A 5 kg rifle fires a 10 g bullet at a velocity of 500 m/s. Find the recoil velocity of the rifle.

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Solution

Given
Mass of the Bullet, $m_{b} = 10 g = 0.01 k g .$
Mass of the rifle, $m_{r} = 5 k g .$
Initial velocity of the gun, $u_{g} = 0 m / s .$ (The gun is at rest)
Initial velocity of the bullet, $u_{b} = 0 m / s .$ (The gun has not been fired)
Velocity of the bullet after getting fired, $v_{b} = 500 m / s .$
Concept to be used
We will use the concept of conservation of momentum.
Momentum before firing the gun = Momentum after firing the gun
Formula for momentum is given by: $p = m v$ .
Calculation of the mass of the gun
Initial momentum of a system = Final momentum of a system. (According to the law of conservation of momentum).
Initial momentum of the rifle + Initial momentum of the bullet = Final momentum of the rifle + Final momentum of the bullet.
$m_{r} u_{r} + m_{b} u_{b} = m_{r} v_{r} + m_{b} v_{b} .$
$5 \times 0 + 0.01 \times 0 = 5 \times (- v_{r}) + 0.01 \times 500 .$
$0 = - 5 v_{r} + 5$
$5 v_{r} = 5$
$v_{r} = \frac{5}{5} = 1 m / s .$
Hence, the recoil velocity of the rifle is 1 m/s.

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