Two bodies of masses $\mathrm{m}$ and $4 \mathrm{~m}$ are placed at a distance $\mathrm{r}$. The…
Two bodies of masses $\mathrm{m}$ and $4 \mathrm{~m}$ are placed at a distance $\mathrm{r}$. The gravitational potential at a point on the line joining them where the gravitational field is zero is:
$-\frac{4 \mathrm{Gm}}{\mathrm{r}}$
$-\frac{6 \mathrm{Gm}}{\mathrm{r}}$
$-\frac{9 \mathrm{Gm}}{r}$
zero
Solution
Position of the null point from mass $\mathrm{m}, \mathrm{x}=\frac{\mathrm{r}}{1+\sqrt{\frac{4 \mathrm{~m}}{\mathrm{~m}}}}=\frac{r}{3}$
$
V=-G m\left(\frac{3}{r}+\frac{12}{2 r}\right)=-9 \frac{G m}{r}
$