Thank you for reporting, we will resolve it shortly
Q.
Two point masses having $m$ and $4 m$ are placed at distance at $r$. The gravitational potential at a point, where gravitational field intensity zero is
Gravitation
Solution:
Gravitational field intensity at $O$ is zero,
$\Rightarrow \frac{G m}{d^{2}}=\frac{4 G m}{(r-d)^{2}} $
$\Rightarrow \frac{(r-d)^{2}}{d^{2}}=4 $
$\frac{r-d}{d}=\pm 2$
$ r-d=\pm 2 d $
$\Rightarrow d=\frac{r}{3},-r$
$(d=-r$, not possible)
Taking the +ve value of $d$,
Calculating gravitational potential at $O$,
$V= \frac{-G m}{r / 3}-\frac{4 G m}{2 r / 3} $
$=\frac{-3 G m}{r}-\frac{6 G m}{r}$
$=\frac{-9 G m}{r}$
