Question

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:

• A. 16 $cm{s}^{-1}$
• B. 8 $cm{s}^{-1}$
• C. 8$m{s}^{-1}$
• D. 2$m{s}^{-1}$

Answer 1

Answer: (A)

16 $cm{s}^{-1}$

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