Question

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10g$and the velocity of the bullets is$600m{s}^{-1}$ , the power (in kW) of the gun is

• A. $43200$
• B. $432$
• C. $72$
• D. $7.2$

Answer 1

The correct option is D

$7.2$

Step 1: Given data:

The machine gun fires $n=240$ bullets per minute

The mass of each bullet$m=10g$$=\begin{array}{rcl}& & 10\end{array}\begin{array}{rcl}& & \times \end{array}\begin{array}{rcl}& & 10\end{array}\begin{array}{rcl}& & \end{array}$

The velocity of bullets$v=600m{s}^{-1}$

The time taken $t=60sec$

Step 2: Formula used and find the power of the gun:

Know that the $power=\frac{Workdone}{Timetaken}$

$\begin{array}{rcl}Power& =& \frac{Totalkineticenergyofbullets}{Timetaken}\\ & =& \frac{n\frac{1}{2}m{v}^2}{t}\\ & =& \frac{240\times \frac{1}{2}\times 10\times {10}^{-3}\times {\left(600\right)}^2}{60}\\ & =& 2\times 10\times {10}^{-3}\times {\left(600\right)}^2\\ & =& 7.2kW\end{array}$

Therefore the power of gun is $7.2KW$.

Hence, the correct option is D.