JEE Main 2025 January Physics: Gravitation – Previous Year Questions

A small point of mass $m$ is placed at a distance $2R$ from the centre 'O' of a big uniform solid sphere of mass $M$ and radius $R$. The gravitational force on 'm' due to $M$ is $F_1$. A spherical part of radius $R/3$ is removed from the big sphere as shown in the figure and the gravitational force on $m$ due to remaining part of $M$ is found to be $F_2$. The value of ratio $F_1:F_2$ is

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is $g$.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

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.

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 $M\sqrt{\frac{GMR}{x}}$. The value of $x$ is , where $M$ and $R$ are the mass and radius of earth, respectively. ($G$ is the gravitational constant)

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 R. The time period of revolution of the second satellite is larger than the first one approximately by

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be :

Two planets, A and B are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2R_A$. The planet B is $4\sqrt2$ times more massive than planet A. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum ($L_B$) of planet B to that of planet A($L_A$) is closest to integer .

Three equal masses $m$ are kept at vertices (A, B, C) of an equilateral triangle of side $a$ in free space. At $t=0$, they are given an initial velocity $\vec V_A=V_0\,\overrightarrow{AC}$, $\vec V_B=V_0\,\overrightarrow{BA}$ and $\vec V_C=V_0\,\overrightarrow{CB}$. Here, $\overrightarrow{AC}$, $\overrightarrow{CB}$ and $\overrightarrow{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :