Question

Two bodies of masses 4m & m are placed d distance apart. What is gravitational potential at the position where gravitational field due to them is zero?

Answer 1

Let the gravitational field be zero at point P which is at a distance x from m. So distance from 4m is d-x.
$\frac{Gm}{x^2}=\frac{G4m}{(d-x{)}^2}\Rightarrow \frac{1}{x^2}=\frac{4}{(d-x{)}^2}\Rightarrow d-x=2x\therefore x=\frac{d}{3}$
So the point P is at a distance $\frac{d}{3}$ from mass m and $\frac{2d}{3}$ from the mass 4m.
The potential at this point is
$V=\frac{-Gm}{\frac{d}{3}}+\frac{-G4m}{\frac{2d}{3}}\Rightarrow V=\frac{-9Gm}{d}$