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A bullet of '4g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 m s⁻¹, the impulse imparted to the gun and velocity of recoil of gun are:

1. 0.4 kg m s⁻¹, 0.1 m s⁻¹
2. 0.2 kg m s⁻¹, 0.05 m s⁻¹
3. 0.2 kg m s⁻¹, 0.1 m s⁻¹
4. 0.4 kg m s⁻¹, 0.05 m s⁻¹

Correct answer: 0.2 kg m s⁻¹, 0.05 m s⁻¹

Solution

The impulse imparted to the gun is equal to the momentum of the bullet, which is calculated as the product of its mass and velocity (0.004 kg * 50 m/s = 0.2 kg m/s). The recoil velocity of the gun can be found using the conservation of momentum, resulting in a velocity of 0.05 m/s when considering the mass of the gun.

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