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

Answer: (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,
$mv-MV=0$
$\Rightarrow V=\frac{mv}{M}$
The KE of the rifle is
$K{E}_r=\frac{1}{2}M{V}^2=\frac{1}{2}M\frac{m^2{v}^2}{M^2}$
$=\frac{m}{M}\frac{1}{2}m{v}^2$
$=\frac{m}{M}\left(K{E}_b\right)$
$\because m<M$
$\therefore K{E}_r<K{E}_b$
$\therefore$ Kinetic energy of the rifle is less than that of the bullet.