Question

A machine gun of mass $5kg$ fires $30$ bullets, each of mass $50g$, per minute at a speed of $400m{s}^{-1}$. What force must be exerted to keep the machine gun in position?

• A. $30N$
• B. $10N$
• C. $27N$
• D. $33N$

Answer 1

The correct option is B $10N$

$\text{Step 1: Applying Newton's IInd law of motion}$

Number of bullets fired per minute, $n=30$

Reaction force from gun is producing the necessary force to change the momentum of bullets. [Refer Fig.]

$\Rightarrow F=\frac{\text{Change in momentum}}{time}=n\frac{\Delta P}{\Delta t}$ (Where Momentum $P=mv$) $....\left(1\right)$

$\Rightarrow F=n\times \frac{m\Delta v}{\Delta t}$

$\text{Step 2: Putting given values}$

We get

$F=\frac{30\times (50\times {10}^{-3}Kg)\times (400m/s-0)}{60sec}$

$\Rightarrow F=10N$
Hence $B$ is the correct option.