The change in potential energy, when a body of mass $m$ is raised to a height $nR$ from the earth's surface is ($R =$ Radius of earth)

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

A satellite orbits the earth at a height of $400\; km$ above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $=200 \;kg ;$ mass of the earth $=6.0 \times 10^{24} \;kg ;$ radius of the earth $=6.4 \times 10^{6}\;m$ ; $G =6.67 \times 10^{-11}\; N m ^{2} kg ^{-2}$

Two satellites $A$ and $B$, having ratio of masses $3 : 1$ are in circular orbits of radius $r$ and $4r$. Calculate the ratio of total mechanical energy of $A$ and $B$.

Two satellites, $A$ and $B,$ have masses $m$ and $2\,m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $K.E._A / K.E._B ,$ is