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 :

Given:

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

Let gravitetional potential is zero at a point $p$

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

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

$r-x=2x$

$3x=r$

$x=r/3$

Potential at point $p$

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

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