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A bullet having a speed of 100 m/sec crashes through a plank of wood. After passing through a plank, its speed is 80 m/s. Another bullet of the same mass and size, but traveling at 80 m/s, is fired at the plank. The speed of the second bullet after traveling through the plank is (Assume that resistance of the plank is independent of the speed of the bullet):

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$10 \sqrt{7} {ms}^{- 1}$

$20 \sqrt{7} {ms}^{- 1}$

$30 \sqrt{7} {ms}^{- 1}$

$20 \sqrt{5} {ms}^{- 1}$

answer is B.

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Detailed Solution

Suppose F be the resistance force offered by the plank. Let thickness of plank be x.
For first case : $\frac{1}{2} m [{(100)}^{2} - {(80)}^{2}] = F x - - - - (i)$
For second case, let V be the final velocity of bullet ,,then

$Fx = \frac{1}{2} m [{(80)}^{2} - V^{2}] - - - - - (ii)$
From (i) and (ii) $80^{2} - V^{2} = 100^{2} - 80^{2}$
or V =20 $\sqrt{7}$ m/s

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