Question

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

A
zero
B
4Gmr
C
6Gmr
D
9Gmr.

Solution

## The correct option is D $$-\displaystyle \frac{9\mathrm{G}\mathrm{m}}{\mathrm{r}}$$.Given:Two masses $$m$$ and $$4m$$ kept at a distance $$r$$Let gravitetional potential is zero at a point $$p$$$$\dfrac{Gm}{x^2}-\dfrac{G(4m)}{(r-x)^2}=0$$$$\dfrac1x = \dfrac 2{(r-x)}$$$$r - x = 2x$$$$3x = r$$$$x = r/3$$Potential at point $$p$$$$V=-\dfrac{4Gmm}{(2r/3)}-\dfrac{Gmm}{(r/3)}$$$$\displaystyle V=-Gm(\dfrac{6}{r}+ \frac{3}{r})= -9\dfrac{Gm}{r}$$Physics

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