Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

What is the minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ to an altitude of $2R$?

Two stars each of one solar mass $\left(=2 \times 10^{30} \; kg\right)$ are approaching each other for a head-on collision. When they are at a distance of $10^{9} \; km$,their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^{4} \; km$. Assume the stars remain undistorted until they collide. (Use $G = 6.67 \times 10^{-11} \; N \cdot m^{2}/kg^{2}$)

$A$ body of mass $m$ starts falling from a distance $3R$ above the Earth's surface. When it reaches a distance $R$ above the surface of the Earth (radius $R$,mass $M$),its kinetic energy is:

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is

The work done to raise a mass $m$ from the surface of the earth to a height $h$,which is equal to the radius of the earth,is