Question

A loaded spring gun of mass $M$ fires a bullet of mass $m$ with a velocity $v$ at an angle of elevation $\theta$. The gun is initially at rest on a horizontal smooth surface. After firing, the centre of mass of the gun and bullet system

• A. Moves with velocity $\frac{v}{M}m$
• B. Moves with velocity $\frac{vm}{Mcos\theta }$ in the horizontal direction
• C. Does not move in horizontal direction
• D. Moves with velocity $\frac{v(M-m)}{M+m}$ in the horizontal direction

Answer 1

Answer: (C)

Does not move in horizontal direction

Initially both the gun and bullet(inside the gun) are at rest.
Since there is no external force in the horizontal direction, the CM of the gun+ bullet will not have any acceleration.
The initial horizontal momentum of the system is also zero.
Hence, from conservation of momentum, the CM will not move in the horizontal direction.