Question

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

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

Answer 1

Answer: (D)

Work done by the gun
=Total kinetic energy of the bullets
$=n=\frac{1}{2}mv^{2}$
$=240\times \frac{1}{2}\times 10\times \left(10\right)^{- 3}\left(600\right)^{2}$
$=120\times \frac{1}{2}\times 10\times 10^{- 3}\times 600\times 600$
$\therefore \, \, \, Power \, of \, gun=\frac{w o r k \, d o n e}{t i m e \, t a k e n}$
$=\frac{120 \times 10 \times 10^{- 3} \times 600 \times 600}{1 m i n}$
$=\frac{120 \times 10 \times 360}{60}=120\times 10\times 6 \, W$
$\frac{120 \times 10 \times 6}{1000} \, kW=7.2 \, kW$