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 :

The correct option is D $-\frac{9Gm}{r}$.

Given:

Two masses $m$ and $4m$ kept at a distance $r$

Let gravitetional potential is zero at a point $p$

$\frac{Gm}{x^2}-\frac{G\left(4m\right)}{(r-x{)}^2}=0$

$\frac{1}{x}=\frac{2}{(r-x)}$

$r-x=2x$

$3x=r$

$x=r/3$

Potential at point $p$

$V=-\frac{4Gmm}{\left(2r/3\right)}-\frac{Gmm}{\left(r/3\right)}$

$V=-Gm(\frac{6}{r}+\frac{3}{r})=-9\frac{Gm}{r}$