Question

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

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

Answer 1

The correct option is A $1.6{cms}^{-1}$

Here, mass of gun, $M=100kg$
Mass of shell, $m=0.02kg$
Speed of shell, $v=80m{s}^{-1}$ and let recoil speed of gun $=-V$
As initially both the gun and the shell are at 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
$=MV+mv=100V+0.02\times 80$
According to law of conservation of linear momentum,
$P_i=P_F$
$0=100V+1.6$
$\Rightarrow V=\frac{-1.6}{100}=0.016m{s}^{-1}$
$\therefore$ Recoil speed of gun, $V=0.016m{s}^{-1}=1.6cm{s}^{-1}$