A machine gun fires a bullet of mass 40 g with a velocity $1200 \mathrm{~ms}^{-1}$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?

JEE Main · 2004 · 24 Apr 2004 · Offline · Conservation of Momentum

A machine gun fires a bullet of mass 40 g with a velocity

1200 ms^{- 1}

. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?

(A)one
(B)four
(C)two
(D)three✓ Correct

Answer: (D)

Solution

Each bullet of mass

40

g leaves the gun at

1200

m/s, so it carries away momentum

\frac{40}{1000} \times 1200 = 48

kg m/s. Firing

n

bullets every second changes momentum at the rate

48 n

, and that rate is the recoil force the man must hold. Since his hand can supply at most

144

48 n \leq 144

, which means

n \leq 3

, so he can fire at most three bullets each second.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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