Question

A shell of mass $0.020kg$ is fired by a gun of mass $100kg$ . If the muzzle speed of the shell is $80m{s}^{-1}$ . What is the recoil speed of the gun?

• A. $1.6cm{s}^{-1}$
• B. $0.5cm{s}^{-1}$
• C. $2cm{s}^{-1}$
• D. $3cm{s}^{-1}$

Answer 1

Answer: (A)

Here, the mass of gun, $M=100kg$
Mass of shell, $m=0.02kg$
Speed of shell, $v=80m{s}^{-1}$ and let recoil speed of the gun $=V$
$\therefore$ Speed of shell $=v+V$
As initially both the gun and the shell are the rest before firing, so the initial momentum $\left(P_i\right)$ of the system = 0
Final momentum $\left(P_f\right)$ of the system after firing
$=MV+mv=100V+0.02\times (80+V)$
According to the law of conservation of linear momentum,
$P_i=P_f$
$0=100V+1.6+0.02V$
$\Rightarrow V\approx \frac{-1.6}{100}=0.016m{s}^{-1}$
$\therefore$ Recoil speed of gun, $V=0.016m{s}^{-1}=1.6cm{s}^{-1}$