Gravitation

A body which is initially at rest at a height $R$ above the surface of the Earth of radius R, falls freely towards the Earth, then its velocity on reaching the surface of the Earth is

The distance between Sun and Earth is $R$. The duration of year if the distance between Sun and Earth becomes $3 R$ will be:

The kinetic energy of a satellite in its orbit around the earth is E . What should be the kinetic energy of the satellite so as to enable it to escape from the gravitational pull of the earth?

For a particle inside a uniform spherical shell, the gravitational force on the particle is

If $\mathrm{V}$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:

Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be:

Two planets $A$ and $B$ of radii $R$ and $1.5 R$ have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to A is :

A point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre C. When released, it reaches $\mathrm{C}$ under the gravitational attraction of the ring. Its speed at $C$ will…

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. F $\propto \frac{1}{r^{3}}$, but still remaining a central force. Then

The potential energy of a satellite of mass $\mathrm{m}$ and revolving at a height $\mathrm{R}_{\mathrm{e}}$ above the surface of earth where $\mathrm{R}_{\mathrm{e}}=$ radius of earth, is

If the the earth is at one-fourth of its present distance from the sun, the duration of year will be

The escape velocity from a planet is $v_{e}$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be