Two bodies of masses$M_1=m$ and $M_2 = 4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining thein where the gravitational field is zero is

If the gravitational field is zero at a point at a distance x from M₁, then

$$\begin{gathered} \frac{G{M}_1}{x^2}=\frac{G{M}_2}{(r-x{)}^2} \\ or \frac{x}{(r-x)}=\sqrt{\frac{M_1}{M_2}}=\sqrt{\frac{m}{4m}}=\frac{1}{2} \end{gathered}$$

which gives $x=\frac{r}{3}$

Therefore, $r-x=\frac{2r}{3}$. The gravitational potential at $x=\frac{r}{3}$ is 

$$\begin{gathered} U=-\frac{G{M}_1}{x}-\frac{G{M}_2}{(r-x)} \\ =-\frac{Gm}{r/3}-\frac{G\left(4m\right)}{2r/3}=-\frac{9Gm}{r} \end{gathered}$$

Hence the correct choice is (4).