Question

A bullet of mass $10g$ moving with the velocity of $1.5m{s}^{-1}$ hits a thick wooden plank of mass $90g$. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank, and both move with a certain speed. Calculate the speed with which the plank containing the bullet moves?

• A. $0.15m{s}^{-1}$
• B. $0.5m{s}^{-1}$
• C. $1.5m{s}^{-1}$
• D. $2m{s}^{-1}$

Answer 1

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

Mass of the bullet, $m=10gm=0.01kg$

Velocity of bullet , $v=1.5m{s}^{-1}$

Mass of plank, $m_p=90gm=0.09kg$

Initial velocity of plank $=0m/s$

Momentum of the bullet, $p=mv=0.01\times 1.5=0.015kgm/s$

Total mass of the plank $=m+m_p=0.01+0.09=0.1kg$

The plank and the bullet both move with the same speed

The momentum of the plank and the embedded bullet is $0.015kgm/s$

($\because$ the momentum is conserved in a collision.)

But the momentum of the plank and the embedded bullet = product of their mass and velocity.

$\therefore 0.015=0.1\times v$

$\Rightarrow \therefore v=\frac{0.015}{0.1}=0.15m/s$

The speed of the plank containing the bullet is $0.15m/s$