If the potential at the surface of the Earth is assigned a zero value,then the potential at the center of the Earth will be (Mass $= M$,Radius $= R$).

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 ..........

On the $x$-axis and at a distance $x$ from the origin,the gravitational field due to a mass distribution is given by $\frac{Ax}{(x^2+a^2)^{3/2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$,taking its value to be zero at infinity,is

$A$ 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 ..... .

If the gravitational field in space is given as $E = -\frac{K}{r^2}$. Taking the reference point at $r = 2\,cm$ with gravitational potential $V = 10\,J/kg$. Find the gravitational potential at $r = 3\,cm$ in $SI$ units. (Given: $K = 6\,J\cdot cm/kg$)

An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. Which of the following quantities increases for the satellite as a result of this change?