Question

Two point masses having mass $M$ and $4M$ are placed at distance $r$. 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)

$\frac{-9GM}{r}$

Let the point be the position when the gravitational field $=0$

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

or, $\frac{1}{x}=\frac{2}{(r-x)}$

or, $r-x=2x$

or, $x=\frac{r}{3}$

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

$V=\frac{-GM}{r/3}-\frac{G\left(4m\right)}{\frac{2r}{3}}=\frac{-9GM}{r}$