Question

A bullet of mass m moving with a velocity $v$ is fired into a large wooden block of mass $M$. If the bullet remains embedded on the wooden block, the velocity of the (block + bullet) system is

• A. $\frac{M}{m+M}v$
• B. $\frac{m}{m+M}v$
• C. $\frac{M}{M-m}v$
• D. $\frac{m}{M-m}v$

Answer 1

The correct option is B

$\frac{m}{m+M}v$

Step-1: Given data

• Mass of the bullet = $m$
• Mass of the block = $M$
• Initial Velocity of the bullet =$v$
• Initial Velocity of the block = $0$
• Let u be the velocity of the bullet wooden block system

Step-2: Finding velocity of block and bullet system

As there are no external forces momentum is conserved, hence:

$$\begin{gathered} mv=(m+M)u \\ u=\frac{m}{m+M}v \end{gathered}$$

Hence final velocity of the system is $u=\frac{m}{m+M}v$ and the correct option is (b)