$A$ mass of $50 \, \text{kg}$ is placed at the centre of a uniform spherical shell of mass $100 \, \text{kg}$ and radius $50 \, \text{m}$. If the gravitational potential at a point $25 \, \text{m}$ from the centre is $V \, \text{J/kg}$,find the value of $V$.

Two point masses having mass $M$ and $4 M$ are placed at a distance $r$. The gravitational potential at a point,where the gravitational field intensity is zero,is ..............

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).

Which of the following most closely depicts the correct variation of the gravitational potential $V(r)$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)

Find the potential energy of a system of four particles,each of mass $m$,placed at the vertices of a square of side $l$. Also,obtain the gravitational potential at the centre of the square.

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 $3$ (as shown in the figure) in the gravitational field of the point mass '$m$',find the correct relation between '$W_1$','$W_2$' and '$W_3$'.