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

Question

Dr. Abubacker · Accepted Answer

(c) Let gravitation field is zero at $P$ as shown in figure.
[image:8_image52.emf]
$	herefore\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{Gm}{x^{2}} = \frac{G(4m)}{(r - x)^{2}}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ {4x}^{2} = (r - x)^{2}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ 2x = r - x$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{r}{3}$
$	herefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ V_{p} = \frac{Gm}{x} - \frac{G(4m)}{r - x}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = \  - \frac{3Gm}{r} - \frac{6Gm}{r} = - \frac{9Gm}{r}$

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

Explanation

Reviewed by Dr. Abubacker

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