Two bodies of mass $m$ and $9 m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero,will be ($G=$ gravitational constant):

In a certain region of space,the gravitational field is given by $E = -\frac{K}{r}$,where $r$ is the distance from a fixed point and $K$ is a constant. Taking the reference point to be at $r = r_0$ with potential $V = V_0$,the potential at a distance $r$ is:

Three masses $m, 2m$ and $3m$ are arranged in two triangular configurations as shown in figure $1$ and figure $2$. The work done by an external agent in changing the configuration from figure $1$ to figure $2$ is:

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).

At some point,the gravitational potential and the gravitational field due to the Earth are both zero. This point is:

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: