Question

Two point masses having $m$ and $4m$ are placed at distance at $r$. The gravitational potential at a point, where gravitational field intensity zero is

• A. $\frac{-9GM}{r}$
• B. $\frac{-2GM}{3r}$
• C. $\frac{-3GM}{r}$
• D. $\frac{-6GM}{5r}$

Answer 1

Answer: (A)

Gravitational field intensity at $O$ is zero,
$\Rightarrow \frac{Gm}{d^2}=\frac{4Gm}{(r-d{)}^2}$
$\Rightarrow \frac{(r-d{)}^2}{d^2}=4$
$\frac{r-d}{d}=\pm 2$
$r-d=\pm 2d$
$\Rightarrow d=\frac{r}{3},-r$
$(d=-r$, not possible)
Taking the +ve value of $d$,
Calculating gravitational potential at $O$,
$V=\frac{-Gm}{r/3}-\frac{4Gm}{2r/3}$
$=\frac{-3Gm}{r}-\frac{6Gm}{r}$
$=\frac{-9Gm}{r}$