If a body is released from a point at a height equal to n times the radius of the earth, its velocity on reaching the surface of the earth is (R is radius of earth)

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$\sqrt{\frac{(n + 1) g R}{2 n}}$

$\sqrt{\frac{n g R}{2 (n + 1)}}$

$\sqrt{\frac{2 ngR}{n + 1}}$

$\sqrt{\frac{n g R}{n + 1}}$

answer is A.

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Detailed Solution

$\frac{- GMm}{(R + nR)} = \frac{- GMm}{R} + \frac{1}{2} {mv}^{2}$

$GM (\frac{n}{R (n + 1)}) = \frac{1}{2} v^{2}$

$\frac{GMR}{R^{2}} (\frac{n}{n + 1}) = \frac{v^{2}}{2}$

$v = \sqrt{\frac{2 ngR}{n + 1}} (\frac{G M}{R^{2}} = g)$

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