Question

A bullet of mass $m$ moving with a velocity $v$, strikes a wooden block of mass $M$ and gets embedded in the block which was initially at rest. The final speed of the system is :

• A. $\sqrt{\frac{M}{m+M}}v$
• B. $\sqrt{\frac{m}{M+m}}v$
• C. $\left(\frac{m}{m+M}\right)v$
• D. $\left(\frac{M+m}{M}\right)v$

Answer 1

The correct option is C $\left(\frac{m}{m+M}\right)v$

Lets, $m=$ mass of the bullet

$M=$ mass of the wooden block which is at rest initially

$v=$ velocity of the bullet

$v^{\prime }=$ velocity of the bullet-block system

from the law of conservation of momentum,

$mv=(m+M)v^{\prime }$

$v^{\prime }=\frac{m}{m+M}v$

The corrrect option is C.