A bullet of mass 10 g moving with a horizontal velocity of 100 m/s passes through a wooden block of mass 100 g. The block is resting on a smooth horizontal floor. After passing through the block the velocity of the bullet is 10 m/s. The velocity of the emerging bullet with respect to the block is:

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9 m/s

10 m/s

5 m/s

1 m/s

answer is C.

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Detailed Solution

Using the law of conservation of momentum

$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

$m_{1} = 10 g$ $, m_{2} = 100 g$

$u_{2} = 0$ $, v_{1} = 10 m / s$

$\Rightarrow 10 \times 100 + 100 \times 0 = 10 \times 10 + 100 \times v_{2}$

$\Rightarrow 1000 = 100 + 100 v_{2} \Rightarrow v_{2} = 9 m / s$

Therefore, $v_{1}$ with respect to $v_{2} = v_{1} - v_{2}$ = 1m/s.

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