Question

A bullet of mass m and velocity v is fired into a large block of wood of mass M . The final velocity of the system is :

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

Answer 1

Answer: (C)

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

Since there is no extra force other than the action and reaction force so the linear momentum should be conserved.

Suppose the system moves with velocity $V$

then momentum before collision is $mv$ and that after collision will be $(M+m)V$

Equating both we get $mv=(M+m)V$

or $V=\frac{m}{m+M}v$