$A$ 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

What is gravitational potential energy? What is zero potential energy?

$A$ body of mass $2M$ is split into four masses $\{m, M-m, m, M-m\}$,which are placed at the corners of a square of side $d$ as shown in the figure. The ratio $\frac{M}{m}$ for which the gravitational potential energy of the system is maximum is $x:1$. The value of $x$ is ..... .

The particles $A$ and $B$ of mass $m$ each are separated by a distance $r$. Another particle $C$ of mass $M$ is placed at the midpoint of $A$ and $B$. Find the work done in moving $C$ to a point equidistant $r$ from $A$ and $B$ without acceleration. ($G$ is the gravitational constant and only gravitational interaction between $A, B$ and $C$ is considered.)

If the gravitational intensity at a height of $8000 \, km$ from the center of the Earth is $6 \, N/kg$,what is the gravitational potential at that point?

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 $\text{ J}$)