Question

A rifle of mass $5kg$ fires a bullet of mass $40g$. The bullet leaves the barrel of the rifle with a velocity $200m{s}^{-1}$. If the bullet takes $0.004s$ to move through the barrel, calculate the recoil velocity of the rifle.

• A. $3.2m{s}^{-1}$
• B. $2m{s}^{-1}$
• C. $4m{s}^{-1}$
• D. $1.6m{s}^{-1}$

Answer 1

The correct option is D $1.6m{s}^{-1}$

Given:
Mass of bullet, $m_b=40g=\frac{40}{1000}kg=0.04kg$
Mass of rifle, $m_r=5kg$
Initially, the bullet and the rifle, both were in rest.
Initial velocity of bullet, $u_b=0$
Initial velocity of rifle, $u_r=0$
Final velocity of the bullet, $v_b=200m{s}^{-1}$

Let recoil velocity of the rifle be $v_r$.
From the law of conservation of momentum, the total initial momentum of the system before firing is equal to the total final momentum of the system after firing.
$m_b{u}_b+m_r{u}_r=m_b{v}_b+m_r{v}_r$
$0=0.04\times 200+5v_r$
$0=8+5v_r$
$v_r=\frac{-8}{5}m{s}^{-1}=-1.6m{s}^{-1}$
Note that the negative sign shows that the rifle recoils in the direction opposite to the bullet after firing.
Therefore, recoil velocity of the rifle is $1.6m{s}^{-1}$.