A bullet 10 g leaves the barrel of gun with a velocity of $600 \mathrm{~m} / \mathrm{s}$. 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 :

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Conservation of Momentum

A bullet 10 g leaves the barrel of gun with a velocity of

600 m / s

. 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 :

(A)12 Ns
(B)6 Ns✓ Correct
(C)36 Ns
(D)3 Ns

Answer: (B)

Solution

By conservation of momentum, the momentum gained by the gun equals the momentum of the bullet (in magnitude).

Momentum of bullet:

p_{b u l l e t} = m_{b u l l e t} \times v_{b u l l e t} = 0.01 \times 600 = 6

kg·m/s

By momentum conservation:

m_{g u n} \times v_{g u n} = m_{b u l l e t} \times v_{b u l l e t}

3 \times v_{g u n} = 6

v_{g u n} = 2

m/s

Impulse on gun = change in momentum of gun =

m_{g u n} \times v_{g u n} = 3 \times 2 = 6

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

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