Find the recoil velocity of a gun having mass equal to 5 kg, if a bullet of 25 g acquires the velocity of 500 m/s after firing from the gun.(in m/s)

The correct option is B 2.5 m/s

Here given,

Mass of bullet (m₁) = 25 g = 0.025 kg

Velocity of bullet before firing (u₁) = 0

Velocity of bullet after firing (v₁) = 500 m/s

Mass of gun (m₂) = 5 kg

Velocity of gun before firing, (u₂) = 0

Velocity of gun after firing = ?

We know that, m₁u₁+m₂u₂ = m₁v₁+m₂v₂

(0.025 kg x 0) + (5 kg x 0) = (0.025 kg x 500 m/s) + (5 kg x v₂)

0 = 12.5 kgm/s + (5 kg x v₂)

5 kg x v₂ = - 12.5 kgm/s

v₂ = $\frac{-12.5kgm/s}{5kg}$ = -2.5 m/s

Thus, recoil velocity of gun is equal to 2.5 m/s. Here negative (- ve) sign shows that gun moves in the opposite direction of bullet.