First slide

Power

Question

If a machine gun fires n bullets per second each with kinetic energy K, then the power of the machine gun
is

Easy

A

$n K^{2}$
B

$\frac{K}{n}$
C

$n^{2} K$
D

$n K$

Solution

Power of the machine gun
$= \frac{Total work done}{Time} = \frac{n \cdot \frac{1}{2} m v^{2}}{t}$
$= n \cdot \frac{1}{2} \frac{m v^{2}}{t} (∵ K = \frac{1}{2} m v^{2}, t = 1 s)$
$∴$ The power of the machine gun = nK

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