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Q.
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
Laws of Motion
Solution:
Here, Mass of the shell, $m$ $=200\, g$ $=200 \times10^{-3} \, kg$
Mass of the gun, $M = 100\, kg$
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,
$m V$ $+ Mv = 0$
$v=-\frac{m V}{M}$ $=-\frac{\left(200\times10^{-3} kg\right)
\left(80\, m\, s^{-1}\right)}{100 \,kg}$
$=-16\times10^{-2}m s^{-1}$ $=-16 \, cm \,s^{-1}$
$-Ve$ sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell.