Q80 / 100 · BITSAT 2022 · Physics
A machine gun fires 300 bullets per $\mathrm{min}$ if the mass of each bullet is $10 \mathrm{~g}$ and the velocity of the bullets is $600 \mathrm{~ms}^{-1}$, the power (in $\mathrm{kW}$ ) of the gun is
- A$43200$
- Correct answerB$9$
- C$72$
- D$7.2$
Solution
Work done by the gun $=$ total kinetic energy of the bullets
$$
\begin{aligned}
& =n \frac{1}{2} m v^2=300 \times \frac{1}{2} \times 10 \times 10^{-3} \times(600)^2 \\
& =150 \times 10 \times 10^{-3} \times 600 \times 600
\end{aligned}
$$
$$
\begin{aligned}
\text { Power of gun } & =\frac{\text { work done }}{\text { Time taken }} \\
& =\frac{150 \times 10 \times 10^{-3} \times 600 \times 600}{60 \mathrm{~s}} \\
& =9 \mathrm{~kW} \quad(\because 1 \text { minute }=60 \text { seconds })
\end{aligned}
$$
Hence, the correct answer is option: 'B'.