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 = 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)` (negative 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