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With what minimum speed should $m$ be projected from point $C$ in presence of two fixed masses $M$ each at $A$ and $B$ as shown in the figure such that mass $m$ should escape the gravitational attraction of $A$ and $B$ ?

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$\sqrt{\frac{2 G M}{R}}$

$\sqrt{\frac{2 \sqrt{2} G M}{R}}$

$2 \sqrt{\frac{G M}{R}}$

$2 \sqrt{2} \sqrt{\frac{G M}{R}}$

answer is B.

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Detailed Solution

$K_{i} + U_{i} = K_{f} + U_{f}$

$∴ \frac{1}{2} m v^{2} - 2 \frac{G M m}{\sqrt{2 R}} = 0 + 0$

$∴ v = \sqrt{\frac{2 \sqrt{2} G M}{R}}$

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