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

Here,

Mass of the shell, $\mathrm{m}=200\mathrm{g}=200\times {10}^{-3} \mathrm{kg}$ ;

Mass of the gun, M = 100 kg ;

Muzzle speed of the shell, V = 80 ${\mathrm{ms}}^{-1}$ ;

Recoil speed of the gun, v = ?

According to the principle of conservation of linear momentum,

mV + Mv = 0

$\mathrm{v} = -\frac{\mathrm{mV}}{\mathrm{M}} = -\frac{(200 \times {10}^{-3}\mathrm{kg})(80 {\mathrm{ms}}^{-1})}{100 \mathrm{kg}}$

$=-16\times {10}^{-2}{\mathrm{ms}}^{-1}=-16 \mathrm{cm} {\mathrm{s}}^{-1}$

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