A bullet of mass 100 g is fired from a gun of mass 20 kg with a velocity of $100m{s}^{-1}$. Calculate the velocity of recoil of the gun:

The correct option is A - 0.5 m/s

Mass of bullet, $m=100g=\frac{100}{1000}kg=\frac{1}{10}kg$
Velocity of bullet, $v=100m{s}^{-1}$
Mass of gun, $M=20kg$
Let recoil velocity of gun $=V$
Before firing, the system (gun+bullet) is at rest, therefore, initial momentum of the system $=0$
Final momentum of the system $=$ momentum of bullet + momentum of gun
$=mv+MV=\frac{1}{10}\times 100+20V=10+20V$
Applying law of conservation of momentum, Final momentum $=$ Initial momentum
i.e., $10+20V=0$
$20V=-10$
or $V=-\frac{10}{20}=-0.5m{s}^{-1}$.
Negative sign shows that the direction of recoil velocity of the gun is opposite to the direction of the velocity of the bullet.