Question

A bullet of mass $m$ is being fired from a stationary gun of mass $M$. If the velocity of the bullet is $v$, the velocity of the gun is

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

Answer 1

Answer: (B)

$\frac{mv}{M}$

$\overrightarrow{P_i}=0$

$\overrightarrow{P_f}=\overrightarrow{P_{fG}}+\overrightarrow{P_{fB}}=M\overrightarrow{V_G}+m\overrightarrow{v_B}$

From conservation of momentum,

$M\overrightarrow{V_G}+m\overrightarrow{v_B}=0\Rightarrow \overrightarrow{V_G}=-\frac{m}{M}\overrightarrow{v_B}\Rightarrow \overrightarrow{V_G}=\frac{m}{M}v$