Question

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

• A. $16cm$ $s^{-1}$
• B. $8cm$ $s^{-1}$
• C. $8m$ $s^{-1}$
• D. $16m$ $s^{-1}$

Answer 1

Answer: (A)

Here, Mass of the shell, $m$ $=200g$ $=200\times 10^{-3}kg$
Mass of the gun, $M=100kg$
Muzzle speed of the shell, $V=80m{s}^{-1}$
Recoil speed of the gun, $v=?$
According to the principle of conservation of linear momentum,
$mV$ $+Mv=0$
$v=-\frac{mV}{M}$ $=-\frac{\left(200\times 10^{-3}kg\right)\left(80m{s}^{-1}\right)}{100kg}$
$=-16\times 10^{-2}m{s}^{-1}$ $=-16cm{s}^{-1}$
$-Ve$ sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell.