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A gun of mass M fires a bullet of mass m horizontally. The energy of firing is such that it is sufficient to project the bullet vertically to a height h. The velocity of recoil of the gun is

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$m \sqrt{\frac{2 g h}{m (M + m)}}$

$\sqrt{\frac{2 M g h}{(M + m)}}$

$\sqrt{\frac{2 m g h}{(M + m)}}$

$m \sqrt{\frac{2 g h}{M (M + m)}}$

answer is A.

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Detailed Solution

$u = \frac{M v}{m}$

$E = \frac{1}{2} m u^{2} + \frac{1}{2} M v^{2}$

$= \frac{1}{2} m \frac{M^{2} v^{2}}{m^{2}} + \frac{1}{2} M v^{2}$

$m g h = \frac{1}{2} M v^{2} [\frac{M}{m} + 1]$

$v = m \sqrt{\frac{2 g h}{M (M + m)}}$

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