A bullet of mass 20g leaves the gun with a velocity of 200 m/s. If the mass of gun is 2kg then the speed of recoil of the gun is:
Correct answer: B. 2 m/s
- A. 2000 m/s
- B. 2 m/s
- C. 20 m/s
- D. 200 m/s
- E. 100 m/s
Explanation
The principle of conservation of momentum states that the total momentum of an isolated system remains constant. Here, the gun and the bullet together form a system. So, the momentum of the gun and the bullet before firing will be equal to the momentum of the gun and the bullet after firing.Initial momentum = Final momentum(mass of gun) x (velocity of gun) = (mass of bullet) x (velocity of bullet) + (mass of gun) x (velocity of recoil)Substituting the values, we get:(2 kg) x 0 m/s = (0.02 kg) x (200 m/s) + (2 kg) x (velocity of recoil)Solving for the velocity of recoil, we get:velocity of recoil = - (0.02 kg) x (200 m/s) / (2 kg) = -2 m/sThe negative sign indicates that the recoil is in the opposite direction to the direction of the bullet. So, the magnitude of the speed of the recoil of the gun is 2 m/s.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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Linear momentum is the vector product of mass and velocity, p = mv, and changes when a net external force acts. Work includes impulse as the change in momentum, conservation of momentum in isolated systems, collisions and explosions, and the distinction between elastic, inelastic and perfectly inelastic collisions.
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