Question

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

• A. $-\frac{4Gm}{r}$
• B. $-\frac{6Gm}{r}$
• C. $-\frac{9Gm}{r}$
• D. zero

Answer 1

Answer: (C)

Let gravitational field at the point $A$ in zero as
shown in figure below

So, $\frac{Gm}{x^2}=\frac{G(4m)}{(r-x{)}^2}$ or $(r-x{)}^2=(2x{)}^2$
or $r-x=2x$
$\Rightarrow 3x=r$(neglecting negative values)
$\therefore x=\frac{r}{3}$
Hence, gravitational potential at point $A$,
$V=\frac{-GM}{x}-\frac{G(4m)}{(r-x)}$
$=-\frac{3Gm}{r}-\frac{3G(4m)}{2r}$
$=\frac{-9Gm}{r}$