Give the formula of gravitational potential at distance $r$ $(r > R_E)$ from the centre of the Earth.

Two masses $m_1$ and $m_2$ 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:

The gravitational field in a region is given by $E = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. If a particle of mass $2 \text{ kg}$ is moved from the origin to the point $(12 \text{ m}, 15 \text{ m})$ in this region,the change in gravitational potential energy is (in $\text{ J}$)

Taking the gravitational potential at a point at an infinite distance away as zero,the gravitational potential at a point $A$ is $-5 \, unit$. If the gravitational potential at a point at an infinite distance away is taken as $+10 \, units$,the potential at point $A$ is ......... $unit$.

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

The bodies of masses $100 \,kg$ and $8100 \,kg$ are held at a distance of $1 \,m$. The gravitational field at a point on the line joining them is zero. The gravitational potential at that point in $J/kg$ is $\left(G = 6.67 \times 10^{-11} \,Nm^2/kg^2\right)$