Question

A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is.

• A. K
• B. More than K
• C. Less than K
• D. $\sqrt{K}$

Answer 1

The correct option is C Less than K

Let mass of bullet and the gun be $m$ and $M$, respectively such that $M>>m$.

Initial momentum of the system is zero. Thus according to law of conservation of momentum, final momentum of the system must also be zero. This implies that recoil momentum of gun must be equal and opposite to that of bullet. i.e. $P_g=P_b$

Kinetic energy of bullet $K=\frac{P_b^2}{2m}$

Kinetic energy of gun $K_g=\frac{P_g^2}{2M}$

But we know $P_b=P_g$ and $M>>m$

$⟹$ $K_g<K$