north pole. How much will it weigh(in ( mathrm{N} ) ) at the equator? Account for the earth’s rotation only.
11
931In the figure it is shown that the velocity
of lift is ( 2 mathrm{ms}^{-1} ) while string ins winding
on the motor shaft with velocity ( 2 mathrm{ms}^{-1} )
and shaft ( A ) is moving downward with
velocity ( 2 mathrm{ms}^{-1} ) with respect lift, then find
out the velocity of block ( mathrm{B} )
( mathbf{A} cdot 2 mathbf{m s}^{-1} uparrow )
B. ( 2 mathrm{ms}^{-1} downarrow )
( mathbf{C} cdot 4 mathrm{ms}^{-1} uparrow )
D. None of these
11
932A body is suspended from a spring balance kept in a satellite The reading
of the balance is ( W_{1} ) when the satellite
goes in an orbit of radius ( R ) and is ( W_{2} )
when it goes in an orbit of radius ( 2 R ) Then
A. ( W_{1}=W_{2} )
B. ( W_{1}W_{2} )
D. ( W_{1} neq W_{2} )
11
933The force of attraction between two unit
point masses separated by a unit distance is called
A. Gravitational potential
B. Acceleration due to gravity.
c. Gravitational field
D. Universal gravitational constant.
11
934The minimum energy required to
launch a ( m ) kg satellite from earth’s surface in a circular orbit at an altitude
of ( 2 R ) where ( R ) is the radius of earth, will
be:
( mathbf{A} cdot 3 m g R )
в. ( frac{5}{6} ) mg ( R )
c. ( 2 m g R )
D. ( frac{1}{5} m g R )
11
935A planet revolves around the sun in an
orbit with an eccentricty ( =0.99, ) the orbit is:
A. almost circular
B. almost elliptical
c. almost straight
D. parabolic
11
936Figure shows the elliptical path of a
planet around the sun. The two shaded
parts have equal areas. If ( t_{1} ) and ( t_{2} ) be
the time taken by the planet to go from
( a ) to ( b ) and from ( c ) to ( d ) respectively, then
( mathbf{A} cdot t_{1}t_{2} )
D. Insufficient information to deduce the relation
between ( t_{1} ) and ( t_{2} )
11
937If earth’s radius were to hypothetically shrink by ( 1 % ), the value of ( G ) would
A. shrink by ( 1 % )
B. expand by ( 1 % )
c. remain the same
D. shrink by ( 0.01 % )
11
938Planets rotate around the Sun in a path
best described as
A. elliptical
B. circular
c. parabola
D. none of the above
11
939A person sitting in a satellite orbiting earth feels weighlessness due to
A. Centripetal acceleration
B. Tangential velocity
c. Large distance from earth
D. zero gravity
11
9401 kgwt is equal to
( mathbf{A} cdot 9.8 N )
B. ( 980 N )
( mathbf{c} .98 N )
D. none of these
9
the earth is best represented by ( :(R rightarrow )
( A )
B.
( c )
( D )
11
942If ( g ) is the acceleration due to gravity on
the Earth’ surface, find the gain in
potential energy of a body of mass ( m ) when taken from the surface of Earth at
a height equal to the radius ( R ) of the
Earth.
11
943The earth pull all objects towards
A. It’s periphery
B. It’s centre
C. Both centre and periphery
D. Earth never pulls any objects.lt is the inbuilt attractive force in a body which attracts it downwards
11
944An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface
of the earth of two earth radii ( (h=2 R )
where ( R ) is the radius of the earth.
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)
A. 81 pounds
B. 40.5 pounds
c. 18 pounds
D. 54 pounds
E. 0 pounds (astronaut is weightless
11
945tood
sonmon
voe vourg
11
946The gravitational force between two objects placed at a distance r is proportional to
( mathbf{A} cdot r )
в. ( r^{2} )
c. ( frac{1}{r^{2}} )
D. ( frac{1}{r} )
11
947The largest and the shortest distance of
the earth from the sun is ( r_{1} ) and ( r_{2} ). Its
distance from the sun when it is at
perpendicular to the major axis of the orbit drawn from the sun:
( mathbf{A} cdotleft(r_{1}+r_{2}right) / 4 )
B . ( left(r_{1}+r_{2}right) /left(r_{1}-r_{2}right) )
( mathbf{c} cdot 2 r_{1} r_{2} /left(r_{1}+r_{2}right) )
D. ( left(r_{1}+r_{2}right) / 3 )
11
948(1) Mass of a book is 500 g on thew surface of the earth. what will be its
mass at a height equal to radius of earth
(2) find the weight of the book at the
surface of the earth
9
949i) Space Stations are used to study the effects of long-space flight on the human body. Justify.
ii) ( boldsymbol{F}=boldsymbol{G} boldsymbol{m}_{1} boldsymbol{m}_{2} / boldsymbol{d}^{2} ) is the
mathematical form of Newton’s law of
gravitation, ( G- ) gravitational constant
( m_{1} m_{2}, ) are the masses of two bodies
separated by a distance ( d ), then given
the statement of Newton’s law of
gravitation.
11
950The mass of the earth is ( 6.00 times 10^{24} k g )
and that of the moon is ( 7.40 times 10^{22} k g )
The constant of gravitation ( G= )
( 6.67 times 10^{-11} N m^{2} k g^{-2} ). calculate
gravitational force of attraction.
( mathbf{A} cdot 38 times 10^{18} )
В. ( 20.2 times 10^{19} )
c. ( 7.60 times 10^{8} )
D. ( 1.90 times 10^{8} )
11
951If the distance between two object in increase two times, they by how many times will the mass of one of the object
be change to maintain the same gravitational force?
11
952While orbiting around the earth in a apaceship, an astronaut experiences
A. more weight
B. lesser weight
c. weightlessness
D. nothing at all
11
953When a satellite has an elliptical orbit, the plane of the orbit
A. sometimes passes through the centre of earth
B. does not pass through the centre of earth
c. passes through the centre of earth always
D. none of the above
11
954A planet has a core and on outer shell of
radii ( boldsymbol{R} ) and ( 2 boldsymbol{R} ) respectively. The density
of the core is ( x ) and that of outer shell is
( y . ) The acceleration due to gravity at
the surface of planet is same as that at
depth ( R ) The ratio of ( x ) and ( y ) is ( frac{-}{3} . ) Find
( n )
11
955An extremely small and dense neutron star of mass ( M ) and radius ( R ) is
rotating at an angular frequency ( omega . ) If an object is placed at its equator, it will remain stuck to it due to gravity if
A ( cdot M>frac{R omega}{G} )
в. ( _{M}>frac{R^{2} omega^{2}}{G} )
( ^{mathbf{C}} cdot M>frac{R^{3} omega^{2}}{G} )
D. ( M>frac{R^{2} omega^{3}}{G} )
11
956If ( W_{1} ) work is done against gravitational
attraction to carry ( 10 mathrm{kg} ) mass from earth’s surface to infinity, then the magnitude of work done by the gravitational attraction in bringing 20 kg mass from infinity to the centre of earth is
( mathbf{A} cdot 2 W_{1} )
в. ( 3 W_{1} )
( c cdot frac{w_{1}}{2} )
D. ( 4 W_{1} )
11
957If the gravitational constant is expressed in terms of dynesm( ^{-2} boldsymbol{k g}^{2} )
how will the value of G change:
A ( .6 .67 times 10^{-11} ) dynes ( k g^{2} m^{-2} )
B . ( 6.67 times 10^{-8} ) dynes ( k g^{2} m^{-2} )
c. ( 6.67 times 10^{-6} ) dynes ( k g^{2} m^{-2} )
D. ( 6.67 times 10^{-3} ) dynes ( operatorname{kg}^{2} m^{-2} )
11
958Calculate the period of revolution of Jupiter around the Sun. The ratio of the
radius of Jupiter’s orbit to that of the Earth’s orbit is 5
(Period of revolution of the Earth is 1
year)
11
959If the spinning speed of the earth is
decreased, then the weight of the body
at the poles.
A. does not change
B. Decresing
c. incresing
D. may increase and decrease
11
960then velocity in circular orbits is given ( operatorname{as} sqrt{frac{boldsymbol{x} boldsymbol{G} boldsymbol{M}}{boldsymbol{r}}} . ) Find ( boldsymbol{x} )11
961The mass of the moon is about ( 1.2 % ) of
the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the
moon exerts on earth
A. Is the same
B. Is smaller
c. Is greater
D. Varies with its phase
9
962Gravitational potential energy is
negative. This implies
A. Energy is rising along negative ( x ) axis
B. A particle is trapped in this potential
C. The particle is moving in the opposite direction
D. Energy is decreasing in the direction of motion of the particle
11
963Two satellites ( A ) and ( B ) of equal mass
move in the equatorial plane of the earth, close to earth’s surface. Satellite A moves in the same direction as that of
the rotation of the earth while satellite ( mathrm{B} )
moves in the opposite direction. Calculate the ratio of the kinetic energy of ( mathrm{B} ) to that of ( mathrm{A} ) in the reference frame
fixed to the earth. ( left(g=9.8 m s^{-2} ) and right.
radius of the earth ( =mathbf{6 . 3 7} times mathbf{1 0}^{6} mathbf{k m} ) ).
11
964A satellite is revolving in a circular
equatorial orbit of radius ( boldsymbol{R}=mathbf{2} times mathbf{1 0}^{mathbf{4}} )
( mathrm{km} ) from east to west. Calculate the
interval after which it will appear at the same equatorial town. Given that the
radius of the earth ( =6400 mathrm{km} ) and
g(acceleration due to gravity) ( =10 mathrm{m} ) ( s^{-2} )
11
965A planet revolves round the sun in an
elliptical orbit of semi minor and major
axes ( x ) and ( y ) respectively. Then the time period of revolution is proportional to:
D. ( frac{3}{y^{frac{3}{2}}} )
11
966If both the mass and radius of the earth
decrease by ( 1 % ) the value of This question has multiple correct options
A. acceleration due to gravity would decrease by nearly ( % )
B. acceleration due to gravity would increase by 1%
c. escape velocity from the earth’s surface would decrease by ( 1 % )
D. the gravitational potential energy of a body on earth’s’s surface will remain unchanged
11
967An earth’s satellite moves in a circular
orbit with an orbital speed ( 6280 mathrm{ms}^{-1} )
Find the time of revolution.
A. 130 min
B. 145 min
c. 155 min
D. 175 min
11
968A spaceship is launched into a circular orbit close to earth’s surface. The
additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is:
(Radius of earth ( =6400 k m ) and ( g= )
( mathbf{9 . 8 m} quad boldsymbol{s}^{-1} mathbf{)} )
( begin{array}{lll}text { A } cdot & 11.2 k m & s^{-1}end{array} )
( mathbf{B} cdot 8 k m quad s^{-1} )
( begin{array}{ll}text { c. } 3.2 k m & s^{-1}end{array} )
D. ( 1.5 k m quad s^{-} )
11
969The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately 81 times the mass of the Moon and the
distance between the Earth and the
Moon is ( 3,85,000 k m . )
A. ( 36,000 mathrm{km} ) from the Moon
B. 38,500 km from the Moon.
c. ( 34500 mathrm{km} ) from the moon
D. 30,000 km from the Moon
11
970Two stars of masses ( m_{1} ) and ( m_{2} ) are
parts of a binary star system. The radii
of their orbits are ( r_{1} ) and ( r_{2} ) respectively,
measured from the centre of mass of
the system. The magnitude of
gravitational force ( boldsymbol{m}_{1} ) exerts on ( boldsymbol{m}_{2} ) is
then
A. ( frac{m_{1} m_{2} G}{left(r_{1}+r_{2}right)^{2}} )
в. ( frac{m_{1} G}{left(r_{1}+r_{2}right)^{2}} )
c. ( frac{m_{2} G}{left(r_{1}+r_{2}right)^{2}} )
D. ( frac{Gleft(m_{1}+m_{2}right)}{left(r_{1}+r_{2}right)^{2}} )
11
971What is the energy required to move a body of mass ( mathrm{m} ) from orbit of radius ( 2 mathrm{r} )
to ( 3 r ? )
11
972The weight of an object at the centre of
the earth of radius R is
A. zero
B. infinite
C . ( R ) times the weight at the surface of the earth
D. ( 1 / R^{2} ) times the weight at surface of the earth
11
973The rotation of the Earth having radius ( mathrm{R} ) about its axis speed upto a value
such that a man at latitude angle ( 60^{circ} )
feels weightless. The duration of the day in such case will be.
( ^{mathrm{A}} cdot_{8 pi} sqrt{frac{R}{g}} )
в. ( 8 pi sqrt{frac{g}{R}} )
( ^{c} cdot sqrt{frac{R}{g}} )
D. ( 4 pi sqrt{frac{g}{R}} )
11
974If the density of a planet is double than
that of the earth and the radius is 1.5
times that of the earth, the acceleration
due to gravity on the surface of the planet is
( A )
( frac{3}{4} ) times that on the surface of earth
B. 3 times that on the surface of earth
c. ( frac{4}{3} ) times that on the surface of earth
D. 6 times that on the surface of earth
11
975Figure shows the orbit of a planet ( mathrm{P} )
round the sun ( S . A B ) and ( C D ) are the
minor and major axes of the ellipse. If ( t_{1} )
is the time taken by the planet to travel
along ( A C B ) and ( t_{2} ) the time along ( B D A )
then:
A ( cdot t_{1}=t_{2} )
B ( cdot t_{1}>t_{2} )
( mathbf{c} cdot t_{1}<t_{2} )
D. nothing can be concluded
11
acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of
oscillations. The observations are
shown in the following table. Least count for length ( =0.1 mathrm{cm}, ) Least count for
time ( =0.1 s )
Length of ( quad ) Number of Student Pendulum ( quad ) oscillations ( (n) )
[
begin{array}{l}
(mathrm{cm}) \
64.0
end{array}
]
[
64.0
]
[
20.0
]
If ( boldsymbol{E}_{boldsymbol{I}}, boldsymbol{E}_{boldsymbol{I I}}, boldsymbol{E}_{boldsymbol{I I I}} ) are the percentage errors
in ( g, ) i.e., ( left(frac{Delta g}{g} times 100right) ) for students I, II and
III, respectively, then
A ( cdot E_{I}=0 )
B. ( E_{I} ) is minimum
( mathbf{c} cdot E_{I}=E_{I I} )
D. ( E_{I I} ) is maximum
11
977If a rock is brought from the surface of
the moon
A. its mass will change
B. its weight will change, but not mass
c. both mass and weight will change
D. its mass and weight will remain the same
9
978When a body is at a depth ‘d’ from the earth surface its distance from the
centre of the earth is
A ( cdot(R-d) )
В. ( 2(R-d) )
c. ( (3 R-d) )
D. ( (R-2 d) )
11
979An iron sphere of mass ( 10 mathrm{kg} ) has the
same diameter as an
aluminium sphere of mass is ( 3.5 mathrm{kg} ) Both spheres are dropped simultaneously from a tower. When they are ( 10 mathrm{m} ) above the ground, they have
the same
A. acceleration
B. momenta
c. potential energy
D. kinetic energy
11
980As the planet revolves from point ( mathrm{P} ) to
point ( Q, ) the velocity of the planet.
A. Increases
B. Decreases
c. Remains same
D. Equal is magnitude and opposite in direction
11
981Acceleration due to gravity on moon is
0.166 times than that on the earth. ( A )
man weighing 60kg on earth would weigh ( _{text {十一一一一一一一一一 }} ) on moon
A. ( 60 mathrm{kg} )
в. 30kg
c. ( 16.6 mathrm{kg} )
D. ( 10 mathrm{kg} )
11
982The weight of a person on earth is ( 600 N . ) His weight on moon will appear
as:
A . zero
B. ( 100 N )
c. ( 600 N )
D. 3600 N
9
983Kepler’s third law states that square of
period of revolution ( (boldsymbol{T}) ) of a planet
around the sun, is proportional to third
power of average distance ( r ) between
sun and planet
i.e ( T^{2}=K r^{3} ) here ( K ) is constant.
If the masses of sun and planet are ( boldsymbol{M} )
and ( m ) respectively than as per
Newton’s law of gravitation force of attraction between them is ( boldsymbol{F}=frac{boldsymbol{G} boldsymbol{M} boldsymbol{m}}{boldsymbol{r}^{2}}, ) here ( boldsymbol{G} ) is gravitational
constant The relation between ( G ) and ( K )
is described as
A. ( K=G )
c. ( G K=4 pi^{2} )
D. ( G M K=4 pi^{2} )
11
984The value of universal gravitational
constant ( G ) is-
A. ( 6.67 times 10^{-11} frac{N m^{2}}{k g} )
в. ( 6.67 times 10^{-11} frac{N m^{2}}{k g^{2}} )
c. ( 66.7 times 10^{-11} frac{N m^{2}}{k g^{2}} )
D. ( _{66.7} times 10^{-11} frac{N m^{2}}{k g} )
11
985The ratio of acceleration due to gravity
at a depth ( h ) below the surface of earth
and at a height ( h ) above the surface for
( boldsymbol{h}<<boldsymbol{R} )
A. is constant
B. increases linearly with h.
c. varies parabolically with h.
D. decreases.
11
986The value of acceleration due to gravity at a height ( R ) from surface of the earth is then(R=radius of the earth and
geacceleration due to gravity on earth surface
( mathbf{A} cdot mathbf{0} )
в. ( sqrt{g} )
c. ( frac{g}{4} )
D. ( frac{g}{2} )
11
987State whether the given statement is True or False :

The value of G depends upon the mass of the two objects.
A. True
B. False

11
988When a small mass ( m ) is suspended at
lower end of the elastic wire having upper end fixed with ceiling. There is loss in gravitational potential energy.
let it be ( x, ) due to extension of wire,
mark correct option,
A. The lost energy can be recovered
B. The lost energy can be irrecoverable
C . only ( frac{x}{2} ) amount of energy recoverable
D. only ( frac{x}{3} ) amount of energy recoverable
11
989The mean distance of Jupiter from the
sun is nearly 5.2 times the corresponding distance between earth and sun. Using Kepler’s Law, find the period of revolution of Jupiter in its
orbit.
11
990Two particles of masses ( m ) and ( M ) are
initially at rest at an infinite distance
apart. They move towards each other
and gain speeds due to gravitational attraction. Find their speeds when the separation between the masses becomes equal to ( d )
11
991Gravitational potential energy of interaction of a system of two particles
of masses ( m_{1} ) and ( m_{2} ) separated by a
distance ( r )
( U=-frac{G m_{1} m_{2}}{r} )
11
992The length of the day from today when the sun is directly overhead till tomorrow again when the sun is directly overhead can be determined by the
A. rotation of earth about its own axis
B. revolution of earth around sun
c. inclination of axis of rotation of earth from the plane of revolution.
D. rotation of earth about its own axis as well as its revolution around sun
11
993What should be the initial downward
speed of the racketeer so that he
catches the student at the top of 100 th
floor for safe landing?
A. It can have many values
B . ( 180 mathrm{ms}^{-1} )
c. ( 137.1 mathrm{ms}^{-1} )
D. cannot be determined
11
994The masses and the radii of the earth
and the moon are ( M_{1}, R_{1} ) and ( M_{2}, R_{2} )
respectively. Their centres are at a
distance ( d ) apart. Find the minimum
speed with which a particle of mass ( boldsymbol{m} )
should be projected from a point
midway between the two centres so as to escape it to infinity.
11
995A planet was suddenly stooped in its orbit supposed to be circular. The time it will fall on to the sun is, if time period
of planet’s revolution is ( T )
A ( cdot frac{T}{2} )
в. ( frac{sqrt{2} T}{4} )
c. ( frac{sqrt{2} T}{8} )
D. ( sqrt{2} T )
11
996A body falls through a distance ‘h’ in a
certain time on the earth. Then if the
same body is related on another planet having mass and radius twice as that of the earth, the distance through which it falls in the same time is:
( A cdot frac{h}{2} )
в. ( 2 h )
( c cdot h )
D. ( 4 h )
11
997What is the magnitude of the gravitational force between the Earth
and ( 1 k g ) object on its surface?
(Mass of the Earth is ( 6 times 10^{24} k g ) and
radius of the Earth is ( 6.4 times 10^{6} m )
A. 9.770
B. 10 N
( c cdot 9 N )
D. 9.5 N
11
998The earth’s radius is ( mathrm{R} ) and acceleration
due to gravity at its surface is g. If a
body of mass ( m ) is sent to a height ( h= ) ( boldsymbol{R} )
( frac{i}{5} ) from the earth’s surface, the
potential energy increases by
A . mgh
в. ( frac{4}{5} m g h )
c. ( frac{5}{6} ) mgh
D. ( frac{6}{7} ) mgh
11
999Astronauts on the orbiting space
station are weightless because…
A. there is no gravity in space and they do not weigh anything.
B. space is a vacuum and there is no gravity in a vacuum.
C. space is a vacuum and there is no air resistance in a
vacuum
D. None of the reasons given above are correct
11
1000Acceleration due to gravity at surface of a planet is equal to that at surface of
the earth and density is 1.5 times that of earth. if radius of earth is ( R ), radius of
planet is
A ( cdot frac{R}{1.5} )
в. ( frac{2}{3} R )
c. ( frac{9}{4} R )
D. ( frac{4}{9} R )
11
1001The angular momentum of the earth revolving round the sun, is proportional
to ( r^{n}, ) where ( r ) is the distance between
the centres of earth and the sun. The
value of ( n ) is :
A . 1
B. -2
c. -1
D. ( frac{1}{2} )
11
1002Gravitational force can be repulsive.
A. True
B. False
9
1003A geo-stationary satellite is orbiting around earth at height of ( 30,000 mathrm{km} ) in circular orbit. The radius of the earth is
taken as ( 6000 mathrm{km} . ) The geo-stationary satellite comes back to its position
after one revolution in exactly 24 hours.
Let the acceleration due to gravity ( (g) ) ( 10 m / s^{2} ) and mass of satellite be 1000
kg; calculate the work done in 12 hours when moving under gravitational force.
A ( left..3 .6 pi times 10^{14}rightrfloor )
В ( cdot 2 pi times 7.2 pi times 10^{14} )
C ( .1 .8 pi times 10^{14} mathrm{J} )
D. 0
11
1004Read the assertion and reason carefully
to mark the correct option out of the
options given below:
Assertion: When radius of orbit of a
satellite is made 4 times, its time period becomes 8 times. Reason : Greater the height above the surface of earth, greater is the time period of revolution.
A. If both assertion and reason are true and the
reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason
is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true
11
1005A particle is kept at rest at a distance ( boldsymbol{R} ) (earth’s radius) above the earth’s surface. The minimum speed with which it should be projected so that it does not return is
A ( cdot sqrt{frac{G M}{4 R}} )
в. ( sqrt{frac{G M}{2 R}} )
c. ( sqrt{frac{G M}{R}} )
D. ( sqrt{frac{2 G M}{4 R}} )
11
1006A solld sphere of radıus ( r ) Is tloating at
the interfare of two immiscible liquids
of densities ( p_{1} ) and ( p_{2}left(p_{2}>p_{1}right), ) half of
its volume lying in each. The height of
the upper liquid column from the
interfare of the two liquids is ( h . ) The
force exerted on the upper liquid is
(atmosphere pressure ( =p_{o} ) and
acceleration due to gravity is ( g ) ):
( ^{mathbf{A}} cdot p_{0} pi r^{2}+left(h-frac{2}{3 r}right) pi r^{2} p_{1} g )
B. ( left(h-frac{2}{3 r}right) pi r^{2} p_{1} g )
c. ( frac{2}{3} pi r^{3} p_{1} g )
( mathbf{D} cdot P_{0} times pi r^{2} )
11
1007A body of weight ( 72 mathrm{N} ) moves from the surfaceof earth at a height half of the radius of theearth, then gravitational force exerted on it will be :
A. 36 N
в. 32 N
c. 144 N
D. 50 N
11
1008The escape velocity for a body projected vertically upwards from the surface of earth is ( 11 mathrm{km} / mathrm{s} ). If the body is projected
at an angle of ( 45^{0} ) with the vertical, the escape velocity will be
A. ( 11 sqrt{2 mathrm{km} / mathrm{s}} )
.
B. 22 km/s
c. ( 11 mathrm{km} / mathrm{s} )
D. ( 11 / sqrt{2 mathrm{m}} / mathrm{s} )
11
1009At perihelion, the gravitational potential energy of Pluto in its orbit has
A. its maximum value
B. its mimimum value
c. the same value as at every other point in the orbitt
D. value which depends on sense of rotation
11
1010whose hemispherical base is of
diameter ( 0.20 mathrm{m} . ) The height of the flask
is ( 0.25 mathrm{m} ). The flask is filled to the brim
with 2.5 litres ( left(1 text { litre }=10^{-3} m^{3}right) ) of
water and sealed with a glass lid.
What is the approximate magnitude of
the total vertical force exerted by the
water on the curved surface of the
flask? (Take the acceleration due to
gravity, ( g, ) to be ( 10 m s^{-2} ) ).
( A cdot O N )
B. 78.5
c. 53.5 N
D. 25.0
11
1011In the relation ( F=frac{G M m}{r^{2}}, ) the quantity ( G )
A. depends on the value of ( g ) at the place of observation.
B. is used only when the earth is one of the two masses.
C. is greatest at the surface of the earth
D. is universal constant in nature.
11
1012There are ( _{–} ) gravitational lines of force inside a spherically symmetric shell
A. Infinitely many
B. Zero
c. varying number depending upon surface area
D. Varying number depending upon volume
11
1013The gravitational force between two
particles is ( F, ) if the objects are stationary and separated by a distance of ( 1 mathrm{m} ). If the objects starts moving in opposite directions, from rest with
uniform acceleration of ( a=1 m / s^{2} )
then the force between them after 3 secs will be
A. 4 F/ 5
B. F/100
c. ( 4 F / 121 )
D. F/2
11
1014What is the gravitational potential
energy?
11
1015Mass of an object on moon will be
A. One sixth of its value on earth
B. Ten times it’s value on earth
c. six times it’s value on earth
D. Same as on earth
9
1016The acceleration due to gravity is:
A. more at the equator than at the poles
B. not effected by the rotation of the earth
C. affected by the rotation of the earth
D. not effected by the latitude
11
1017Calculate the distance from the surface
of the earth at which the acceleration
due to gravity is the same below and
above the surface of the earth.
11
1018The acceleration due to gravity at a
place is ( 0.2 m / s 2 . ) Find its height above
the earth’s surface.
11
1019If a particle is slowly brought from
reference point to another point ( boldsymbol{P} ) in a gravitational field, then work done per
unit mass by the external agent is (at that point)
A. gravitational force
B. gravitational field intensity
c. gravitation potential
D. none of the above
11
the surface of Mars it is ( 4.0 m s^{-2} . A 60 )
kg passenger goes from the Earth to the
Mars in a spaceship moving with a constant velocity. Neglect all other
objects in the sky. Which part of figure
best represents the weight (net gravitational force) of the passenger as
a function of time.??
( A )
B. B
( c cdot c )
( D )
11
1021A particle of mass ( mathrm{M} ) is situated at the
centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be
A. ( -frac{3 G M}{a} )
В. ( -frac{2 G M}{a} )
c. ( -frac{G M}{a} )
D. ( -frac{4 G M}{a} )
11
1022The kinetic energy needed to project a body of mass ( m ) from earth’s surface
radius ( R ) ) to infinity is
A ( cdot frac{m g R}{2} )
в. ( 2 m g R )
c. ( m g R )
D. ( frac{m g R}{4} )
11
1023An artificial satellite in the presence of frictional forces will move into an orbit
closer to the earth and may have increased kinetic energy. Explain this.
11
1024Find the binding energy of a body of
mass ( 50 mathrm{kg} ) at rest on the surface of the
earth.
( operatorname{given} G=6.67 times 10^{-11} N m^{2} / k g^{2} )
( boldsymbol{R}=mathbf{6 4 0 0 k m}, boldsymbol{M}=mathbf{6} times mathbf{1 0}^{mathbf{2 4}} boldsymbol{k g} )
11
1025If suddenly the gravitational force of attraction between earth and a satellite
revolving aroung it becomes zero, then the satellite will
A. continue to move in its orbit with same velocity
B. Move tangentialy to the original orbit with the same velocity
c. Become satationary in its orbit
D. Move towards the earth
9
1026Two particles of masses ( m_{1} ) and ( m_{2} ) initially at rest at infinite distance from each other, move under the action of
mutual gravitational pull. Show that at any instant their relative velocity of approach is ( sqrt{2 Gleft(m_{1}+m_{2}right) / R, text { where }} ) ( mathrm{R} ) is their separation at that instant.
11
1027The maximum and minimum distance
of earth from sun are ( r_{1} ) and ( r_{2} )
respectively What will be the distance of earth from sun when its position vector is perpendicular to the major axis of its orbit
A ( cdot frac{r_{1}+r_{2}}{4} )
в. ( left(frac{r_{1}+r_{2}}{r_{1}-r_{2}}right) )
c. ( frac{2 r_{1} r_{2}}{r_{1}+r_{2}} )
D. ( frac{r_{1}+r_{2}}{3} )
11
1028The kinetic energy needed to project a body of mass ( m ) from the earth surface
(radius ( R ) ) to infinity is
( mathbf{A} cdot m g R / 2 )
в. ( 2 m g R )
( c . m g R )
D. ( m g R / 4 )
11
1029A satellite of mass m revolves around
the earth of radius ( R ) at a height ( x ) from its surface. If ( g ) is the acceleration due
to gravity on the surface of the earth, the orbital speed of the satellite is
( mathbf{A} cdot g x )
B. ( sqrt{frac{g R^{2}}{R+x}} )
c. ( frac{g R^{2}}{R+x} )
D. ( frac{g R}{R-x} )
11
1030If the earth stops rotating about its axis, then the magnitude of gravity
A. increases everywhere on the surface of earth
B. will increase only at the poles
c. will not change at the poles
D. All of the above
11
1031A planet of mass ( m ) is moving in an elliptical orbit round the sun of mass
( M . ) If the maximum and minimum
distances of the planet from the sun be
( l_{1} ) and ( l_{2}, ) the angular momentum of
the planet about the sun will be
A ( cdot m frac{G M m}{sqrt{left(l_{1}+l_{2}right)}} )
в. ( m sqrt{frac{l_{1}+l_{2}}{G M l_{1} l_{2}}} )
c. ( m sqrt{frac{2 G M l_{1} l_{2}}{left(l_{1}+l_{2}right)}} )
( D )
11
1032Two stationary particles of masses ( mathbf{M}_{1} )
and ( mathrm{M}_{2} ) are at distance d apart. A third
particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from ( mathbf{M}_{mathbf{1}} ) is
( ^{mathrm{A}} cdot mathrm{d}left(frac{sqrt{mathrm{M}_{2}}}{sqrt{mathrm{M}_{1}}-sqrt{mathrm{M}_{2}}}right) )
В. ( mathrm{d}left(frac{sqrt{mathrm{M}_{1}}}{sqrt{mathrm{M}_{1}}+sqrt{mathrm{M}_{2}}}right) )
( ^{mathrm{c}} cdot mathrm{d}left(frac{sqrt{mathrm{M}_{1}}}{sqrt{mathrm{M}_{1}}-sqrt{mathrm{M}_{2}}}right) )
D. ( mathrm{d}left(frac{mathrm{M}_{1}}{mathrm{M}_{1}+mathrm{M}_{2}}right) )
11

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