A machine gun fires bullets of mass $30 \mathrm{~g}$ with velocity of $1000 \mathrm{~m} / \mathrm{s}$. The…

A machine gun fires bullets of mass $30 \mathrm{~g}$ with velocity of $1000 \mathrm{~m} / \mathrm{s}$. The man holding the gun can exert a maximum force of $300 \mathrm{~N}$ on it. How many bullets can he fire per second at most?
  1. 3
  2. 6
  3. 10
  4. 9

Solution

Momentum of bullets per second: $\mathrm{P}=\mathrm{nmv}$ According to Newton's second law of motion, $\begin{aligned} \mathrm{F} & =\frac{\mathrm{dp}}{\mathrm{dt}}=\frac{\mathrm{d}(\mathrm{nmv})}{\mathrm{dt}} \\ \therefore \quad \frac{\mathrm{dn}}{\mathrm{dt}} & =\frac{\mathrm{F}}{\mathrm{mv}} \\ & =\frac{300}{0.03 \times 1000} \\ & =10 \end{aligned}$

Asked in: MHT CET 2023 (14 May Shift 2)

Practice more Center of Mass Momentum and Collision questions on Aicharya