Question

A bullet is fired from a rifle. If the rifle recoils freely, then the kinetic energy of the rifle, is

• A. same as that of the bullet
• B. more than that of the bullet
• C. less than that of the bullet
• D. equal or less than that of the bullet

Answer 1

The Correct Option is C

Let the mass of the bullet be $m$ and that of the rifle be $M$. Initially both arc at rest. Hence the total linear momentum of the system $=0$ Now, after the bullet is fired, let the velocity of the bullet be $v$ and the recoil speed of the rifle be $V$, then from law of conservation of linear momentum, $m v-M V =0$ $\Rightarrow V =\frac{m v}{M}$ The KE of the rifle is $KE _{r}=\frac{1}{2} M V^{2} =\frac{1}{2} M \frac{m^{2} v^{2}}{M^{2}}$ $=\frac{m}{M} \frac{1}{2} m v^{2}$ $=\frac{m}{M}\left(K E_{b}\right)$ $\because m < M$ $\therefore KE _{r} < KE _{b}$ $\therefore$ Kinetic energy of the rifle is less than that of the bullet.