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Q.

Two bodies of masses M₁ = m and M₂ = 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

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a

zero

b

- \frac{4 Gm}{r}

c

- \frac{6 Gm}{r}

d

\frac{- 9 Gm}{r}

answer is D.

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Detailed Solution

$x = \frac{r}{\sqrt{\frac{4 m}{m} + 1}}$

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

$V = \frac{- Gm}{r / 3} - \frac{G (4 m)}{2 r / 3}$

$V = \frac{- 3 Gm}{r} - \frac{12 Gm}{2 r}$

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

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