A particle is projected vertically upwards from the surface of Earth with a speed equal to half the escape velocity. The maximum height reached by the particle, measured from the surface of Earth, is (R = radius of Earth):

The depth d at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value of the surface, is [ R = radius of the earth]

An object is allowed to fall from a height $R$ above the earth, where $\mathrm{R}$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

As we move away from a mass, the gravitational potential:

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct

If the earth stops rotating, the value of $g$ at the equator

Statement-1: The gravitational field intensity on the surface of the sphere is $E=\frac{G M}{R^2}$Statement-2: The gravitational potential on the surface of the sphere is $V=\frac{-G M}{R}$.

Three identical particles of equal mass $m$ are made to move along the circumference of a circle of radius $r$ under the action of their own mutual gravitational attraction. The binding energy of the system is

If four identical particles each of mass $m$, are kept at the four vertices of a square of side length ' $a$ ', the gravitational force of attraction on any one of the particles is

Two masses 2 kg and 4 kg are separated in air by 10 cm. Now air is replaced by water of density $1000\,kg/{m^3}$, then the percentage change in force is

Gravitational potential at a point due to a mass $M$ at a distance $r$ from it is given by: