Question

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

• A.

  $0.10m{s}^{-1}$

• B. $0.15m{s}^{-1}$
• C. $0.25m{s}^{-1}$
• D. $0.35m{s}^{-1}$

Answer 1

The correct option is B $0.15m{s}^{-1}$

Given, the mass of bullet, $m_1=10g=0.01kg$, initial velocity of bullet, $u_1=1.5m{s}^{-1}$, mass of wooden plank, $m_2=90g=0.09kg$, final velocity of plank and bullet (since bullet gets embedded in the plank) = $v$ and initial velocity of wooden plank, $u_2=0$

Applying, the law of conservation of momentum, i.e. Final momentum = Initial momentum.

$m_1{u}_1+m_2{u}_2=m_{1}v+m_{2}v$

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

$0.015=0.1v$

$\Rightarrow$ $v=0.15m{s}^{-1}$