Two masses $m_1\, \& m_2$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of $d$ is :

Two satellites of earth $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statement is true ?

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy ?

The masses and radii of the earth and the moon are $M_1$, $R_1$ and $M_2$,$R_2$ respectively. Their centres are distance $d$ apart. The minimum speed with which particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is :

A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 \mathrm{R}$. If $\frac{10^4 \mathrm{R}}{6} \mathrm{~J}$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius:

(use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{R}=$ radius of earth)