Gravitation · JEE Main previous year questions

2025 8 questions

1. Q342025 · 4 Apr 2025 · Shift 2

   An object is kept at rest at a distance of $3R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)

   1. A.$\sqrt{\frac{3\mathrm{GM}}{\mathrm{R}}}$
   2. B.$\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}$
   3. C.$\sqrt{\frac{\mathrm{GM}}{2\mathrm{R}}}$
   4. D.$\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$
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   Answer: C

2. Q312025 · 3 Apr 2025 · Shift 1

   Match the LIST-I with LIST-II $$\begin{array}{llll}\text{List - I}& & \text{List - II}& \\ \text{A.}& \text{Gravitational constant}& \text{I.}& \left[\mathrm{L}{\mathrm{T}}^{-2}\right]\\ \text{B.}& \text{Gravitational potential energy}& \text{II.}& \left[{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]\\ \text{C.}& \text{Gravitational potential}& \text{III.}& \left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]\\ \text{D.}& \text{Acceleration due to gravity}& \text{IV.}& \left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]\end{array}$$ Choose the correct answer from the options given below:

   1. A.A-IV, B-III, C-II, D-I
   2. B.A-II, B-IV, C-III, D-I
   3. C.A-I, B-III, C-IV, D-II
   4. D.A-III, B-II, C-I, D-IV
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   Answer: A

3. Q492025 · 3 Apr 2025 · Shift 1· Numerical answer

   Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length $a$. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4\mathrm{seconds}$. If the sides of the triangle are increased to length $2a$ and also the masses of the spheres are made 2 m , then they will collide after____seconds.

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   Answer: 8

4. Q502025 · 2 Apr 2025 · Shift 2· Numerical answer

   A satellite of mass $1000\mathrm{kg}$ is launched to revolve around the earth in an orbit at a height of $270\mathrm{km}$ from the earth's surface. Kinetic energy of the satellite in this orbit is ____ $\times 10^{10}\mathrm{J}$. (Mass of earth $=6\times 10^{24}\mathrm{kg}$, Radius of earth $=6.4\times 10^6\mathrm{m}$, Gravitational constant $=6.67\times 10^{-11}\mathrm{N}{\mathrm{m}}^2\mathrm{k}{\mathrm{g}}^{-2}$ )

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   Answer: 3

5. Q312025 · 24 Jan 2025 · Shift 1

   A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius $1.03\mathrm{R}$ . The time period of revolution of the second satellite is larger than the first one approximately by

   1. A.$3\%$
   2. B.$2.5\%$
   3. C.$4.5\%$
   4. D.$9\%$
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   Answer: C

6. Q282025 · 23 Jan 2025 · Shift 2

   If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.

   1. A.3 days
   2. B.27 days
   3. C.81 days
   4. D.1 day
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   Answer: D

7. Q502025 · 23 Jan 2025 · Shift 2· Numerical answer

   A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $\mathrm{M}\sqrt{\frac{\mathrm{GMR}}{x}}$. The value of $x$ is _________ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

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   Answer: 3

8. Q262025 · 22 Jan 2025 · Shift 1
   
   1. A.$11:10$
   2. B.$12:11$
   3. C.$16:9$
   4. D.$12:9$
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   Answer: B