IMPULSE

PREVIOUS YEARS QUESTIONS

GRAVITATION
Objective Questions I (Only one correct option) 8. Two planets 𝐴 and 𝐵 of equal mass are having their
KEPLER’S LAWS AND NEWTON’S LAW OF GRAVITATION period of revolutions 𝑇𝐴 and 𝑇𝐵 such that 𝑇𝐴 = 2 𝑇𝐵 .
1. Two identical particles each of mass 𝑚 go round a circle These planets are revolving in the circular orbits of radii
of radius 𝑎 under the action of their mutual gravitational 𝑟𝐴 and 𝑟𝐵 , respectively.
attraction. The angular speed of each particle will be Which out of the following would be the correct
relationship of their orbits?
𝐺𝑚 𝐺𝑚 𝐺𝑚 𝐺𝑚
(a) √4𝑎3 (b) √2𝑎3 (𝑐) √ 𝑎3 (d) √8𝑎3 (a) 2 𝑟𝐴2 = 𝑟𝐵2 (b) 𝑟𝐴3 = 2 𝑟𝐵3
𝜋2
(2023 Main, 15 April 1) (c) 𝑟𝐴3 = 4 𝑟𝐵3 (d) 𝑇𝐴2 − 𝑇𝐵2 = 𝐺 𝑀 (𝑟𝐵3 − 4 𝑟𝐴3 )
2. Two particles of equal mass 𝑚 move in a circle of radius (2022 Main, 28 June)
𝑟 under the action of their mutual gravitational 9. The minimum and maximum distances of a planet
attraction. The speed of each particle will be revolving around the Sun are 𝑥1 and 𝑥2 . If the minimum
𝐺𝑚 4𝐺𝑚 𝐺𝑚 𝐺𝑚 speed of the planet on its trajectory is 𝑣0 , then its
(a) √ 4𝑟 (b) √ (c) √ 2𝑟 (d) √
𝑟 𝑟 maximum speed will be
(2023 Main, 29 Jan 1) 𝑣0 𝑥12 𝑣0 𝑥22 𝑣0 𝑥1 𝑣0 𝑥2
3. The time period of a satellite of earth is 24 hours. If the (a) (b) (c) (d)
𝑥22 𝑥12 𝑥2 𝑥1
separation between the earth and the satellite is (2022 Main, 25 June 1; 2021, 25 July 1)
decreased to one-fourth of the previous value, then its Key idea To solve this question, you should use the law
new time period will become of conservation of angular momentum.
(a) 1 hour (b) 6 hours (c) 3 hours (d) 4 hours 10. A particle is moving with uniform speed along the
(2023 Main, 29 Jan II) circumference of a circle of radius 𝑅, under the action of
4. Every planet revolves around the sun in an elliptical a central fictitious force 𝐹 which is inversely
orbit. proportional to 𝑅³. Its time period of revolution will be
A. The force acting on a planet is inversely proportional given by
4 3
to square of distance from sun.
(a) 𝑇 ∝ 𝑅 3 (b) 𝑇 ∝ 𝑅 2
B. Force acting on planet is inversely proportional to 5
product of the masses of the planet and the sun. (c) 𝑇 ∝ 𝑅² (d) 𝑇 ∝ 𝑅 2
(2021 Main, 26 Feb 1)
C. The Centripetal force acting on the planet is directed
11. A straight rod of length 𝐿 extends from 𝑥 = 𝑎 to 𝑥 =
away from the sun.
𝐿 + 𝑎. The gravitational force it exerts on a point mass
D. The square of time period of revolution of planet
𝑚 at 𝑥 = 0, if the mass per unit length of the rod is 𝐴 +
around sun is directly proportional to cube of semi-
𝐵 𝑥² is given by
major axis of elliptical orbit. 1 1
Choose the correct answer from the options given (a) 𝐺 𝑚 [𝐴 (𝑎 + 𝐿 − 𝑎) − 𝐵 𝐿]
below. 1
(b) 𝐺 𝑚 [𝐴 (𝑎 + 𝐿 − 𝑎) + 𝐵 𝐿]
1

(a) C and D only (b) A and D only 1 1

(c) A and C only (d) B and C only (c) 𝐺 𝑚 [𝐴 (𝑎 − 𝑎 + 𝐿) + 𝐵 𝐿]
(2023 Main, 25 Jan II) 1 1
(d) 𝐺 𝑚 [𝐴 (𝑎 − 𝑎 + 𝐿) − 𝐵 𝐿]
5. If the distance of the Earth from the Sun is 1.5 ×
(2019 Main, 12 Jan 1)
106 𝑘𝑚, then the distance of an imaginary planet from
12. Four identical particles of mass 𝑀 are located at the
the Sun, if its period of revolution is 2.83 years is
corners of a square of side 𝑎. What should be their
(a) 3 × 107 𝑘𝑚 (b) 6 × 106 𝑘𝑚
6 speed, if each of them revolves under the influence of
(c) 3 × 10 𝑘𝑚 (d) 6 × 107 𝑘𝑚
(2023 Main, 24 Jan II)
other's gravitational field in a circular orbit
6. Three identical particles 𝐴, 𝐵 and 𝐶 of mass 100 kg each circumscribing the square?
are placed in a straight line with 𝐴𝐵 = 𝐵𝐶 = 13 𝑚.
The gravitational force on a fourth particle 𝑃 of the same
mass is 𝐹, when placed at a distance 13 𝑚 from the
particle 𝐵 on the perpendicular bisector of the line 𝐴𝐶.
The value of 𝐹 will be approximately
(a) 21 𝐺 (b) 100 𝐺 (c) 59 𝐺 (d) 42 𝐺 𝐺𝑀 𝐺𝑀
(a) 1.35 √ (b) 1.16 √
𝑎 𝑎
(2022 Main, 25 July 1)
𝐺𝑀 𝐺𝑀
Key idea: To solve this question, you should be familiar (c) 1.21 √ (d) 1.41 √
𝑎 𝑎
with the concept of gravitational force.
(2019 Main, 8 April 1)
7. The time period of a satellite revolving around Earth in a 13. A particle is moving with a uniform speed in a circular
given orbit is 7 ℎ. If the radius of orbit is increased to
orbit of radius 𝑅 in a central force inversely proportional
three times its previous value, then approximate new
time period of the satellite will be (2022 Main, 29 June II) to the 𝑛𝑡ℎ power of 𝑅. If the period of rotation of the
(a) 40 ℎ (b) 36 ℎ (c) 30 ℎ (d) 25 ℎ particle is 𝑇, then
IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158
 𝑛 3 𝐹 𝑟2
(a) 𝑇 ∝ 𝑅 2 (b) 𝑇 ∝ 𝑅 2 for any value of 𝑛 (d) 𝐹1 = 𝑟12 , if 𝑟₁ < 𝑅 and 𝑟₂ < 𝑅
𝑛 𝑛+1 2 2
(c) 𝑇 ∝ 𝑅 2 + 1 (d) 𝑇 ∝ 𝑅 2 (2018 Main) 20. A solid sphere of uniform density and radius 4 units is
14. A spherically symmetric gravitational system of particles located with its centre at the origin 𝑂 of coordinates.
𝜌 𝑓𝑜𝑟 𝑟 ≤ 𝑅 Two spheres of equal radii 1 unit, with their centres at
has a mass density, 𝜌 = { 0 , where 𝜌0 is a
0 𝑓𝑜𝑟 𝑟 > 𝑅 𝐴(−2, 0, 0) and 𝐵(2, 0, 0) respectively, are taken out of
constant. A test mass can undergo circular motion under the solid leaving behind spherical cavities as shown in
the influence of the gravitational field of particles. Its figure. (1993)
speed 𝑣 as a function of distance 𝑟(0 < 𝑟 < ∞) from
the centre of the system is represented by (2018 Main)

Then,
(a) the gravitational field due to this object at the origin
is zero
(b) the gravitational field at the point 𝐵 (2, 0, 0) is zero
(c) the gravitational potential is the same at all points of
circle 𝑦² + 𝑧² = 36
(d) the gravitational potential is the same at all points on
the circle 𝑦² + 𝑧² = 4
Numerical Value/Integer Answer Question
15. A double star system consists of two stars 𝐴 and 𝐵 which 21. The distance between two stars of masses 3 𝑀𝑆 and
have time periods 𝑇𝐴 and 𝑇𝐵 . Radius 𝑅𝐴 and 𝑅𝐵 , and 6 𝑀𝑆 is 9 𝑅. Here 𝑅 is the mean distance between the
masses 𝑀𝐴 and 𝑀𝐵 . Choose the correct option. centers of the Earth and the Sun, and 𝑀𝑆 is the mass of
(a) If 𝑇𝐴 > 𝑇𝐵 then 𝑅𝐴 > 𝑅𝐵 (2006) the Sun. The two stars orbit around their common
(b) If 𝑇𝐴 > 𝑇𝐵 then 𝑀𝐴 > 𝑀𝐵 center of mass in circular orbits with period 𝑛 𝑇, where
𝑇 2 𝑅 3 𝑇 is the period of Earth's revolution around the Sun. The
(c) (𝑇𝐴 ) = (𝑅𝐴 ) value of 𝑛 is ________. (2021 Adv.)
𝐵 𝐵
(d) 𝑇𝐴 = 𝑇𝐵 Key idea To solve this question, you should use the
4 𝜋2
16. If the distance between the Earth and the Sun were half following relation: 𝜏02 = 𝐺 𝑀 × 𝑅 3
its present value, the number of days in a year would 22. A large spherical mass 𝑀 is fixed at one position and two
have been (1996) identical masses 𝑚 are kept on a line passing through
(a) 64.5 (b) 129 (c) 182.5 (d) 730 the centre of 𝑀 (see figure). The point masses are
17. Imagine a light planet revolving around a very massive connected by a rigid massless rod of length 𝑙 and this
star in a circular orbit of radius 𝑅 with a period of assembly is free to move along the line connecting
revolution 𝑇. If the gravitational force of attraction them.
5
between the planet and the star is proportional to 𝑅 −2 ,
then (1989)
7
(a) 𝑇² ∝ 𝑅² (b) 𝑇² ∝ 𝑅 2
3 All three masses interact only through their mutual
(c) 𝑇² ∝ 𝑅 2 (d) 𝑇² ∝ 𝑅 3.75 gravitational interaction. When the point mass nearer to
Objective Questions II 𝑀 is at a distance 𝑟 = 3 𝑙 from 𝑀, the tension in the
(One or more than one correct option) 𝑀
rod is zero for 𝑚 = 𝑘 ( ). The value of 𝑘 is
18. A spherical body of radius 𝑅 consists of a fluid of 288
(2015 Adv.)
constant density and is in equilibrium under its own
Objective Questions I (Only one correct option)
gravity. If 𝑃(𝑟) is the pressure at 𝑟 (𝑟 < 𝑅), then the
correct options is/are (2015 Adv.) Acceleration due to gravity, gravitational potential and
3𝑅
𝑃(𝑟 = 4 ) 63 potential energy
(a) 𝑃(𝑟 = 0) = 0 (b) 2𝑅 = 80
𝑃(𝑟 = 3 ) 23. The weight of a body on the Earth is 400 𝑁. Then weight
3𝑅 𝑅
𝑃(𝑟 = 5 ) 16 𝑃(𝑟 = 2 ) 20 of the body when taken to a depth half of the radius of
(c) 2𝑅 = 21 (d) 𝑅 = 27 the earth will be
𝑃(𝑟 = 5 ) 𝑃(𝑟 = 3 )

19. The magnitudes of the gravitational field at distances (a) 300 𝑁 (b) 𝑍𝑒𝑟𝑜 (c) 100 𝑁 (d) 200 𝑁
(2023 Main, 8 April 1)
𝑟1 and 𝑟2 from the centre of a uniform sphere of radius
24. The acceleration due to gravity at height ℎ above the
𝑅 and mass 𝑀 are 𝐹1 and 𝐹2 , respectively. Then, (1994)
𝐹 𝑟 earth if ℎ << 𝑅 (Radius of earth) is given by
(a) 1 = 1 , if 𝑟₁ < 𝑅, 𝑟₂ < 𝑅 ℎ2 2 ℎ2
𝐹2 𝑟2 (a) g ′ = g (1 − 2 𝑅2 ) (b) g ′ = g (1 − )
𝑅2
𝐹1 𝑟22
(b) 𝐹 = 𝑟2 , if 𝑟₁ > 𝑅, 𝑟₂ > 𝑅 2ℎ ℎ
2 1 (c) g ′ = g (1 − ) (d) g ′ = g (1 − 2 𝑅)
𝑅
𝐹 𝑟13
(c) 𝐹1 = , if 𝑟₁ < 𝑅, 𝑟₂ < 𝑅 (2023 Main, 8 April 11)
2 𝑟23

IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158

25. Assuming the Earth to be a sphere of uniform mass (a) 9:4 (b) 9:8 (c) 9:10 (d) 2:5
𝑅 (2022 Main, 30 June 1)
density, the weight of a body at a depth 𝑑 = 2 from the
35. If the radius of the Earth were to shrink by one percent,
surface of earth, if its weight on the surface of the Earth
its mass remaining the same, the acceleration due to
is 200 𝑁, will be
gravity on the Earth's surface would
(Given, 𝑅 = radius of earth)
(a) decrease (b) remain unchanged
(a) 500 𝑁 (b) 300 𝑁 (c) 400 𝑁 (d) 100 𝑁
(c) increase (d) be zero
(2023 Main, 10 April 1)
(2022 Main, 28 July 1)
26. Two planets 𝐴 and 𝐵 of radii 𝑅 and 1.5 𝑅 have densities
36. The approximate height from the surface of Earth at
𝜌 and 𝜌/2 respectively. The ratio of acceleration due to
which the weight of the body becomes 1/3 of its weight
gravity at the surface of 𝐵 to 𝐴 is
on the surface of Earth is
(a) 3:4 (b) 4:3 (c) 2:3 (d) 2:1
(2023 Main, 13 April II) (Radius of Earth 𝑅 = 6400 𝑘𝑚 and √3 = 1.7321)
27. A body of weight 𝑤, is projected vertically upwards from (a) 3840 𝑘𝑚 (b) 4685 𝑘𝑚
Earth's surface to reach a height above the earth which (c) 2133 𝑘𝑚 (d) 4267 𝑘𝑚
(2022 Main, 24 June 1)
is equal to nine times the radius of Earth. The weight of
37. Four spheres each of mass 𝑚 form a square of side 𝑑 (as
the body at that height will be
shown in figure). A fifth sphere of mass 𝑀 is situated at
(a) 𝑤/100 (b) 𝑤/3 (c) 𝑤/9 (d) 𝑤/91
(2023 Main, 31 Jan II) the centre of square. The total gravitational potential
28. At a certain depth 𝑑 below surface of Earth, value of energy of the system is
acceleration due to gravity becomes four times that of
its value at a height 3 𝑅 above Earth surface, where 𝑅 is
radius of Earth (Take 𝑅 = 6400 𝑘𝑚). The depth 𝑑 is
equal to
(a) 640 𝑘𝑚 (b) 4800 𝑘𝑚
(c) 5260 𝑘𝑚 (d) 2560 𝑘𝑚
(2023 Main, 31 Jan 1)
𝐺𝑚
Key idea: To solve this question use formula for variation (a) − [(4 + √2)𝑚 + 4√2𝑀]
g 𝑑
of acceleration due to gravity with height. g ′ = ℎ 2
𝐺𝑚
(1+2 ) (b) − [(4 + √2)𝑀 + 4√2𝑚]
𝑑
𝐺𝑚
29. The weight of a body at the surface of Earth is 18 𝑁. The (c) − [3 𝑚2 + 4√2𝑀]
𝑑
weight of the body at an altitude of 3200 𝑘𝑚 above the 𝐺𝑚
(d) − [6 𝑚2 + 4√2𝑀]
Earth's surface is (Given, radius of Earth, 𝑅𝐸 = 𝑑
(2022 Main, 27 June II)
6400 𝑘𝑚) (2023 Main, 24 Jan)
38. Consider a planet in some solar system which has a mass
(a) 9.8 𝑁 (b) 19.6 𝑁 (c) 8 𝑁 (d) 4.9 𝑁 double the mass of Earth and density equal to the
30. If 𝑉 is the gravitational potential due to a sphere of average density of Earth. If the weight of an object on
uniform density on its surface, then its value at the Earth is 𝑤, the weight of the same object on that planet
centre of the sphere will be (2023 Main, 11 April II)
will be (2021 Main, 25 July II)
𝑉 3𝑉 4
(a) 2 (b) 𝑉 (c) 2 (d) 3 𝑉 1

𝐾
(a) 2𝑤 (b) 𝑤 (c) 23 𝑤 (d) √2𝑤
31. If the gravitational field in the space is given as − 𝑟2 , 39. A body weighs 49 𝑁 on a spring balance at the north
taking the reference point to be at 𝑟 = 2 𝑐𝑚 with pole. What will be its weight recorded on the same
gravitational potential 𝑉 = 10 𝐽/𝑘g, find the weighing machine if it is shifted to the equator?
gravitational potential at 𝑟 = 3 𝑐𝑚 in SI unit (Use radius of Earth, 𝑅 = 6400 𝑘𝑚)
(Given, 𝐾 = 6 𝐽𝑚 / 𝑘g) (2023 Main, 30 Jan) (a) 49.83 𝑁 (b) 49 𝑁
(a) 12 (b) 9 (c) 10 (d) 11 (c) 48.83 𝑁 (d) 49.17 𝑁
32. A body of mass 𝑚 is projected with velocity 𝜆𝑣𝑒 in (2021 Main, 24 Feb II; 2017)
vertically upward direction from the surface of the Earth Key idea: To solve this question, use the formula of
into space. It is given that 𝑣𝑒 is escape velocity and 𝜆 < apparent acceleration due to gravity at the equator:
1. If air resistance is negligible, then the maximum g′ = g − 𝜔²𝑅
height from the centre of Earth to which the body can 40. On the 𝑋-axis and at a distance 𝑥 from the origin, the
go will be (𝑅 is radius of Earth) gravitational field due to a mass distribution is given by
𝐴𝑥
𝑅 𝑅 𝑅 𝜆2 𝑅 in the 𝑋-direction. The magnitude of
(a) 1 + 𝜆2 (b)1 − 𝜆2 (c) 1 − 𝜆 (d) 1 − 𝜆2 3
(𝑥 2 + 𝑎 2 )2
(2022 Main, 27 July II) gravitational potential on the 𝑋-axis at a distance 𝑥,
33. The percentage decrease in the weight of a rocket, when taking its value to be zero at infinity, is
taken to a height of 32 𝑘𝑚 above the surface of Earth, 𝐴 𝐴
(a) 2 2 (b) (𝑥2 + 𝑎2 )3/2
will be (Radius of Earth = 6400 𝑘𝑚) √𝑥 + 𝑎
1
(a) 1% (b) 3% (c) 4% (d) 0.5% (c) 𝐴(𝑥 2 + 𝑎2 )2 (d) 𝐴(𝑥 2 + 𝑎2 )3/2
(2022 Main, 26 July 1) (2020 Main, 4 Sep 1)
34. The radii of two planets 𝐴 and 𝐵 are in the ratio 2:3. 41. The ratio of the weights of a body on the Earth's surface
Their densities are 3𝜌 and 5𝜌, respectively. The ratio of to that on the surface of a planet is 9:4. The mass of the
their acceleration due to gravity is planet is 1/9th of that of the Earth. If 𝑅 is the radius of

IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158

 the Earth, what is the radius of the planet? (Take the 47. If g is the acceleration due to gravity on the Earth's
planets to have the same mass density) surface, the gain in the potential energy of an object of
𝑅 𝑅 𝑅 𝑅
(a) 3 (b) 4 (c) 9 (d) 2 mass 𝑚 raised from the surface of the Earth to a height
(2019 Main, 12 April 1) equal to the radius 𝑅 of the Earth, is (1983)
1 1
42. The variation of acceleration due to gravity g with (a) 𝑚g𝑅 (b) 2 𝑚g𝑅 (c) 𝑚g𝑅 (d) 𝑚g𝑅
2 4
distance 𝑑 from the centre of the Earth is best Statements Type Questions
represented by (𝑅 = radius) 48. Given below are two statements:
Statement I: Rotation of the Earth shows effect on the
value of acceleration due to gravity (g)
Statement II: The effect of rotation of the Earth on the
value of 'g' at the equator is minimum and that at the
pole is maximum.
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) Statement I is true but Statement II is false
(c) Both Statement I and Statement II are false
(2017 Main)
(d) Statement I is false but Statement II is true
43. From a solid sphere of mass 𝑀 and radius 𝑅, a spherical (2023 Main, 10 April II)
portion of radius 𝑅/2 is removed as shown in the figure. 49. Given below are two statements:
Taking gravitational potential 𝑉 = 0 at 𝑟 = ∞, the Statement I: Acceleration due to gravity is different at
potential at the centre of the cavity thus formed is (𝐺 = different places on the surfaces of Earth.
gravitational constant) (2015 Main) Statement II: Acceleration due to gravity increases as we
go down below the Earth's surface.
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 false but Statement II is true
𝐺𝑀 𝐺𝑀 2𝐺𝑀 2𝐺𝑀
(a) − (b) − 2𝑅 (c) − (d) − (d) Statement I is true but Statement II is false
𝑅 3𝑅 𝑅
1 (2023 Main, 1 Feb)
44. A planet of radius 𝑅 = 10 × (radius of Earth) has the
50. Given below are two statements:
𝑅
same mass density. Scientists dig a well of depth 5 on it Statement I: Acceleration due to Earth's gravity
and lower a wire of the same length and of linear mass decreases as we go 'up' or 'down' from Earth's surface
density 10−3 𝑘g/𝑚 into it. If the wire is not touching Statement II: Acceleration due to Earth's gravity is same
anywhere, the force applied at the top of the wire by a at a height ℎ and depth 𝑑 from Earth's surface, if ℎ = 𝑑.
person holding it in place is (Take the radius of Earth = In the light of the above statements, choose the most
6 × 106 𝑚 and acceleration due to gravity on Earth = appropriate answer from the options given below:
10 𝑚/𝑠²) (2014 Adv.) (a) Both Statement I and II are correct
(a) 96 𝑁 (b) 108 𝑁 (c) 120 𝑁 (d) 150 𝑁 (b) Statement I is correct but Statement II is incorrect
45. What is the minimum energy required to launch a (c) Both Statement I and Statement II are incorrect
satellite of mass 𝑚 from the surface of a planet of mass (d) Statement I is incorrect but Statement II is correct
𝑀 and radius 𝑅 in a circular orbit at an altitude of 2𝑅? (2023 Main, 24 Jan 1)
5𝐺𝑚𝑀 2𝐺𝑚𝑀 𝐺𝑚𝑀 𝐺𝑚𝑀 51. Given below are two statements:
(a) (b) (c) (d)
6𝑅 3𝑅 2𝑅 3𝑅 Statement I: The law of gravitation holds good for any
(2013 Main)
pair of bodies in the universe.
46. A thin uniform annular disc (see figure) of mass 𝑀 has
Statement II: The weight of any person becomes zero
outer radius 4𝑅 and inner radius 3𝑅. The work required
when the person is at the centre of the Earth.
to take a unit mass from point 𝑃 on its axis to infinity is
In the light of the above statements, choose the correct
(2010)
answer from the options given below:
(a) Both Statement I and II are true
(b) Both Statement I and II are false
(c) Statement I is true but Statement II is false
(d) Statement I is false but Statement II is true
(2022 Main, 27 June)
Assertion & Reason
52. Assertion (A): An astronaut in an orbiting space station
2𝐺𝑀 2𝐺𝑀 above the Earth experiences weightlessness.
(a) (4√2 − 5) (b) − (4√2 − 5) Reason (R): An object moving around the Earth under
7𝑅 7𝑅
𝐺𝑀 2𝐺𝑀 the influence of Earth's gravitational force is in a state of
(c) (d) (√2 − 1) 'free-fall'.
4𝑅 5𝑅

IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158

 Given below are two statements, one is labelled as escape velocity in 𝑘𝑚/𝑠 given by (Given, escape velocity
Assertion (A) and the other is labelled as Reason (R). on Earth 𝑣𝑒 = 11.2 × 10³ 𝑚/𝑠)
(a) If Assertion is true, Reason is true; Reason is the (a) 11.2 (b) 33.6 (c) 67.2 (d) 16.8
correct explanation for Assertion (2023 Main, 13 April I)
(b) If Assertion is true, Reason is true; Reason is not a 59. Two satellites of masses 𝑚 and 3𝑚 revolve around the
correct explanation for Assertion Earth in circular orbits of radii 𝑟 & 3𝑟 respectively. The
(c) If Assertion is true; Reason is false ratio of orbital speeds of the satellites respectively is
(d) If Assertion is false; Reason is true (2008) (a) 9: 1 (b) √3: 1 (c) 1: 1 (d) 3: 1
Numerical Value/Integer Answer Questions (2023 Main, 10 April I)
53. If the acceleration due to gravity experienced by a point 60. A space ship of mass 2 × 10⁴ 𝑘g is launched into a
mass at a height ℎ above the surface of Earth is same as circular orbit close to the Earth's surface. The additional
that of the acceleration due to gravity at a depth velocity to be imparted to the space ship in the orbit to
𝛼ℎ (ℎ << 𝑅𝑒 ) from the Earth's surface. The value of 𝛼 overcome the gravitational pull will be
will be _______. (Use, 𝑅 = 6400 𝑘𝑚) (if g = 10 𝑚/𝑠² and radius of Earth = 6400 𝑘𝑚)
(2022 Main, 29 July) (a) 11.2 (√2 − 1) 𝑘𝑚/𝑠 (b) 7.9 (√2 − 1) 𝑘𝑚/𝑠
54. The elongation of a wire on the surface of the Earth is (c) 8 (√2 − 1) 𝑘𝑚/𝑠 (d) 7.4 (√2 − 1) 𝑘𝑚/𝑠
10−4 𝑚. The same wire of same dimensions is elongated (2023 Main, 11 April II)
by 6 × 10−5 𝑚 on another planet. The acceleration 61. Choose the incorrect statement from the following:
due to gravity on the planet will be_____ 𝑚𝑠 −2 (Take (a) The linear speed of a planet revolving around the Sun
acceleration due to gravity on the surface of Earth = remains constant.
10 𝑚/𝑠²) (2022 Main, 26 June 1) (b) When a body falls towards the Earth, the
Key idea: To solve this question, use the relation: displacement of Earth towards the body is negligible.
∆𝑙 g
Elongation in wire 𝛥𝑙 ∝ g or ∆𝑙 𝑒 = g 𝑒 (c) The speed of a satellite in a given circular orbit
𝜌 𝜌
remains constant.
55. In the reported figure of Earth, the value of acceleration (d) For a planet revolving around the Sun in an elliptical
due to gravity is same at point 𝐴 and 𝐶, but it is smaller orbit, the total energy of the planet remains constant.
than that at point 𝐵 (surface of the Earth). The value of (2023 Main, 6 April II)
𝑂𝐴 ∶ 𝐴𝐵 will be 𝑥 ∶ 𝑦. The value of 𝑥 is 62. The ratio of escape velocity of a planet to the escape
velocity of the Earth will be: Mass of the planet is 16
times the mass of Earth and radius of the planet is 4
times the radius of the Earth.
(a) 1: 4 (b) 1: √2 (c) 2: 1 (d) 4: 1
(2023 Main, 12 April I)
63. Two satellites 𝐴 and 𝐵 move round the Earth in the same
orbit. The mass of 𝐴 is twice the mass of 𝐵. The quantity
which is same for the two satellites will be
(a) total energy (b) kinetic energy
(2021 Main, 26 Feb II; 2020 Main, 2 Sep II) (c) speed (d) potential energy
56. A body of mass 2𝑀 splits into four masses {𝑚, 𝑀 − (2023 Main, 12 April I)
𝑚, 𝑚, 𝑀 − 𝑚}, which are rearranged to form a square as 64. If Earth has a mass nine times and radius twice that of a
𝑀 𝑣
shown in the figure. The ratio of 𝑚 for which the planet 𝑃, then 3𝑒 √𝑥 𝑚/𝑠 will be the minimum velocity
gravitational potential energy of the system becomes required by a rocket to escape the gravitational force of
maximum is 𝑥: 1. The value of 𝑥 is ________. 𝑃, where 𝑣𝑒 is the escape velocity on Earth. The value of
𝑥 is (2023 Main, 1 Feb I)
(a) 18 (b) 1 (c) 2 (d) 3
65. The escape velocities of two planets 𝐴 and 𝐵 are in the
ratio 1:2. If the ratio of their radii respectively is 1:3, then
the ratio of acceleration due to gravity of planet 𝐴 to
that of planet 𝐵 will be
(a) 4/3 (b) 3/4 (c) 3/2 (d) 2/3
(2023 Main, 1 Feb II)
(2021 Main, 27 Aug 1) 66. Two satellites 𝑃 and 𝑄 are moving in different circular
Objective Questions I (Only one correct option) orbits around the Earth (radius 𝑅). The heights of 𝑃 and
Escape Velocity And Motion Of Satellite 𝑄 from the Earth surface are ℎ𝑃 and ℎ𝑄 respectively,
𝑅
57. The time period of a satellite, revolving above Earth's where ℎ𝑃 = 3 . The accelerations of 𝑃 and 𝑄 due to
g𝑃 36
surface at a height equal to 𝑅 will be Earth's gravity are g 𝑃 and g 𝑄 respectively. If = 25,
g𝑄
(Given, g = 𝜋² 𝑚/𝑠² and 𝑅 = radius of Earth)
what is the value of ℎ𝑄 ? (2023, JEE Adv. I)
(a) √2𝑅 (b) √8𝑅 (c) √4𝑅 (d) √32𝑅 3𝑅 𝑅 6𝑅 5𝑅
(2023 Main, 10 April II) (a) 5 (b) 6 (c) 5 (d) 6
58. A planet having mass 9 𝑀𝑒 and radius 4 𝑅𝑒 , where 𝑀𝑒 67. Two satellites 𝐴 and 𝐵 having masses in the ratio 4:3 are
and 𝑅𝑒 are mass and radius of Earth respectively, has revolving in circular orbits of radii 3𝑟 and 4𝑟
IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158
 respectively, around the Earth. The ratio of total (a) 2.8 × 10⁵ 𝑚/𝑠 (b) 3.8 × 10⁴ 𝑚/𝑠
mechanical energy of 𝐴 to 𝐵 is (c) 2.4 × 10⁴ 𝑚/𝑠 (d) 1.14 × 10⁵ 𝑚/𝑠
(a) 9:16 (b) 16:9 (c) 1:1 (d) 4:3 (2019 Main, 10 Jan II)
(2022 Main, 27 July I) 75. A satellite is moving with a constant speed 𝑣 in a circular
68. A body is projected vertically upwards from the surface orbit about the Earth. An object of mass 𝑚 is ejected
of Earth with a velocity equal to one third of escape from the satellite such that it just escapes from the
velocity. The maximum height attained by the body will gravitational pull of the Earth. At the time of its ejection,
be: (Take, radius of Earth = 6400 𝑘𝑚 and g = 10 𝑚/ the kinetic energy of the object is: (2019 Main, 10 Jan I)
𝑠²) (2022 Main, 26 July II) 1 3
(a) 2 𝑚 𝑣² (b) 𝑚𝑣² (c) 2 𝑚 𝑣² (d) 2 𝑚 𝑣²
(a) 800 𝑘𝑚 (b) 1600 𝑘𝑚 76. A rocket is launched normal to the surface of the Earth,
(c) 2133 𝑘𝑚 (d) 4800 𝑘𝑚
away from the Sun, along the line joining the Sun and
Key idea: To solve this question, you should use the
the Earth. The Sun is 3 × 105 times heavier than the
conservation of mechanical energy.
Earth and is at a distance 2.5 × 10⁴ times larger than
69. The escape velocity of a body on a planet 𝐴 is 12 𝑘𝑚/𝑠.
the radius of Earth. The escape velocity from Earth's
The escape velocity of the body on another planet 𝐵,
gravitational field is 𝑣𝑒 = 11.2 𝑘𝑚/𝑠. The minimum
whose density is four times and radius is half of planet
initial velocity (𝑣𝑠 ) required for the rocket to be able to
𝐴 is (2022 Main, 29 June I)
leave the Sun-Earth system is closest to: (Ignore the
(a) 2 𝑘𝑚/𝑠 (b) 24 𝑘𝑚/𝑠
rotation and revolution of the Earth and the presence of
(c) 36 𝑘𝑚/𝑠 (d) 6 𝑘𝑚/𝑠
any other planet) (2017 Adv)
70. The masses and radii of the Earth and Moon are
(a) 𝑣𝑠 = 72 𝑘𝑚/𝑠 (b) 𝑣𝑠 = 22 𝑘𝑚/𝑠
(𝑀1 , 𝑅1 ) and (𝑀2 , 𝑅2 ) respectively. Their centres
(c) 𝑣𝑠 = 42 𝑘𝑚/𝑠 (d) 𝑣𝑠 = 62 𝑘𝑚/𝑠
distance 𝑟 apart. Find the minimum escape velocity for
77. A geostationary satellite orbits around the Earth in a
a particle of mass 𝑚 to be projected from the middle of
circular orbit of radius 36,000 𝑘𝑚. Then, the time
these two masses. (2021 Main, 31 Aug I)
period of a spy satellite orbiting a few hundred 𝑘𝑚
1 4𝐺(𝑀1 +𝑀2 ) 4𝐺(𝑀1 +𝑀2 )
(a) 𝑣 = 2 √ (b) 𝑣 = √ above the Earth's surface (𝑅𝑒 = 6400 𝑘𝑚) will
𝑟 𝑟
approximately be: (2002)
1 2𝐺(𝑀1 +𝑀2 ) √2𝐺 (𝑀1 +𝑀2 )
(c) 𝑣 = 2 √ (d) 𝑣 = (a) 1/2 ℎ (b) 1 ℎ (c) 2 ℎ (d) 4 ℎ
𝑟 𝑟
78. A simple pendulum has a time period 𝑇₁ when on the
71. Two satellites 𝐴 and 𝐵 of masses 200 𝑘g and 400 𝑘g are
Earth's surface and 𝑇2 when taken to a height 𝑅 above
revolving round the Earth at heights of 600 𝑘𝑚 and
the Earth's surface, where 𝑅 is the radius of the Earth.
1600 𝑘𝑚, respectively. 𝑇𝐴 and 𝑇𝐵 are the time periods
The value of 𝑇2 /𝑇1 is: (2001)
of 𝐴 and 𝐵, respectively. Then the value of 𝑇𝐵 − 𝑇𝐴
(a) 1 (b) √2 (c) 4 (d) 2
(radius of Earth = 6400 𝑘𝑚, mass of Earth = 6 ×
79. A satellite 𝑆 is moving in an elliptical orbit around the
10²⁴ 𝑘g) (2021 Main, 25 Feb I)
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
(a) 4.24 × 10² 𝑠 (b) 1.33 × 10³ 𝑠
constant
(c) 4.24 × 10³ 𝑠 (d) 3.33 × 10² 𝑠
(c) The total mechanical energy of 𝑆 varies periodically
72. Two stars of masses 𝑚 and 2𝑚 at a distance 𝑑 rotate
with time
about their common centre of mass in free space. The
(d) The linear momentum of 𝑆 remains constant in
period of revolution is: (2020 Main, 25 Feb I)
magnitude (1998)
1 𝑑3 𝑑3
(a) 2𝜋 √3𝐺𝑚 (b) 2𝜋 √3𝐺𝑚 Objective Questions II
(One or more than one correct option)
1 3𝐺𝑚 3𝐺𝑚
(c) 2𝜋 √ (d) 2𝜋 √ 80. Two bodies, each of mass 𝑀, are kept fixed with a
𝑑3 𝑑3
separation 2𝐿. A particle of mass 𝑚 is projected from
73. A body is moving in a low circular orbit about a planet of
the mid-point of the line joining their centres,
mass 𝑀 and radius 𝑅. The radius of the orbit can be
perpendicular to the line. The gravitational constant is
taken to be 𝑅 itself. Then, the ratio of the speed of this
𝐺. The correct statement(s) is (are): (2013 Adv)
body in the orbit to the escape velocity from the planet
(a) The minimum initial velocity of the mass 𝑚 to escape
is: (2020 Main, 4 Sep II)
𝐺𝑀
(a) 1/√2 (b) 2 (c) 1 (d) √2 the gravitational field of the two bodies is 4√ 𝐿
74. Two stars of masses 3 × 10³¹ 𝑘g each and at distance (b) The minimum initial velocity of the mass 𝑚 to escape
2 × 10¹¹ 𝑚 rotate in a plane about their common
𝐺𝑀
centre of mass 𝑂. A meteorite passes through 𝑂 moving the gravitational field of the two bodies is 2√
𝐿
perpendicular to the star's rotation plane. In order to (c) The minimum initial velocity of the mass 𝑚 to escape
escape from the gravitational field of this double star,
2𝐺𝑀
the minimum speed that meteorite should have at 𝑂 is the gravitational field of the two bodies is √ 𝐿
(𝐺 = 6.67 × 10−11 𝑁𝑚²/𝑘g²) is:
IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158
 (d) The energy of the mass 𝑚 remains constant velocities from 𝐴 and 𝐵 after the interaction process, the
81. Two spherical planets 𝑃 and 𝑄 have the same uniform 𝑣 10𝑛
ratio 𝑣𝐵 = √ 1 . The value of 𝑛 is: (2022 Adv.)
density 𝜌, masses 𝑀𝑃 and 𝑀𝑄 , and surface areas 𝐴 and 𝐴 153
4𝐴, respectively. A spherical planet 𝑅 also has uniform 87. Suppose two planets (spherical, in shape) of radii 𝑅 and
density 𝜌 and its mass is 𝑀𝑃 + 𝑀𝑄 . The escape 2𝑅, but masses 𝑀 and 9𝑀 respectively have a centre-
velocities from the planets 𝑃, 𝑄 and 𝑅 are 𝑣𝑃 , 𝑣𝑄 , and to-centre separation 8𝑅. A satellite of mass 𝑚 is
𝑣𝑅 , respectively. Then: (2012) projected from the surface of the planet of mass 𝑀
(a) 𝑣𝑄 > 𝑣𝑅 > 𝑣𝑃 (b) 𝑣𝑅 > 𝑣𝑄 > 𝑣𝑃 directly towards the centre of the second planet. The
(c) 𝑣𝑅 /𝑣𝑃 = 3 (d) 𝑣𝑃 /𝑣𝑄 = 1/2 minimum speed 𝑣 required for the satellite to reach the
Statement Type Questions surface of the second planet is √7 ×
𝑎 𝐺𝑀
. The value of 𝑎
82. Given below are two statements. 𝑅

Statement I: For a planet, if the ratio of mass of the is:

planet to its radius increases, the escape velocity from [Take, the two planets are fixed in their position]
(2021 Main, 27 July I)
the planet also increases.
Statement II: Escape velocity is independent of the
radius of the planet.
In the light of the above statements, choose the correct
answer from the options given below.
(a) Statement I is incorrect but Statement II is correct
88. The initial velocity 𝑣𝑖 required to project a body
(b) Both Statement I and Statement II are correct
vertically upward from the surface of the Earth to reach
(c) Statement I is correct but Statement II is incorrect
a height of 10𝑅, where 𝑅 is the radius of the Earth, may
(d) Both Statement I and Statement II are incorrect
(2023 Main, 13 April II) be described in terms of escape velocity 𝑣𝑒 such that
Assertion & Reason 𝑥
𝑣𝑖 = √𝑦 × 𝑣𝑒 . The value of 𝑥 will be: (2021 Main, 25 Feb)
83. Assertion (A): Earth has atmosphere whereas Moon
doesn't have any atmosphere. Key idea: Use energy conservation:
𝐺𝑀 𝑚 1 𝐺𝑀 𝑚
Reason (R): The escape velocity on Moon is very small − 𝑅𝑒 + 2 𝑚 𝑣12 = − 11𝑒𝑅
as compared to that on Earth. 89. A bullet is fired vertically upwards with velocity 𝑣 from
(a) Both A and R are correct but R is not the correct the surface of a spherical planet. When it reaches its
explanation of A maximum height, its acceleration due to the planet's
(b) A is true but R is false gravity is 1/4 of its value at the surface of the planet. If
(c) A is false but R is true the escape velocity from the planet is 𝑣𝑠𝑒𝑐 = 𝑣√𝑁, then
(d) Both A and R are correct and R is the correct the value of 𝑁 is:(Ignore energy loss due to atmosphere)
explanation of A (2015 Adv)
84. Assertion (A): The escape velocities of planet 𝐴 and 𝐵 90. Gravitational acceleration on the surface of a planet is
are same, but 𝐴 and 𝐵 are of unequal mass. √6
g,where g is the gravitational acceleration on the
Reason (R): The product of their mass and radius must 11
surface of the Earth. The average mass density of the
be same, 𝑀₁ × 𝑅₁ = 𝑀₂ × 𝑅₂ 2
(a) Both A and R are correct but R is not the correct planet is 3 times that of the Earth. If the escape speed
explanation of A on the surface of the Earth is 11 𝑘𝑚/𝑠, the escape
(b) A is correct but R is not correct speed on the surface of the planet in 𝑘𝑚/𝑠 will be:
(c) Both A and R are correct and R is the correct (2010)
explanation of A 91. A planet of mass 𝑀 has two natural satellites with
(d) A is not correct but R is correct masses 𝑚₁ and 𝑚₂. The radii of their circular orbits are
(2021 Main, 25 Feb I) 𝑅₁ and 𝑅₂, respectively. Ignore the gravitational force
Numerical Value / Integer Answer Questions between the satellites. Define 𝑣1 , 𝐿1 , 𝐾1 , and 𝑇1 to be
85. Two satellites 𝑆1 and 𝑆2 are revolving in circular orbits respectively the orbital speed, angular momentum,
around a planet with radius 𝑅1 = 3200 𝑘𝑚 and 𝑅2 = kinetic energy, and time period of revolution of satellite
800 𝑘𝑚, respectively. The ratio of speed of satellite 𝑆₁ 1; and 𝑣₂, 𝐿₂, 𝐾₂, and 𝑇₂ to be the corresponding
to the speed of satellite 𝑆2 in their respective orbits quantities of satellite 2. Given 𝑚₁ / 𝑚₂ = 2 and
1 𝑅₁ / 𝑅₂ = 1/4. Match the ratios in column-I to the
would be 𝑥. Where 𝑥 = (2022 Main, 25 June II)
numbers in column-II.
86. Two spherical stars 𝐴 and 𝐵 have densities 𝜌𝐴 and 𝜌𝐵 ,
Column-I Column-II
respectively. 𝐴 and 𝐵 have the same radius, and their
A. 𝑣1 /𝑣2 p. 1/8
masses 𝑀𝐴 and 𝑀𝐵 are related by 𝑀𝐵 = 2 𝑀𝐴 . Due to
B. 𝐿1 /𝐿2 q. 1
an interaction process, star 𝐴 loses some of its mass, so
C. 𝐾1 /𝐾2 r. 2
that its radius is halved, while its spherical shape is
D. 𝑇1 /𝑇2 s. 8
retained and its density remains 𝜌𝐴 . The entire mass lost
(a) 𝐴 → 𝑟; 𝐵 → 𝑞; 𝐶 → 𝑝; 𝐷 → 𝑟
by 𝐴 is deposited as a thick spherical shell on 𝐵 with the
(b) 𝐴 → 𝑟; 𝐵 → 𝑞; 𝐶 → 𝑠; 𝐷 → 𝑝
density of the shell being 𝜌𝐴 . If 𝑣𝐴 and 𝑣𝐵 are the escape
(c) 𝐴 → 𝑞; 𝐵 → 𝑟; 𝐶 → 𝑝; 𝐷 → 𝑠
(d) 𝐴 → 𝑞; 𝐵 → 𝑟; 𝐶 → 𝑠; 𝐷 → 𝑝
IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158
 GRAVITATION (PYQ) ANSWER KEY
Que 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans a b c b c b b c c c c b d c d
Que 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Ans b b b,c a,b a,c,d 9 7 d c d a a b c c
Que 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Ans d b a d c b a c c c d c a b a
Que 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans a a b d b a a 2 6 4 2 d d b c
Que 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Ans a c c c b a b a a b b b a a b
Que 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
Ans c c d a b,d b,d c a b 2 2.30 4 10 2 3
Que 91
Ans b

IMPULSE CLASSES PHYSICS by NILANJAN Sir, 14/13 SEPCO, DURGAPUR-05, Ph-8250641902/7289820158