A bullet having a mass of 10 g and moving with a speed of 1.5 $m s^{- 1}$ , penetrates a thick wooden plank of mass 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

$0.10 m s^{- 1}$

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$0.15 m s^{- 1}$

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$0.15 m s^{- 2}$

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$0.10 m s^{- 2}$

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Solution

The correct option is C. $0.15 m s^{- 1}$ .
Given,
the mass of bullet $m_{1} = 10 g = 0.01 k g$ ,
initial speed of bullet $u_{1} = 1.5 m s^{- 1}$ ,
mass of wooden plank $m_{2} = 90 g = 0.09 k g$ ,
final velocity of plank + bullet = $v$ and
initial speed of wooden plank $u_{2} = 0$

Here, we apply the law of conservation of momentum, i.e., Final momentum = Initial momentum.

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

$0.01 \times 1.5 + 0.09 \times 0 = 0.01 \times v + 0.09 \times v$

$0.015 = 0.1 v$

On solving $v = 0.15 m s^{- 1}$ .

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A bullet having a mass of 10 g and moving with a speed of 1.5 ms−1, penetrates a thick wooden plank of mass 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

A bullet having a mass of 10 g and moving with a speed of 1.5 $m s^{- 1}$ , penetrates a thick wooden plank of mass 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.