Question

Two bodies of masses $m$ and $4m$ placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational filed is zero is:

• A. $-\frac{4Gm}{r}$
• B. $-\frac{6Gm}{r}$
• C. $-\frac{9Gm}{r}$
• D. zero

Answer 1

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

Given: Mass of first body = m

Mass of second body= 4m

Distance between bodies =r

Solution: Let us consider the point at which the gravitational field is zero be "P" and let "x" be the distance of the point "P" from first body (mass= m ).

So, distance from the body of mass $4m=r-x$

Therefore, $\frac{Gm}{x^2}=\frac{G\left(4m\right))}{(r-x{)}^2}$ (1)

On solving we get,

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

So, gravitational potential at point "P" is,

$-\frac{Gm}{\left(\frac{r}{3}\right)}-\frac{G\left(4m\right)}{(r-\frac{r}{3})}$ (Using 1)

On solving we get,

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

Hence, the correct option is (C).