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

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 ....... $J$.

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.

$A$ thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$. The work required to take a unit mass from point $P$ on its axis to infinity is

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \text{ N/kg}$. If a particle of mass $2 \text{ kg}$ is moved from the origin $(0, 0)$ to the point $(12 \text{ m}, 5 \text{ m})$ in this region, the change in gravitational potential energy is: (in $\text{ J}$)

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)