$A$ 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 $V$.

Compare the gravitational potential at the center $O$ for the given arcs,each having mass $M$ and radius $R$.

On the $x$-axis and at a distance $x$ from the origin,the gravitational field due to a mass distribution is given by $\frac{Ax}{(x^2+a^2)^{3/2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$,taking its value to be zero at infinity,is

Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

The diagram showing the variation of gravitational potential of Earth with distance from the centre of Earth is

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: