Q125 / 160 · TS EAMCET 2005 · Physics
The machine gun fires 240 bullets per minute. If the mass of each bullet is $10 \mathrm{~g}$ and the velocity of the bullets is $600 \mathrm{~ms}^{-1}$, the power (in kW) of the gun is
- A43200
- B432
- C72
- Correct answerD7.2
Solution
Work done by the gun $=$ Total kinetic energy of the bullets
$\begin{aligned}
& =n \frac{1}{2} m v^2 \\
& =240 \times \frac{1}{2} \times 10 \times 10^{-3}(600)^2 \\
& =120 \times 10 \times 10^{-3} \times 600 \times 600
\end{aligned}$
$\begin{aligned} \therefore \text { Power of gun } & =\frac{\text { work done }}{\text { time taken }} \\ & =\frac{120 \times 10 \times 10^{-3} \times 600 \times 600}{1 \mathrm{~min}} \\ & =\frac{120 \times 10 \times 360}{60} \\ & =120 \times 10 \times 6 \mathrm{~W} \\ & =\frac{120 \times 10 \times 6}{1000} \mathrm{~kW}=7.2 \mathrm{~kW}\end{aligned}$
Hence, the correct answer is option: 'D'.