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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
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B
4Gmr
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C
6Gmr
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D
9Gmr.
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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 $$p$$

$$V=-\dfrac{4Gmm}{(2r/3)}-\dfrac{Gmm}{(r/3)}$$

$$\displaystyle V=-Gm(\dfrac{6}{r}+ \frac{3}{r})= -9\dfrac{Gm}{r}$$



1534025_40429_ans_4025e132740b4e7daeefd819623b7598.PNG

Physics

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