Question

From an automatic gun a man fires $240$ bullet per minute with a speed of $360km/h$. If each weighs $20g$, the power of the gun is

• A. $400W$
• B. $300W$
• C. $600W$
• D. $150W$

Answer 1

The correct option is A

$400W$

Step 1. Given data

Total number of bullet $n=240permin$

Time $t=1min$

$\Rightarrow$ $t=60sec$ (since $1min=60sec$)

Speed of bullet, $v=360km/h$,

$\Rightarrow v=\frac{360\times 1000}{3600}m/s$ (since $1km=1000m$ and $1hour=3600sec$)

$\Rightarrow$ $v=100m/s$

Mass of bullet, $m=20g$,

$\Rightarrow$ $m=0.02kg$ (since $1g=\frac{1}{1000}kg$)

Step 2. Finding the power of gun,

We know that, Power $P=\frac{K.E}{t}$,

Where, $P$ is the power of the gun, $K.E$is the kinetic energy of a bullet and$t$ is the time taken by bullet to fire.

We know that, $K.E=\frac{1}{2}m{v}^2$ (where $m$ is mass and $v$ is velocity.)

Since the total $240permin$ number of bullets being fired therefore Power $P$,

$$\begin{gathered} \Rightarrow P=\frac{{\displaystyle n\left(\frac{1}{2}m{v}^2\right)}}{t} \\ \Rightarrow P=\frac{240\left[\frac{1}{2}\times 0.02\times {\left(100\right)}^2\right]}{60} \\ \Rightarrow P=4\times \left(100\right)W \\ \Rightarrow P=400W \end{gathered}$$

Hence, option A is correct.