Question

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

Answer: (A)

Here, the mass of gun, $M=100 \, kg$
Mass of shell, $m=0.02 \, kg$
Speed of shell, $v= \, 80 \, ms^{- 1}$ 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
$=MV+mv=100V+0.02\times \left(\right. 80 + V \left.\right)$
According to the law of conservation of linear momentum,
$P_{i}=P_{f}$
$0=100 \, V+1.6+0.02V$
$\Rightarrow \, \, \, V\approx\frac{- 1.6}{100}=0.016 \, ms^{- 1}$
$\therefore \, \, \, $ Recoil speed of gun, $V=0.016 \, ms^{- 1}=1.6 \, cms^{- 1}$