A bullet of mass 25 gram fired at 100 m/s from a gun of mass 5 kg.Calculate recoil velocity of gun. In this process which quantity is constant.
Answers
Answer:
The recoil velocity of the gun is -0.5 m/s. In this process, the momentum of the system remains constant.
Explanation:
Mass of the bullet, m = 25 g = 0.025 Kg
Velocity of the bullet, v = 100 m/s
Mass of the gun, M = 5 Kg
Let the recoil velocity of the gun = V
The momentum of the bullet, P₁ = mv = 0.025 × 100 = 2.5 Kgm/s
The momentum of the gun, P₂ = MV = 5V Kgm/s
∴ Final momentum of the gun, P = mv + MV
= (2.5 + 5V) Kgm/s
Since the gun is at rest before firing, the initial momentum of the gun will be zero.
By the law of conservation of momentum,
Final momentum = Initial momentum
⇒ 2.5 + 5V = 0
5V = -2.5
V = -2.5 / 5
∴ Recoil velocity of the gun, V = -0.5 m/s
In this process, the momentum before and after firing remains constant.