Question

Two particles of masses $m$ and $4m$ are separated by a distance $r$. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is ($G=$ Universal constant of gravitation)

• A. $-\frac{4Gm}{r}$
• B. $-\frac{9Gm}{r}$
• C. $-\frac{15Gm}{r}$
• D. $-\frac{32Gm}{r}$

Answer 1

The correct option is B $-\frac{9Gm}{r}$

Let $x$ be the point where gravitational field is zero.

$\therefore \frac{Gm}{x^2}=\frac{G\left(4m\right)}{{(r-x)}^2}$

So, $\frac{1}{x}=\frac{2}{r-x}$

$\Rightarrow (r-x)=2x$

$\Rightarrow x=\frac{r}{3}$

Therefore, the point $P$ is at a distance $\frac{r}{3}$ from $m$ and $\frac{2r}{3}$ from $4m$

$\therefore V=\frac{-Gm}{\frac{r}{3}}-\frac{G\left(4m\right)}{\frac{2r}{3}}$

$\Rightarrow V=\frac{-9Gm}{r}$