Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is

In a gravitational field,at a point where the gravitational potential is zero,

Give the difference between gravitational potential energy and gravitational potential.

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 $\text{ J}$)

$A$ uniform solid sphere of mass $M$ and radius $a$ is surrounded by a concentric uniform thin spherical shell of mass $0.5 M$ and radius $1.5 a$. The gravitational potential energy of a unit mass kept at a distance of $2.5 a$ from the center is

The gravitational field due to a mass distribution is $E = K/x^3$ in the $X$-direction ($K$ is a constant). Taking the gravitational potential to be zero at infinity,its value at a distance $x$ is: