Question

A loaded spring gun of mass $M$ fires a shot of mass $m$ with a velocity $v$ at an angle of elevation $\theta$. The gun was initially at rest on a horizontal frictionless surface. After firing, the centre of mass of gun-shot system:

• A. moves with a velocity $\frac{mv}{M}$
• B. moves with a velocity $\frac{mv}{M\cos \theta }$ in the horizontal direction
• C. remains at rest
• D. moves with velocity $\frac{(M-m)v}{(M+m)}$ in the horizontal direction

Answer 1

The correct option is C remains at rest

If we consider a system consists of gun plus mass m. Then no external force is present on the system. So, the acceleration of center of mass of system will be zero. Since initially the system is in rest. So center of mass will always remain at rest.