If $V$ is the gravitational potential due to a sphere of uniform density on its surface,then its value at the center of the sphere will be:

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 ....... $J$.

$A$ shell of mass $M$ and radius $R$ has a point mass $m$ placed at a distance $r$ from its centre. The gravitational potential energy $U(r)$ vs $r$ graph will be:

What is potential energy and gravitational potential energy? Write the dimensional formula of gravitational potential energy.

Calculate the energy needed to move a mass of $4 \, kg$ from the center of the Earth to its surface (in joules),given that the radius of the Earth is $6400 \, km$ and the acceleration due to gravity at the surface of the Earth is $g = 10 \, m/s^2$.

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).