A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of $100 \mathrm{~m} \mathrm{~s}^{-1}$ each. The recoil velocity of the gun is :

(D) $0.6 \mathrm{~m} / \mathrm{s}$

(A) $0.02 \mathrm{~m} / \mathrm{s}$

(B) $2.5 \mathrm{~m} / \mathrm{s}$

(C) $1.5 \mathrm{~m} / \mathrm{s}$

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Conservation of Momentum

A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of

100 m s^{- 1}

each. The recoil velocity of the gun is :

(A) $0.02 m / s$
(B) $2.5 m / s$
(C) $1.5 m / s$
(D) $0.6 m / s$ ✓ Correct

Answer: (D)

Solution

In one second the gun fires

\frac{180}{60} = 3

bullets, each of mass

20

= 0.02

kg leaving with a speed of

100

^{- 1}

. The forward momentum carried away by these bullets every second is

3 \times 0.02 \times 100 = 6

kg ms

^{- 1}

. With no external horizontal force on the gun--bullet system, the gun must acquire an equal and opposite momentum in the same time, so

M v_{recoil} = 6

. Taking the gun mass

M = 10

kg, the recoil speed of the gun is

v_{recoil} = \frac{6}{10} = 0.6

^{- 1}

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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