A bullet of $$10$$ g leaves the barrel of gun with a velocity of $$600$$ m s$$^{-1}$$. If the barrel of gun is $$50$$ cm long and mass of gun is $$3$$ kg, then value of impulse supplied to the gun will be:

Impulse equals the change in momentum. By Newton's third law, the impulse on the gun equals the impulse on the bullet (in magnitude).

The bullet starts from rest and leaves with velocity $$v = 600$$ m/s. Mass of bullet $$m = 10$$ g $$= 0.01$$ kg.

Impulse on bullet = change in momentum of bullet:

$$J = mv - 0 = 0.01 \times 600 = 6 \text{ N s}$$

By Newton's third law, the impulse supplied to the gun is also $$\mathbf{6}$$ N s (in the opposite direction).