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PHYSICS
JEE (MAIN+ADVANCED)
ENTHUSIAST COURSE

EXERCISE
Gravitation

English Medium
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® Gravitation

EXERCISE (O-1)

A. Gravitational Force
1. Two identical particles of combined mass M, placed in space with certain separation, are released.
Interaction between the particles is only of gravitational in nature and there is no external force present.
Acceleration of one particle with respect to the other when separation between them is R, has a
magnitude :
GM
(A)

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2R 2

GM
(B)
R2

2GM
(C)
R2
(D) not possible to calculate due to lack of information
GR0133
2. Two particles each of mass m are placed at points P and Q as shown in the figure. R is the mid-point
of PQ = l. The gravitational force on the third particle of mass m placed at point S on the perpendicular
bisector of PQ at distance l from R is:-
m S

m m
P R Q
l
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Gm 2 16Gm 2 16Gm 2 4 2Gm2

(A) (B) (C) 5 5 l 2 (C) 5 l 2
l2 5l 2

GR0134
3. If the law of gravitation be such that the force of attraction between two particles vary inversely as the
5/2th power of their separation, then the graph of orbital velocity v0 plotted against the distance r of a
satellite from the earth's centre on a log-log scale is shown alongside. The slope of line will be-
lnv0

lnr
5 5 3
(A) - (B) - (C) - (D) –1
4 2 4
GR0135
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4. The gravitational force of attraction between two bodies is F newtons. If the mass of each body and
the distance between them are doubled, then the gravitational force between them in newton is
(A) 16 F (B) F/16 (C) F/4 (D) F
GR0136
5. Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of
a planet in circular orbit of radius R around the sun will be proportional to
n +1 n -1
(A) R n
(B) R 2
(C) R 2 (D) R - n
GR0137
6. If three uniform spheres, each having mass M and radius R, are kept in such a way that each touches
the other two, the magnitude of the gravitational force on any sphere due to the other two is
GM
2
2 GM
2
2 GM 2 3 GM 2
(A) 2 (B) 2 (C) 2 (D) 2
4r r 4r 4r

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GR0138
B. Gravitational Intensity, Potential and Potential energy
7. An object is placed at a distance of R/2 from the centre of earth. Knowing mass is distributed uniformly,
acceleration of that object due to gravity at that point is: (g = acceleration due to gravity on the surface
of earth and R is the radius of earth)
(A) g (B) 2 g (C) g/2 (D) none of these
GR0139
8. A spherical shell has mass M and radius R. A point mass m/2 kept inside the shell at a distance R/2
from centre. Then force of attraction on the mass is:
2Gm 2 Gm 2 Gm 2
(A) (B) (C) 2R (D) zero
R2 R2
GR0140
9. At certain height h from surface of earth the value of g become 6.25% of its value at earth surface.
h
The ratio of R is. (R is radius of earth)
(A) 3 (B) 2 (C) 4 (D) 1
GR0141
10. How much deep inside the earth (radius R) should a man go, so that his weight becomes one-fourth
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of that on the earth's surface–
R R 3R
(A) 4 (B) 2 (C) 4 (D) None
GR0142
11. If the radius of the earth were to shrink by one percent, its mass remaining the same, the value of g on
the earth’s surface would
(A) increase by 0.5% (B) increase by 2%
(C) decrease by 0.5% (D) decrease by 2%
GR0143
12. The acceleration due to gravity (on earth) depends upon
(A) size of the body (B) gravitational mass of the body
(C) gravitational mass of the earth (D) none of the above factors
GR0144

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13. The average magnitude of intensity of the gravitational field on the surface of the earth in SI unit is
about
(A) zero (B) 10 (C) 100 (D) more than 100
GR0145
14. If the earth stops rotating about its axis, the acceleration due to gravity will remain unchanged at
(A) equator (B) latitude 45° (C) latitude 60° (D) poles
GR0146
15. One goes from the centre of the earth to an altitude half the radius of the earth, where will the g be
greatest ?
(A) centre of the earth
(B) At a depth half the radius of the earth
(C) At the surface of the earth

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(D) At an altitude equal to half the radius of the earth.
GR0147
16. An iron sphere and an aluminium sphere, both of same radius are dropped from the top of a tower
100m high. At a height 40 m above the ground, both of them will have same.
(A) momentum (B) kinetic energy
(C) potential energy (D) acceleration
GR0148
17. The acceleration due to gravity increases by 0.5 % when we go from the equator to the poles. What
will be the time period of the pendulum at the equator which beats seconds at the poles?
(A) 1.950 s (B) 1.995 s (C) 2.050 s (D) 2.005 s
GR0149
18. A thin rod of length L is bent to form a circle. Its mass is M. What force will act on the mass m placed
at the centre of the circle ?
2 GMm
4p GMm 2p GMm
(A) (B) 2 2 (C) 2 (D) zero
2
L 4p L L
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GR0150
19. Two equal masses m and m are hung from a balance whose scale pans differ in vertical height by ‘h’.
The error in weighing in terms of density of the earth r is :

1 8 4
(A) p Grmh (B) p Grmh (C) p Grmh (D) p Grmh
3 3 3
GR0151
20. Two bodies of masses m and M are placed at distance d apart. What is the gravitational potential (V)
at the position where the gravitational field due to them is zero is V :
G G GM G
( )
2
(A) V = - ( m + M ) (B) V = - m (C) V = - (D) V = - m+ M
d d d d

GR0152

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21. Gravitational potential difference between a point on surface of planet and another point 10m above
is 4J/kg. Considering gravitational field to be uniform, how much work is done in moving a mass of
2.0 kg from the surface to a point 5.0m above the surface?
(A) 0.40 J (B) 2.5 J (C) 4.0 J (D) 8.0 J
GR0153
22. Two concentric shells have mass M and m and their radii are R and r respectively, where R > r . What
is the gravitational potential at their common centre ?

GM GM éM mù éM mù
(A) - (B) - (C) - G ê - ú (D) - G ê + ú
R r ëR rû ëR rû
GR0154
23. The gravitational force between two particles with masses m and M, initially at rest at great separation,

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pulls them together. When their separation becomes d, then speed of either particle relative to the
other will be :
(A) G(M + m)/ 2d (B) G(M + m)/ d (C) 4G(M + m)/ d (D) 2G(M + m) / d
GR0155
24. A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having
radius a.

(A) Gravitational field and potential both are zero at centre of the shell.
(B) Gravitational field is zero not only inside the shell but at a point outside the shell also.
(C) Inside the shell, gravitational field alone is zero.
(D) Neither gravitational field nor gravitational potential is zero inside the shell.
GR0156
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25. If escape velocity from earth is 11.2 km/s, Then escape velocity from a planet of mass as that of
earth but of its one fourth radius
(A) 11.2 km/s (B) 22.4 km/s (C) 5.6 km/s (D) 44.8 km/s
GR0157
26. A tunnel is dug along the diameter of the earth (radius R and mass M). There is a particle of mass 'm'
at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to
the surface of the earth is:

GM GM
(A) (B)
R 2R

2GM
(C) (D) it will reach with the help of negligible velocity
R
GR0158
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27. What is the increase in gravitational potential energy of an object of mass m raised from the surface
of earth to a height equal to n times of earth radius ?
æ n + 1ö æ n - 1ö æ n ö æ n ö
(A) çè n ÷ø mgR (B) çè n ÷ø mgR (C) çè n - 1÷ø mgR (D) çè n + 1÷ø mgR

GR0159
28. The escape velocity for a planet is ve. A particle starts from rest at a large distance from the planet,
reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its
centre. Its speed at the centre of the planet will be-
ve
(A) 1.5v e (B) (C) ve (D) zero
2
GR0160
29. The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space.

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The value of 'g' and 'R' (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy
for this work will be :- [AIEEE-2012]
(A) 6.4 × 1010 Joules (B) 6.4 × 1011 Joules
(C) 6.4 × 108 Joules (D) 6.4 × 109 Joules
GR0053
C. Kepler's Law and Satellite motion
30. A planet revolves in elliptical orbit around the sun. The linear speed of the planet will be maximum
at
B
S
A C

D
(A) A (B) B (C) C (D) D
GR0161
31. A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 600
latitude on the earth. Then the angular velocity of the satellite is :

GM GM GM 3 3GM
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(A) 3 (B) 3 (C) 3 (D)

8R 2R 4R 8R 3
GR0162
32. A satellite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is
opposite to the earth. The time interval after which it can be seen at the same place when the sense of
rotation of earth & satellite is same will be :
(A) 8 hours (B) 12 hours (C) 24 hours (D) 6 hours
GR0163
33. A satellite of mass m is in a circular orbit of radius 2R about the earth. How much energy is required
to transfer it to a circular orbit of radius 4R :- (R = Radius of earth)
mgR mgR mgR
(A) (B) (C) (D) None of these
8 4 2
GR0164

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34. The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the
shaded area SAB. If t1 be the time for the planet to move from C to D and t2 is the time to move from
A to B, then :
v
m
B C

S D
A

(A) t1 = t2 (B) t1 = 8t2 (C) t1 = 4t2 (D) t1 = 2t2

GR0165
35. If the earth be at one half its present distance from the sun, number of days in the year will be nearly
(A) 129 (B) 30 (C) 200 (D) 60

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GR0166
36. The period of a satellite in a circular orbit of radius R is T. What is the period of another satellite in a
circular orbit of radius 4R ?
(A) 4T (B) T/8 (C) T/4 (D) 8 T
GR0167
37. Two satellites S and S ' revolve around the earth at distances 3R and 6R from the centre of earth.
Their periods of revolution will be in the ratio
0.67
(A) 1 : 2 (B) 2 : 1 (C) 1 : 21.5 (D) 1 : 2
GR0168
38. A satellite revolves around a planet in an elliptical orbit of minor and major axes a and b respectively.
If T be the time period of the satellite, then T 2 is proportional to
3 3
æa+bö æ a -b ö
(A) ç ÷ (B) ç ÷ (C) a 3 (D) b3
è 2 ø è 2 ø
GR0169
39. A geostationary satellite has an orbital period of node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

(A) 2 hours (B) 6 hours (C) 12 hours (D) 24 hours

GR0170
40. Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period
of revolution T. If the gravitational force of attraction between the planet and the star is proportional
to r 5 / 2 , then the square of the time period will be proportional to
2 3.5
(A) r 3 (B) r (C) r 2.5 (D) r
GR0171
41. Satellites A and B are orbiting around the earth in orbits of ratio R and 4R respectively. The ratio of
their areal velocities is :
(A) 1 : 2 (B) 1 : 4 (C) 1 : 8 (D) 1 : 16
GR0033

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EXERCISE (O-2)

SINGLE CORRECT TYPE QUESTIONS

A. Gravitational Force
1. If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes
zero, then the satellite will- [AIEEE-2002]
(A) continue to move in its orbit with same velocity
(B) move tangentially to the original orbit with same velocity

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(C) become stationary in its orbit
(D) move towards the earth
GR0035
B. Gravitational Intensity, Potential and Potential energy
2. If the distance between the centres of Earth and Moon is D and mass of Earth is 81 times that of
Moon. At what distance from the centre of Earth gravitational field will be zero?

D 2D 4D 9D
(A) (B) (C) (D)
2 3 5 10
GR0018
3. A hollow spherical shell is compressed to half its radius. The gravitational potential at the centre
(A) increases
(B) decreases
(C) remains same
(D) during the compression increases then returns at the previous value.
GR0020
4. Let w be the angular velocity of the earth’s rotation about its axis. Assume that the acceleration due to
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gravity on the earth’s surface has the same value at the equator and the poles in absence of rotation of
earth. An object weighed at the equator gives the same reading as a reading taken at a depth d below
earth’s surface at a pole (d<<R) The value of d is

w 2 R2 w 2 R2 2w 2 R2 Rg
(A) (B) (C) (D)
g 2g g g
GR0021
5. A 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 1/2 of g at poles. The
escape velocity of a particle on the pole of planet in terms of V is
(A) Ve = 2V (B) Ve = V (C) Ve = V 2 (D) Ve = 3V
GR0025
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6. A (nonrotating) star collapses onto itself from an initial radius Ri with its
mass remaining unchanged. Which curve in figure best gives the
gravitational acceleration ag on the surface of the star as a function of
the radius of the star during the collapse?
(A) a (B) b
(C) c (D) d
GR0027
7. A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work
required to take a unit mass from point P on its axis to infinity is [IIT-JEE 2010]

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2GM 2GM GM 2GM
(A) ( 4 2 - 5) (B) - ( 4 2 - 5) (C) (D) ( 2 - 1)
7R 7R 4R 5R
GR0061
8. Time period of simple pendulum of infinite length oscillating near the surface of the earth is:
[Me = mass of the earth, R = radius ]

R2 R3 R R4
(A) 2p (B) 2p G M (C) 2p G M (D) 2p
G Me e e G Me

GR0172
C. Kepler's Law and Satellite motion
9. The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a
pendulum on this planet if it is a seconds pendulum on earth?
1 1
(A) 2 second (B) 2 2 seconds (C) second (D) second
2 2 2
GR0023
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10. The figure shows the variation of energy with the orbit radius of a body in circular planetary motion.
Find the correct statement about the curves A, B and C

(A) A shows the kinetic energy, B the total energy and C the potential energy of the system.
(B) C shows the total energy, B the kinetic energy and A the potential energy of the system.
(C) C and A are kinetic and potential energies respectively and B is the total energy of the system.
(D) A and B are kinetic and potential energies and C is the total energy of the system.
GR0029
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11. A satellite of mass 5M orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes
into two pieces, one of mass M and the other of mass 4M. After the explosion the mass M ends up
travelling in the same circular orbit, but in opposite direction. After explosion the mass 4M is :-
(A) In a circular orbit
(B) unbound
(C) elliptical orbit
(D) data is insufficient to determine the nature of the orbit.
GR0030
12. A satellite can be in a geostationary orbit around earth at a distance r from the centre. If the angular
velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if
its distance from the centre is :-

r r r r

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(A) (B) (C) 1/ 3 (D)
2 2 2 ( 4) (2)1 / 3
GR0031
13. An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit.
The following quantities increase for the satellite as a result of this change:-
(A) gravitational potential energy (B) angular velocity
(C) linear orbital velocity (D) centripetal acceleration
GR0032
MULTIPLE CORRECT TYPE QUESTIONS
C. Kepler's Law and Satellite motion
14. A communications Earth satellite
(A) goes round the earth from east to west
(B) can be in the equatorial plane only
(C) can be vertically above any place on the earth
(D) goes round the earth from west to east
GR0037
15. A geostationary satellite is at a height h above the surface of earth. If earth radius is R
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(A) The minimum colatitude on earth upto which the satellite can be used for communication is
sin–1 (R R + h ) .
(B) The maximum latitudes on earth upto which the satellite can be used for communication is
cos–1 (R R + h ) .
(C) The area on earth escaped from this satellite is given as 2pR2 (1 + sinq)
(D) The area on earth escaped from this satellite is given as 2pR2 (1 + cosq)
GR0045

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16. A double star is a system of two stars of masses m and 2m, rotating about their centre of mass only
under their mutual gravitational attraction. If r is the separation between these two stars then their time
period of rotation about their centre of mass will be proportional to :
(A) r3/2 (B) r (C) m1/2 (D) m–1/2
GR0048
17. Two spherical planets P and Q have the same uniform density r, masses MP and MQ, and surface
areas A and 4A, respectively. A spherical planet R also has uniform density r and its mass is
(MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. Then
[IIT-JEE 2012]
(A) VQ > VR > VP (B) VR > VQ > VP (C) VR/VP =3 (D) VP/VQ = 1/2
GR0063
COMPREHENSION TYPE QUESTIONS

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C. Kepler's Law and Satellite motion
Paragraph for Question No. 18 and 19
Figure shows the orbit of a planet P around the sun S. AB and CD are the minor and major axes of the
ellipse.

18. If t1 is the time taken by the planet to travel along ACB and t2 the time along BDA, then
(A) t1 = t2 (B) t1 > t2
(C) t1 < t2 (D) nothing can be concluded
GR0050
19. If U is the potential energy and K kinetic energy then |U| > |K| at
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(A) Only D (B) Only C (C) both D & C (D) neither D nor C
GR0050
MATRIX MATCH TYPE QUESTIONS
C. Kepler's Law and Satellite motion
20. In elliptical orbit of a planet, as the planet moves from apogee position to perigee position,
Column–I Column–II
(A) Speed of planet (P) Remains same
(B) Distance of planet from centre of Sun (Q) Decreases
(C) Potential energy (R) Increases
(D) Angular momentum about centre of Sun (S) Can not say
GR0040

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EXERCISE (S)

B. Gravitational Intensity, Potential and Potential energy

1. A sphere of radius R has its centre at the origin. It has a uniform mass density
ro except that there is a spherical hole of radius r = R/2 whose centre is at O x
x = R/2 as in fig. (a) Find gravitational field at points on the axis for |x| > R (b)
Show that the gravitational field inside the hole is uniform, find its magnitude
and direction.
GR0008
2. A particle is fired vertically from the surface of the earth with a velocity kue , where ue is the escape
velocity and k < 1. Neglecting air resistance and assuming earth's radius as Re. Calculate the height to

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which it will rise from the surface of the earth.
GR0001
3. Calculate the distance from the surface of the earth at which above and below the surface acceleration
due to gravity is the same.
GR0002
C. Kepler's Law and Satellite motion
4. A satellite close to the earth is in orbit above the equator with a period of rotation of 1.5 hours. If it is
above a point P on the equator at some time, it will be above P again after time________.
GR0004
5. A satellite is moving in a circular orbit around the earth. The total energy of the satellite is
E = – 2 ×105J. The amount of energy to be imparted to the satellite to transfer it to a circular orbit
where its potential energy is U= – 2 × 105J is equal to ________.
GR0005
6. A satellite of mass m is orbiting the earth in a circular orbit of radius r. It starts losing energy due to
small air resistance at the rate of C J/ s. Then the time taken for the satellite to reach the earth is ____.
GR0006
7. A pair of stars rotates about a common center of mass. One of the stars has a mass M which is twice
as large as the mass m of the other. Their centres are at a distance d apart, d being large compared to
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the size of either star. (a) Derive an expression for the period of rotation of the stars about their
common centre of mass in terms of d,m, G. (b) Compare the angular momentum of the two stars
about their common centre of mass by calculating the ratio Lm/ LM. (c) Compare the kinetic energies
of the two stars by calculating the ratio Km/KM.
GR0007
8. A satellite of mass m moves in an elliptic orbit around a planet of mass M, so that its maximum and
minimum distances from the planet are r1 and r2 respectively. Find the angular momentum L of this
satellite relative to the centre of planet.
GR0173
9. A binary star consists of two stars A (mass 2.2 MS) and B (mass 11 MS), where MS is the mass of the
sun. They are separated by distance d and are rotating about their centre of mass, which is stationary.
The ratio of the total angular momentum of the binary star to the angular momentum of star B about
the centre of mass is :- [IIT-JEE 2010]
GR0060
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EXERCISE (JM)

1. What 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 2R ? [JEE-Main 2013]
5GmM 2GmM GmM GmM
(1) (2) (3) (4)
6R 3R 2R 3R
GR0054
2. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under
the action of their mutual gravitational attraction. The speed of each particle is : [JEE-Main 2014]

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GM 1 GM GM GM
(1) (1 + 2 2) (2) (1 + 2 2) (3) (4) 2 2
R 2 R R R
GR0055
R
3. From a solid sphere of mass M and radius R, a spherical portion of radius is removed, as shown in
2
the figure. Taking gravitational potential V = 0 at r = ¥, the potential at the centre of the cavity thus
formed is : (G = gravitational constant) [JEE-Main 2015]

-2GM -2GM -GM -GM

(1) (2) (3) (4)
3R R 2R R
GR0056
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4. A satellite is reolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R ;
h << R). The minimum increase in its orbital velocity required, so that the satellite could escape from
the earth's gravitational field, is close to : (Neglect the effect of atmosphere). [JEE-Main 2016]
(1) gR ( 2 - 1) (2) 2gR (3) gR (4) gR / 2
GR0057
5. The variation of acceleration due to gravity g with distance d from centre of the earth is best represented
by (R = Earth's radius) :- [JEE-Main 2017]
g g g g

(1) (2) (3) (4)

d d d d
O R O R O O R

GR0058
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SELECTED PROBLEMS FROM JEE-MAINS ONLINE PAPERS
6. Two stars of masses 3 × 1031 kg each, and at distance 2 × 1011m rotate in a plane about their common
centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In
order to escape from the gravitational field of this double star, the minimum speed that meteorite
should have at O is : (Take Gravitational constant G = 6.67 ×10–11 Nm2 kg–2)
[JEE-Main-2019_Jan]
(1) 1.4 ×10 m/s
5
(2) 24 ×10 m/s
4
(3) 3.8 ×10 m/s
4
(4) 2.8 ×105 m/s
GR0096
7. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm'
is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time
of ejection, the kinetic energy of the object is : [JEE-Main-2019_Jan]

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3 1
(1) mv 2 (2) mv2 (3) 2mv2 (4) mv 2
2 2
GR0097
8. A straight rod of length L extends from x = a to x=L + a. The gravitational force is exerts on a point
mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2, is given by:
[JEE-Main-2019_Jan]

(1) Gm éê A æç 1 - 1 ö÷ - BL ùú (2) Gm éê A æç 1 - 1 ö÷ + BL ùú
ë è a+L a ø û ë è a a+L ø û

éæ 1 1 ö ù é
æ 1 1 ö ù
(3) Gm ê A ç a + L - a ÷ + BL ú (4) Gm ê A ç a - a + L ÷ - BL ú
ë è ø û ë è ø û

GR0098
9. A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the
same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of
the satellite and the meteorite are the same, just before the collision. The subsequent motion of the
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

combined body will be : [JEE-Main-2019_Jan]

(1) in a circular orbit of a different radius (2) in the same circular orbit of radius R
(3) in an elliptical orbit (4) such that it escapes to infinity
GR0099
10. A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy
delivered by the rocket launcher, what should be the minimum energy that the launcher should have
if the same rocket is to be launched from the surface of the moon ? Assume that the density of the
earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-
[JEE-Main-2019_April]
E E E E
(1) (2) (3) (4)
4 16 32 64
GR0100

E 93
JEE-Physics ALLEN
®

11. A test particle is moving in a circular orbit in the gravitational field produced by a mass density
K
r(r) = . Identify the correct relation between the radius R of the particle's orbit and its period T :
r2

[JEE-Main-2019_April]
(1) T/R2 is a constant (2) TR is a constant
(3) T2/R3 is a constant (4) T/R is a constant
GR0101
12. A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only
gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions
made by the spaceship in 24 hours around the planet ? [Given : Mass of planet = 8 × 1022 kg ; Radius
of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2/kg2]

®
[JEE-Main-2019_April]
(1) 9 (2) 11 (3) 13 (4) 17
GR0102
13. A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth.
m
After it reaches height R (R = radius of the earth), it ejects a rocket of mass so that subsequently the
10
satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant;
M is the mass of the earth): [JEE-Main-2020_Jan]

2
mæ 2GM ö æ 2 119 GM ö
(1) 20 çç u - 3R ÷÷ (2) 5m ç u - ÷
è ø è 200 R ø

2
3m æ 5GM ö m æ 2 113 GM ö
(3) 8 çç u + 6R ÷÷ (4) çu + ÷
è ø 20 è 200 R ø
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

GR0103
14. A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass
r
m ævö
collides with A with a velocity which is half ç ÷ the instantaneous velocity vr of A. The collision
2 è2ø
is completely inelastic. Then, the combined body : [JEE-Main-2020_Jan]
(1) starts moving in an elliptical orbit around the planet.
(2) continues to move in a circular orbit
(3) Falls vertically downwards towards the planet
(4) Escapes from the Planet's Gravitational field.
GR0104

94 E
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® Gravitation

K
15. The mass density of a spherical galaxy varies as over a large distance 'r' from its centre. In that
r
region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:
[JEE-Main-2020_Sep]

1
(1) T µ R (2) T µ (3) T2 µ R (4) T2 µ R3
2

R3
GR0105
16. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of
the earth's radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction

3
of its motion so that is become times larger. Due to this the farthest distance from the centre of the

®
2

earth that the satellite reaches is R, value of R is : [JEE-Main-2020_Sep]

(1) 4Re (2) 3Re (3) 2Re (4) 2.5Re
GR0106
17. On the x-axis and a dsitance x from the origin, the gravitational field due to a mass distribution is

Ax
given by in the x-direction. The magnitu [JEE-Main-2020_Sep]
(x + a 2 )3/2
2

A A
(1) (2) (3) A(x2 + a2)3/2 (4) A(x2 + a2)1/2
(x + a 2 )1/2
2
(x + a 2 )3/2
2

GR0107
18. A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the
same weighing machine, if it is shifted to the equator ?
GM
(Use g = = 9.8 ms–2 and radius of earth, R = 6400 km.] [JEE-Main-2021_Feb]
R2
(1) 49 N (2) 48.83 N
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

(3) 49.83 N (4) 49.17 N

GR0174
19. Two satellites A and B of masses 200kg and 400kg are revolving round the earth at height of 600 km
and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of
TB – TA: [Given : radius of earth = 6400km, mass of earth = 6 × 1024 kg] [JEE-Main-2021_Feb]
B
A
E

(1) 1.33 × 103 s (2) 3.33 × 102 s

(3) 4.24 × 103 s (4) 4.24 × 102 s
GR0175

E 95
JEE-Physics ALLEN
®

20. A solid sphere of radius R gravitationally attracts a particle placed at 3R form its centre with a force
æRö
F1. Now a spherical cavity of radius ç ÷ is made in the sphere (as shown in figure) and the force
è2ø
becomes F2. The value of F1 : F2 is : [JEE-Main-2021_Feb]

B A
O m
2R
M
(1) 25 : 36 (2) 36 : 25 (3) 50 : 41 (4) 41 : 50
GR0176
21. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.

®
Reason R : The product of their mass and radius must be same, M1R1 = M2R2
In the light of the above statements, choose the most appropriate answer from the options given
below : [JEE-Main-2021_Feb]
(1) Both A and R are correct but R is NOT the correct explanation of A
(2) A is correct but R is not correct
(3) Both A and R are correct and R is the correct explanation of A
(4) A is not correct but R is correct
GR0177
22. Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where
the plane of the ring is perpendicular to the line joining the centres. If 8 R is the distance between
the centres of a ring (of mass 'm') and a sphere (mass 'M') where both have equal radius 'R'.
[JEE-Main-2021_Feb]
m M

R R

x – Y
Ö8R
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

8 GmM 2 2 GMm 1 GMm 8 GmM

(1) × (2) × (3) × 2 (4) ×
9 R 3 R2 3 8 R 27 R 2
GR0178
23. Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the
earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is
released in this tunnel, it will execute a simple harmonic motion with a time period :
[JEE-Main-2021_Feb]

2 pR g 1 g R
(1) g (2) (3) (4) 2p g
2 pR 2p R
GR0179
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® Gravitation
24. In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it
is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y.
The value of x is .......... [JEE-Main-2021_Feb]
C
3200 km
B

A
Earth O

R = 6400 km

GR0180
25. If one wants to remove all the mass of the earth to infinity in order to break it up completely. The

®
x GM2
amount of energy that needs to be supplied will be where x is ____ (Round off to the Nearest
5 R
Integer) (M is the mass of earth, R is the radius of earth, G is the gravitational constant)
[JEE-Main-2021_March]
GR0181
26. If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the
duration of the day would be approximately :
(Take : g = 10 ms–2, the radius of earth, R = 6400 × 103 m, Take p = 3.14)
[JEE-Main-2021_March]
(1) 60 minutes (2) does not change
(3) 1200 minutes (4) 84 minutes
GR0182
27. A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in
sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s2 and 4 m/s2
respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

a function of time. [JEE-Main-2021_July]

1000N A

(a)
Weight (b)
B
400N
(c)
(d) time
(1) (c) (2) (a) (3) (d) (4) (b)
GR0183

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®

28. A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to
carry it to infinity. The time taken by it to reach height h is ______ S. [JEE-Main-2021_July]

Re éæ h ö
3/2
ù 2 Re éæ h ö
3/2
ù
(1) êç 1 + ÷ - 1ú (2) êç 1 + ÷ - 1ú
2g êëè R e ø úû g êëè R e ø úû

1 R e éæ ù éæ ù
3/2 3/2
h ö 1 2 Re h ö
(3) 3 2g ê ç 1 + ÷ - 1ú (4) 3 êç 1 + ÷ - 1ú
êëè R e ø úû g êëè R e ø úû

GR0184
29. Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a
centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the

®
surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed

a GM
'v' required for the satellite to reach the surface of the second planet is then the value of 'a' is
7 R
________.
[Given : The two planets are fixed in their position] [JEE-Main-2021_July]
GR0185
R 9M 2R
M

8R

30. The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius
of 9.0 × 103 km. Find the mass of Mars.

ïì 4 p2 ïü
íGiven = 6 ´1011 N -1 m -2 kg 2 ý [JEE-Main-2021_July]
îï G þï
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65
(1) 5.96 × 1019 kg (2) 3.25 × 1021 kg (3) 7.02 × 1025 kg (4) 6.00 × 1023 kg
GR0186
31. A body of mass (2M) splits into four masses {m, M – m, m, M – m}, which are rearranged to form a
M
square as shown in the figure. The ratio of for which, the gravitational potential energy of the
m
system becomes maximum is x : 1. The value of x is ...... . [JEE-Main-2021_Aug]
m M–m

M–m m
d
GR0187
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® Gravitation
32. The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are
at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from
the middle of these two masses: [JEE-Main-2021_Aug]

1 4G (M1 + M2 ) 4G (M1 + M2 )
(1) V = (2) V =
2 r r

1 2G (M1 + M2 ) 2G (M1 + M2 )
(3) V = (4) V =
2 r r

GR0188
1
33. The approximate height from the surface of earth at which the weight of the body becomes of its
3

®
weight on the surface of earth is : [Radius of earth R = 6400 km and 3 = 1.732 ]
[JEE-Main-2022_June]
(A) 3840 km (B) 4685 km
(C) 2133 km (D) 4267 km
GR0189
34. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth
always points towards the center of earth without any variation in its magnitude.
Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below :
[JEE-Main-2022_June]
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is NOT the correct explanation of A.
(C) A is true but R is false
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

(D) A is false but R is true

GR0190
35. Given below are two statements : [JEE-Main-2022_June]
Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.
(A) Both statement I and Statement II are true
(B) Both statement I and Statement II are false
(C) Statement I is true but Statement II are false
(D) Statement I is false but Statement II is true
GR0191

E 99
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®

36. The distance of the Sun from earth is 1.5 × 1011 m and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be : [JEE-Main-2022_June]
(A) 2.45 × 10 m 10
(B) 1.45 × 10 m
10

(C) 1.45 × 10 m 9
(D) 0.14 × 109 m
GR0192
37. Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M
is situated at the centre of square. The total gravitational potential energy of the system is :
[JEE-Main-2022_June]

®
Gm é Gm é
(A) - (4 + 2 )m + 4 2M ùû (B) - (4 + 2 )M + 4 2m ùû
d ë d ë

Gm é 2 Gm é 2
(C) - 3m + 4 2M ù (D) - 6m + 4 2M ù
d ë û d ë û
GR0193
38. The escape velocity of a body on a planet 'A' is 12 kms . The escape velocity of the body on another
–1

planet 'B', whose density is four times and radius is half of the planet 'A', is :
[JEE-Main-2022_June]
(A) 12 kms –1
(B) 24 kms –1
(C) 36 kms –1
(D) 6 kms–1
GR0194
39. The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface
of earth will, be : (Radius of earth = 6400km) [JEE-Main-2022_July]
(A) 1 % (B) 3% (C) 4% (D) 0.5%
GR0195
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65
40. A body of mass m is projected with velocity lve in vertically upward direction from the surface of the
earth into space. It is given that ve is escape velocity and l < 1. If air resistance is considered to the
negligible, then the maximum height from the centre of earth, to which the body can go, will be
(R : radius of earth) [JEE-Main-2022_July]
R R R l2 R
(A) (B) (C) (D)
1 + l2 1 – l2 1– l 1 – l2
GR0196
41. Assume there are two identical simple pendulum. Clock-1 is placed on the earth and Clock-2 is
placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate
at time periods 4s and 6s respectively. Then the value of h is - [JEE-Main-2022_July]
(consider radius of earth RE = 6400 km and g on earth 10 m/s ) 2

(A) 1200 km (B) 1600 km (C) 3200 km (D) 4800 km

GR0197
100 E
 ALLEN
® Gravitation

EXERCISE (JA)

1
1. A planet of radius R = ´ (radius of Earth) has the same mass density as Earth. Scientists dig a well
10
R
of depth on it and lower a wire of the same length and of linear mass density 10–3 kgm–1 into it. If
5
the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in
place is (take the radius of Earth = 6 × 106 m and the acceleration due to gravity on Earth is 10 ms–2)
[JEE-Advance 2014]

®
(A) 96 N (B) 108 N (C) 120 N (D) 150 N
GR0064
2. A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it
reaches its maximum height, its acceleration due to the planet's gravity is 1/4th of its value at the
surface of the planet. If the escape velocity from the planet is vesc = v N , then the value of N is
(ignore energy loss due to atmosphere) [JEE-Advance 2015]
GR0065
3. A large spherical mass M is fixed at one position and two identical point masses m are kept on a line
passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of
length l and this assembly is free to move along the line connecting them. All three masses interact only
through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l
æ M ö
from M, the tension in the rod is zero for m = k ç ÷ . The value of k is : [JEE-Advance 2015]
è 288 ø

M m m

l
GR0066
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

4. A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own
gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is(are) :- [JEE-Advance 2015]
P ( r = 3R / 4 ) 63 P ( r = 3R / 5) 16 P ( r = R / 2 ) 20
(A) P(r = 0) = 0 (B) = (C) = (D) =
P ( r = 2R / 3) 80 P ( r = 2R / 5 ) 21 P ( r = R / 3) 27
GR0067
5. A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining
the sun and the Earth. The Sun is 3 × 105 times heavier than the Earth and is at a distance
2.5 × 104 times larger than the radius of the Earth. The escape velocity from Earth's gravitational
field is ve = 11.2 km s–1. The minimum initial velocity (vs) required for the rocket to be able to
leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the
presence of any other planet) [JEE-Advance 2017]
–1 –1 –1
(A) vs = 22 km s (B) vs = 72 km s (C) vs = 42 km s (D) vs = 62 km s–1
GR0068
E 101
JEE-Physics ALLEN
®

6. A planet of mass M, has two natural satellites with masses m1 and m2. The radii of their circular
orbits are R1 and R2 respectively. Ignore the gravitational force between the satellites. Define v1,
L1, K1 and T1 to be, respectively, the orbital speed, angular momentum, kinetic energy and time
period of revolution of satellite 1 ; and v2, L2, K2 and T2 to be the corresponding quantities of satellite
2. Given m1/m2 = 2 and R1/R2 = 1/4, match the ratios in List-I to the numbers in List-II.
[JEE-Advance 2018]
List–I List–II
n1 1
P. n2 1.
8
L1
Q. L2 2. 1

®
K1
R. K2 3. 2

T1
S. T2 4. 8

(A) P ® 4 ; Q ® 2 ; R ® 1 ; S ® 3 (B) P ® 3 ; Q ® 2 ; R ® 4 ; S ® 1
(C) P ® 2 ; Q ® 3 ; R ® 1 ; S ® 4 (D) P ® 2 ; Q ® 3 ; R ® 4 ; S ® 1
GR0069
7. Consider a spherical gaseous cloud of mass density r(r) in free space where r is the radial distance
from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits
about the common center with the same kinetic energy K. The force acting on the particles is their
mutual gravitational force. If r(r) is constant in time, the particle number density n(r) = r(r)/m is :
[G is universal gravitational constant] [JEE-Advance 2019]
K K 3K K
(A) pr 2 m 2G (B) 6pr 2 m 2G (C) pr 2 m 2G (D) 2pr 2 m2 G

GR0070
8. The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

the centers of the Earth and the Sun, and MS is the mass of the Sun. The two stars orbit around their
common center of mass in circular orbits with period nT, where T is the period of Earth's revolution
around the Sun. The value of n is ___. [JEE-Advance 2021]
GR0108
9. Two spherical stars A and B have densities rA and rB, respectively. A and B have the same radius,
and their masses MA and MB are related by MB = 2MA. Due to an interaction process, star A loses
some of its mass, so that its radius is halved, while its spherical shape is retained, and its density
remains rA. The entire mass lost by A is deposited as a thick spherical shell on B with the density of
the shell being rA. If vA and vB are the escape velocities from A and B after the interaction process, the

nB 10 n
ratio = . The value of n is _______ [JEE-Advance 2022]
nA 151/3
GR0198
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 ALLEN
® Gravitation

ANSWER KEY

EXERCISE # O-1

Que. 1 2 3 4 5 6 7 8 9 10
Ans. B C C D B D C D A C
Que. 11 12 13 14 15 16 17 18 19 20
Ans. B C B D C D B D C D
Que. 21 22 23 24 25 26 27 28 29 30
Ans. C D D D B A D A A A
Que. 31 32 33 34 35 36 37 38 39 40
Ans. A C A D A D C D D D

®
Que. 41
Ans. A

EXERCISE # O-2
Que. 1 2 3 4 5 6 7 8 9 10
Ans. B D B A A B A B B D
Que. 11 12 13 14 15 16 17 18 19
Ans. B C A B,D A,B,C A,D B,D B C
Que. A B C D
20
Ans. R Q Q P

EXERCISE # S
r pGr 0 R 3 é 1 8ù r 2pGr0 R
1. g = + ê - 2 ú î
, g =- î
êë (x - ( R 2))
2
6 x úû 3
node06\B0BC-BD\Kota\JEE(Advanced)\Enthuse\Phy\Module\2-Electro-Gravi-Current Elec.-Capa\Eng\02_Gravitation\01_Eng.p65

R ek 2 5 -1
2. 2 3. h=R
1- k 2
4. 1.6 hours if it is rotating from west to east, 24/17 hours if it is rotating from east to west
GMm æ 1 1 ö 2pd 3 / 2
5. 1 × 10 J 5
6. t= ç - ÷ 7. (a) T= , (b) 2, (c) 2
2C èç R e r ÷ø 3Gm
8. L = m [2GMr1r2 /(r1 + r2 )] 9. 6

E 103
JEE-Physics ALLEN
®

EXERCISE # JEE-MAIN

Que. 1 2 3 4 5 6 7 8 9 10
Ans. 1 2 4 1 2 4 2 2 3 2
Que. 11 12 13 14 15 16 17 18 19 20
Ans. 4 2 2 1 3 2 1 2 1 3
Que. 21 22 23 24 25 26 27 28 29 30
Ans. 2 4 4 4 3 4 1 4 4 4
Que. 31 32 33 34 35 36 37 38 39 40
Ans. 2 2 B D A C A A A B
Que. 41
Ans. C

®
EXERCISE # JEE-ADVANCED
Que. 1 2 3 4 5 6 7 8 9
Ans. B 2 7 B,C C B D 9 2.30

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104 E