Question

A machine gun fires a bullet of mass 40 g with a velocity of $1200m{s}^{-1}$. The gun can exert a maximum force of 144 N on the bullet. How many bullets can it fire per second at the most?
(AIEEE 2004)

• A. Two
• B. Four
• C. One
• D. Three

Answer 1

The correct option is D

Three

F = $\frac{\Delta p}{\Delta t}$

When the gun applies maximum force

$F_{max}=144N$

$\therefore$ $\Delta t$ = $\frac{\Delta p}{F_{max}}$ = $\frac{m(v-u)}{F_{max}}$

$=\frac{0.04(1200-0)}{144}=\frac{1}{3}s$

$\therefore$To achieve the same change in momentum, the minimum time will be $\frac{1}{3}$ s. Any lesser time and the force applied will be greater.

$\therefore$ In one second 3 bullets can be fired.