GRAVITATION

UPDATED PYQ SHEETS

1) A satellite is orbiting just above the surface of the earth with period T. If D is the
density of the earth and G is the gravitational constant, the quantity 3π/Gd
represents (NEET 2023)

(a)T (b) T2 (c)T3 (d)√T

2) A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25

10-6 m above the surface of earth. If earth’s radius is 6.38 106 and g = 9.8ms2 , then
the orbital speed of the satellite is [CBSE AIPMT 2015]

(a)7.76kms (b) 8.56kms (c) 9.13kms (d) 6.67kms

3) The escape velocity from the earth’s surface is v. The escape from the surface of
another planet having a radius a, four times that of earth and same mass density is
(NEET 2021)

(a)v (b)2v (c)3v (d)4v

4) The time period of a geo-stationary satellite is 24 h, at a height 6RE (RE is the

radius of earth) from surface of earth. The time period of another satellite whose
height is 2.5RE from surface will be [NEET (Odisha) 2019]

(a) 6√2 h (b) 12√2 h

(c)24/2.5h (d)12/2.5h

5) The kinetic energies of a planet in an elliptical orbit about the Sun, at positions
A,B and C are KA, kB and KC , respectively. AC is the major axis and SB is

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perpendicular to AC at the position of the Sun S as shown in the figure. Then
[NEET 2018]

(a) KB<KA<KC (b) KA>KB>KC

(b) (c) KA<KB<KC (d) KB>KA>KC

6) Two spherical bodies of masses M and 5M and radii R and 2R are released in free
space with initial separation between their centres equal to12R. If they attract each
other due to gravitational force only, then the distance covered by the smaller
body before collision is [CBSE AIPMT 2015]

(a) 2.5R (b) 4.5 R (c) 7.5 R (d) 1.5 R

7) A geostationary satellite is orbiting the earth at a height of 5R above that surface

of the earth, R being the radius of the earth. The time period of another satellite in
hour at a height of 2R from the surface of the earth is [CBSE AIPMT 2012]

(a) 5 (b)10 (c) 6√2 (d) 6/√2

8) The escape velocity from the Earth’s surface is v. The escape velocity from the
surface of another planet having a radius, four times that of Earth and same mass
density Is [NEET 2021]
(a) v (b) 2v (c) 3v (d) 4v

9)The ratio of escape velocity at earth (v ) e to the escape velocity at a planet (v ) p

whose radius and mean density are twice as that of earth is [NEET 2016]

(a) 1:2√2 (b) 1: 4 (c) 1:√2 (d) 1: 2

10 ) A black hole is an object whose gravitational field is so strong that even light
cannot escape from it. To what approximate radius would earth (mass 5.98*1024
kg) have to be compressed to be a black hole? [CBSE AIPMT 2014]

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(a) 10-9 m (b) 10-6 m (c) 10-2 m (d) 10-7 m

11) The work done to raise amassm from the surface of the earth to a height h,
which is equal to the radius of the earth, is [NEET (National) 2019]

(a)2mgR
(b)1/2 mgR
(c)3/2mgR
(d) mgR

12) A body weighs 200 N on the surface of the earth. How much will it weigh half
way down to the centre of the earth ? [NEET (National) 2019]

(a)200 N (b) 250 N (c) 100 N (d) 150 N

13) The acceleration due to gravity at a height 1 km above the earth is the same as
at a depth d below the surface of earth. Then [NEET 2017]

(a)d = 1/2 km (b)d = 1km (c)d = 3/2 km (d)d = 2 km

14) Two astronauts are floating in gravitational free space after having lost contact
with their spaceship. The two will [NEET 2017]

(a) keep floating at the same distance between them

(b) move towards each other
(c) move away from each other
(d) will become stationary

15) A body of mass m 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
[NEET 2013]

(a) mg2R (b)2/3 mgR (c) 3mgR (d)1/3 mgR

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16) At what height from the surface of earth the gravitation potential and the value
of g are 5.4*107Jkg and 6.0 ms2 respectively? Take, the radius of earth as 6400 km.
[NEET 2016]

(a) 1600 km (b)1400 km (c) 2000 km (d) 2600 km

17) The height at which the weight of a body becomes 1/16th, its weight on the
surface of the earth (radius R), is [CBSE AIPMT 2012]

(a)5 R n (b) 15 R (c) 3 R (d)4 R

18 ) A compass needle which is allowed to move in a horizontal plane is taken to a

geomagnetic pole. It [CBSE AIPMT 2012]

(a) will become rigid showing no movement

(b) will stay in any position
(c) will stay in North-South direction only
(d) will stay in East-West direction only

19) A roller coaster is designed such that riders experience ‘‘weightlessness’’ as

they go round the top of a hill whose radius of curvature is 20m. The speed of the
car at the top of the hill is between [CBSE AIPMT 2008]

(a) 14 m/s and 15 m/s (b) 15 m/s and 16 m/s

(c) 16 m/s and 17 m/s (d) 13 m/s and 14 m/s

20) The 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 R, the radius of the planet would
be [CBSE AIPMT 2004]

(a) 2 R (b) 4R (c)1/4 R (d)1/2R

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21) A body projected vertically from the earth reaches a height equal to earth’s
radius before returning to the earth. The power exerted by the gravitational force
is greatest [CBSE AIPMT 2011]

(a) at the instant just before the body hits the earth
(b) it remains constant all through
(c) at the instant just after the body is
projected
(d) at the highest position of the body

22) The acceleration due to gravity on the planet A is 9 times the acceleration due
to gravity on the planet B. Aman jumps to a height of 2m on the surface of A. What
is the height of jump by the same person on the planet B?
[CBSE AIPMT 2003]

(a) 6 m (b)2/3m (c)2/9m (d) 18 m

23) The mass of a plant is 1 / 10 to that of earth and its diameter is half that of
earth. The acceleration due to gravity on that planet is : [NEET 2024]

a) 19.6 ms-2 b) 9.8 ms-2

c) 4.9 ms-2 d) 3.92 ms-2

24) The minimum energy required to launch a satellite of mass m from the surface
of earth of mass m and radius R in a circular orbit at an altitude of 2R from the
surface of the earth is : [NEET 2024]

a) 5GmM / 6R b) 2GmM / 3R
c) GmM / 2R d) GmM / 3R

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ANSWERS
QUES 1 2 3 4 5 6 7 8 9
ANS b a d a b c c d a

QUES 10 11 12 13 14 15 16 17 18
ANS c b c d b b d c c

QUES 19 20 21 22 23 24 25 26 27
ANS a d a d d a

QUES 28 29 30 31 32 33 34 35 36
ANS

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HINTS AND SOLUTIONS
3. Problem Solving Strategy

4. Problem Solving Strategy From Kepler’s third law, the time period of revolution
of satellite around earth is

T 2 =r 3 or T =r 3/2 …(i) where, r is the radius of satellite’s orbit.

5. Problem Solving Strategy. Since, as per the result the Kepler’s second law of
area, that the planet will move slowly min v only when it is farthest from the Sun
and more rapidly max v when it is nearest to the Sun.]

6. Problem Solving Strategy Mx =5M (9R - x)

or x = 45R = 5x
or x= R = 45/6= 7.5 R

7. Problem Solving Strategy From Kepler’s third law T2 = R3

8. Problem Solving Strategy We know that,
escape velocity from Earth’s surface,
√2GM/R
where, G is the gravitational constant, Re is the radius of the Earth, Me is the mass
of the Earth.

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Also, density mass/volume Mass = Density/Volume

9. Problem Solving Strategy Since, the escape velocity of earth can be given as
v= √2Gr = R √8/3 density of earth]

10. Problem Solving Strategy For the black hole, the escape speed is more than c
(speed of light). We should compare the escape speed with the c (Note that the
escape speed should be at least just greater than c).
v =√2GM/R

11. Problem Solving Strategy Amount of work done in moving the given body from
one point to another against the gravitational force is equal to the change in
potential energy of the body. As we know, the potential energy of body of mass m
of the surface of earth is

U = GMm/R
where, G =gravitational constant, M mass of earth and R = radius of earth. When
the mass is raised to a height h from the surface of the earth, then the potential
energy of the body

12. Problem Solving Strategy Given, weight of the body, w = 200N

As we know, w = mg, where m is the mass of the body
and g (10 m/s2 ) is acceleration due to gravity of the body at the surface of the
earth. Since, mass m remains constant irrespective of the position of the body on
the earth. However, g is not constant and its value at a depth d below the earth’s
surface is given as
g’ = g (1 – d/R)

14. Problem Solving Strategy In the space, there is no external gravity. Due to
masses of the astronauts, there will be small gravitational attractive force between
them. Thus, these astronauts will move towards each other.

16. Problem Solving Strategy Gravitational potential at some height h from the
surface of the earth is given by

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 V = -GM/(R+H)……………..…(i)
And acceleration due to gravity at some height h from the earth surface.

17. Problem Solving Strategy According to the question,

GMm/(R+H)2 = 1/16 GMm/R2 ,m = mass of the body

18. Problem Solving Strategy It will stay in North-South direction only at

geomagnetic North and South poles.

19. Problem Solving Strategy The appearance of weightlessness occurs in space

when the gravitational attraction of the earth on a body in space is equal to the
centripetal force.
Mv2/r = mg
20. Problem Solving Strategy The acceleration due to gravity on an
object of mass m
g= F/m

but from Newton’s law of gravitation

F = GMm/R2

21. Problem Solving Strategy We know that, Power, P = F = V = Fcosθ

So, just before hitting, s = zero, power
will be maximum.

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