Question

A machine gun fires a bullet of mass $40g$ with a velocity $1200m/s$. The man holding it can exert a maximum force of $144N$ on the gun. How many bullets can be fired per second at the most?

• A. Only one
• B. Three
• C. Can fire any number of bullets
• D. $144\times 48$

Answer 1

Answer: (B)

$\text{Step 1: Newton's Second Law,}$

From Newton's second law

$F=\frac{dP}{dt}$ $....\left(1\right)$

Where, $P=mv$ is the momentum

$\text{Step 2: Total bullets fired per sec}$

Let n be the total number of bullets fired

The force exerted by man must balance the change in momentum of the bullets per second.

$\therefore P=nmv$ $;$ $m$ and $v$ are constant (Given)

$\Rightarrow F=\frac{d}{dt}\left(nmv\right)$

$\Rightarrow$ $\frac{dn}{dt}=\frac{F}{mv}=\frac{144\left(N\right)}{40\times {10}^{-3}\left(kg\right)\times 1200\left(m/s\right)}=3$

Hence total number of bullets fired per second i.e., $\frac{dn}{dt}=3$.

Hence, Option $B$ is correct