Gravitation

The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

The escape velocity from the surface of the Earth is \(11.2 \mathrm{~km} / \mathrm{s}\). Find the escape velocity from a planet whose radius is 2 times that of Earth and mass is 8 times that of Earth.

A particle of mass m is under the influence of the gravitational field of a body of mass M(≫ m). The particle is moving in a circular orbit of radius r₀ with time period T₀ around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy V_c(r) = mα/r³, where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r₀ in the combined gravitational potential due to M and V_c(r), but with a new time period T₁, then\(\left({\mathrm{T}}_{1}^{2}-{\mathrm{T}}_{0}^{2}/{\mathrm{T}}_{1}^{2}\right)\) is given by
[G is the gravitational constant.]

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.

[JEE Main 2025, 23 Jan (Shift 2)]

Two planet A and B are revolving around a massive star such that \(r_A=2 r_B\) and \(m_A=4 \sqrt{3} m_B\). Find ratio of angular momentum of planet B to planet A.(Shift - II Memory Based)

A particle of mass m is under the influence of the gravitational field of a body of mass M(≫ m). The particle is moving in a circular orbit of radius r₀ with time period T₀ around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy V_c(r) = mα/r³, where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r₀ in the combined gravitational potential due to M and V_c(r), but with a new time period T₁, then\(\left({\mathrm{T}}_{1}^{2}-{\mathrm{T}}_{0}^{2}/{\mathrm{T}}_{1}^{2}\right)\) is given by
[G is the gravitational constant.]

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

[JEE Main 2024, 5 Apr (Shift 1)]

Consider a star of mass \(m_2 kg\) revolving in a circular orbit around another star of mass \(m_1 kg\) with \(m_1 \gg m_2\). The heavier star slowly acquires mass from the lighter star at a constant rate of \(\gamma kg / s\). In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is \(r\), then its relative rate of change \(\frac{1}{r} \frac{d r}{d t}\) (in \(s ^{-1}\) ) is given by:

[JEE Advanced 2025]

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

[JEE Main 2024, 5 Apr (Shift 1)]

Satellite A is launched into a circular orbit of radius R. Satellite B is launched into a circular orbit of radius 1.03R. By approximately what percentage is the time period of B greater than that of A?

(Shift I - Memory Based)

Consider a star of mass \(m_2 kg\) revolving in a circular orbit around another star of mass \(m_1 kg\) with \(m_1 \gg m_2\). The heavier star slowly acquires mass from the lighter star at a constant rate of \(\gamma kg / s\). In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is \(r\), then its relative rate of change \(\frac{1}{r} \frac{d r}{d t}\) (in \(s ^{-1}\) ) is given by:

[JEE Advanced 2025]

The mass of the moon is \(\frac{1}{144}\) times the mass of a planet and its diameter is \(\frac{1}{16}\) times the diameter of a planet. If the escape velocity on the planet is \(v\), the escape velocity on the moon will be :

A body weight \(W\), is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

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, \(M_1 R_1=M_2 R_2\)
In the light of the above statements, choose the most appropriate answer from the options given below:

[JEE Main 2021, 25 Feb (Shift 1)]

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

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

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :