A shell of mass $200 g$ is fired by a gun of mass $100 kg$. If the muzzle speed of the shell is $80 m{s}^{-1}$, then the recoil speed of the gun is

Here, Mass of the shell, $m=200g=200\times {10}^{-3}kg$ Mass of the gun, $M=100kg$ 
Muzzle speed of the shell, $V=80 m{s}^{-1}$, Recoil speed of the gun, $v=?$
 According to the principle of conservation of linear momentum, $mV+Mv=0$

$v=-\frac{mV}{M}=-\frac{\left(200\times {10}^{-3}kg\right)\left(80 m{s}^{-1}\right)}{100kg}=-16\times {10}^{-2}m{s}^{-1}=-16 cm s^{-1}$

 $-$ve sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell