A gun fires a bullet of mass 50 g with a velocity of 30 m `s^(-1)` because of which the gun recoils with a velocity 1 m `s^(-1)`. Find the mass of the gun.

Explanation

Mass of the bullet = `m_(1)` = 50 g = 0.05 kg
Initial velocity of bullet, `u_(1)` = 0
Final velocity of the bullet, `v_(1) = 30 m s^(-1)`
Mass of the gun, `m_(2) = ?`
Initial velocity of the gun, `u_(2) = 0`
Final velocity of the gun = -1 m `s^(-1)` (nagative sign indicates that its direction is opposite to that of the bullet's velocity)
From the law of conservation of momentum
`m_(1)u_(1) + m_(2)u_(2) = m_(1)v_(1) + m_(2)v_(2)`
`0 + 0 = 0.05 xx 30 - m_(2) xx 1`
`m_(2) = (0.05 xx 30)/(1) = 1.5 kg `