Question

A bullet of mass $20\text{g}$ is fired from a rifle of mass $5\text{kg}$, with a velocity of $180{\text{m s}}^{-1}$. What is the recoil velocity (in ${\text{m s}}^{-1}$ ) of the rifle?

• A. -0.72

Answer 1

The correct option is A -0.72
Given:
Mass of the bullet, ${\text{m}}_1=20\text{g}=20\times {10}^{-3}\text{kg}$
Mass of the rifle, ${\text{m}}_2=5\text{kg}$
Velocity of the bullet, ${\text{v}}_1=180{\text{m s}}^{-1}$
If the recoil velocity of the rifle is given by ${\text{v}}_2$, then according to the law of conservation of momentum, the total momentum of a system is always conserved, i.e. the momentum of the bullet = the momentum of the rifle
${\text{m}}_1{\text{v}}_1=-{\text{m}}_2{\text{v}}_2$
${\text{v}}_2$ is taken negative, because the rifle moves in a direction opposite to that of the bullet.
$⟹20\times {10}^{-3}\times 180=-5{\text{v}}_2$

$⟹{\text{v}}_2=\frac{-2\times 18\times {10}^{-1}}{5}$

$⟹{\text{v}}_2=\frac{-3.6}{5}=\frac{-36}{50}=\frac{-18}{25}$

$⟹{\text{v}}_2=-0.72{\text{m s}}^{-1}$

The recoil velocity of the rifle is $-0.72{\text{m s}}^{-1}$