In a certain region of space,the gravitational field is given by $E = -k/r$,where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ is $V_0$,then what is the expression for the gravitational potential $V$?

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:

If one wants to remove all the mass of the earth to infinity in order to break it up completely,the amount of energy that needs to be supplied will be $\frac{x}{5} \frac{GM^2}{R}$,where $x$ is .......... (Round off to the Nearest Integer). ($M$ is the mass of earth,$R$ is the radius of earth,$G$ is the gravitational constant)

$A$ person brings a mass of $1 \ kg$ from infinity to a point $A.$ Initially,the mass was at rest but it moves at a speed of $3 \ m/s$ as it reaches $A.$ The work done by the person on the mass is $-5.5 \ J.$ The gravitational potential at $A$ is $:$ (in $J/kg$)

Why does the potential energy of an object increase when it is raised above the surface of the Earth?

Four particles $A, B, C$ and $D$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $D$ is taken to infinity by an external agent,keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $D$ during its movement is ..........