A machine gun fires `420` bullets per minute. The velocity of each bullet is `300 ms^(-1)` and the mass of each bullet is `1 gm`. The power of the machine gun is

Options

A. `315 W`
B. `315000 W`
C. `630 W`
D. `3150 W`

Explanation

To calculate the power of the machine gun, we will follow these steps:

### Step 1: Understand the Given Information
- The machine gun fires **420 bullets per minute**.
- The **velocity** of each bullet is **300 m/s**.
- The **mass** of each bullet is **1 gram** (which is **0.001 kg**).

### Step 2: Calculate the Change in Kinetic Energy for One Bullet
The kinetic energy (KE) of one bullet when it is fired can be calculated using the formula:
\[ KE = \frac{1}{2} m v^2 \]
Where:
- \( m \) is the mass of the bullet in kg.
- \( v \) is the velocity of the bullet in m/s.

Substituting the values:
\[ KE = \frac{1}{2} \times 0.001 \, \text{kg} \times (300 \, \text{m/s})^2 \]
Calculating \( (300)^2 \):
\[ (300)^2 = 90000 \]
Now substituting back:
\[ KE = \frac{1}{2} \times 0.001 \times 90000 = 0.0005 \times 90000 = 45 \, \text{J} \]

### Step 3: Calculate the Total Kinetic Energy for All Bullets Fired in One Minute
Since the machine gun fires **420 bullets** in one minute, the total kinetic energy (TKE) for all bullets is:
\[ TKE = n \times KE \]
Where \( n = 420 \):
\[ TKE = 420 \times 45 = 18900 \, \text{J} \]

### Step 4: Calculate the Power of the Machine Gun
Power (P) is defined as the work done (or energy transferred) per unit time. Since we calculated the total kinetic energy for one minute, we need to convert this into power:
\[ P = \frac{TKE}{t} \]
Where \( t \) is the time in seconds (1 minute = 60 seconds):
\[ P = \frac{18900 \, \text{J}}{60 \, \text{s}} = 315 \, \text{W} \]

### Final Answer
The power of the machine gun is **315 watts**.

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