Question

Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is?

Answer 1

Gravitation Potential due to m is zero at a distance x = -Gm/x

Gravitational Potential due to 4m is zero at a distance 4-x = G4m/(4-x)

$$\begin{gathered} \frac{-Gm}{x}=\frac{-G4m}{r-x} \\ 4x=r-x \\ 5x=r \\ x=\frac{r}{5} \end{gathered}$$