The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the Earth is $U$. Express the weight of the body at this point in terms of $U$.

$A$ point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre $C$. When released,it reaches $C$ under the gravitational attraction of the ring. Its speed at $C$ will be

Gravitational potential at the centre of curvature of a hemispherical bowl of radius $R$ and mass $M$ is $V.$

If the potential energy of a body of mass $m$ on the surface of the Earth is taken as zero,then its potential energy at height $h$ above the surface of the Earth is ($R$ is the radius of the Earth and $M$ is the mass of the Earth).

The gravitational field in a region is given by $E = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. If a particle of mass $2 \text{ kg}$ is moved from the origin to the point $(12 \text{ m}, 15 \text{ m})$ in this region,the change in gravitational potential energy is (in $\text{ J}$)

$A$ 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?