Question

A bullet of mass, m and velocity v is fired into a block of mass M and stricks to it. What would be the final velocity?

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

Answer 1

Answer: (B)

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

Lets consider, $m_1=m$ mass of bullet

$m_2=M$ mass of block

$u_1=v$ velocity of bullet before collision

$u_2=0m/s$ block is at rest before collision

$v_f=$ final velocity after collision

From the conservation of linear momentum,

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

$mv+M\left(0\right)=(m+M)v_f$

$v_f=\frac{mv}{m+M}$

The correct option is B.