The gravitational potential energy of a body of mass $m$ at the earth's surface is $-mgR_e$. Its gravitational potential energy at a height $R_e$ from the earth's surface will be (Here $R_e$ is the radius of the earth).

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 $\text{ J}$)

Which curve depicts the variation of gravitational potential $V$ of a hollow sphere of radius $R$ with distance $r$ from its center?

If the gravitational potential energy of two point masses infinitely away is taken to be zero,then the gravitational potential energy of a galaxy is ...............

$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is:

From a solid sphere of mass $M$ and radius $R$,a spherical portion of radius $R/2$ is removed,as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty$,the potential at the centre of the cavity thus formed is
($G =$ gravitational constant)