$A$ 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 $V$.

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the center of the circle?

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

Two heavy spheres each of mass $100 \; kg$ and radius $0.10 \; m$ are placed $1.0 \; m$ apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so,is the equilibrium stable or unstable?

What is the potential energy of a satellite at a height of $6.4 \times 10^6 \, m$ from the surface of the Earth? ($R_e$ = radius of the Earth)

$A$ particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell is