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

The masses $m$ in figures $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

If the mass of the Earth is $M$,its radius is $R$,and the gravitational constant is $G$,then the work done to take a $1 \, kg$ mass from the Earth's surface to infinity will be:

The gravitational field in a region is given by $\vec{g} = 5\,N/kg\hat{i} + 12\,N/kg\hat{j}$. The change in the gravitational potential energy of a particle of mass $1\,kg$ when it is taken from the origin to a point $(7\,m, -3\,m)$ is ....... $J$.

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$ respectively (as shown) in the gravitational field of a point mass $m$,find the correct relation between $W_1, W_2$ and $W_3$.

The particles $A$ and $B$ of mass $m$ each are separated by a distance $r$. Another particle $C$ of mass $M$ is placed at the midpoint of $A$ and $B$. Find the work done in moving $C$ to a point equidistant $r$ from $A$ and $B$ without acceleration. ($G$ is the gravitational constant and only gravitational interaction between $A, B$ and $C$ is considered.)