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

Options

A. 600 W
B. 300 W
C. 150 W
D. 75 W

Explanation

To find the power of the gun, we can follow these steps:

### Step 1: Convert the speed of the bullet from km/h to m/s
The speed of the bullet is given as 360 km/h. To convert this to meters per second, we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
Calculating this:
\[ \text{Speed} = 360 \times \frac{5}{18} = 100 \text{ m/s} \]

### Step 2: Determine the mass of each bullet in kg
The mass of each bullet is given as 20 g. To convert this to kilograms:
\[ \text{Mass in kg} = \text{Mass in g} \div 1000 \]
Calculating this:
\[ \text{Mass} = 20 \div 1000 = 0.02 \text{ kg} \]

### Step 3: Calculate the kinetic energy of one bullet
The kinetic energy (KE) of a bullet can be calculated using the formula:
\[ \text{KE} = \frac{1}{2} m v^2 \]
Substituting the values:
\[ \text{KE} = \frac{1}{2} \times 0.02 \times (100)^2 \]
Calculating this:
\[ \text{KE} = \frac{1}{2} \times 0.02 \times 10000 = 100 \text{ Joules} \]

### Step 4: Calculate the total kinetic energy per minute
Since 360 bullets are fired per minute, the total kinetic energy per minute is:
\[ \text{Total KE} = \text{Number of bullets} \times \text{KE of one bullet} \]
Calculating this:
\[ \text{Total KE} = 360 \times 100 = 36000 \text{ Joules} \]

### Step 5: Calculate the power of the gun
Power is defined as the total energy transferred per unit time. Since we have the total kinetic energy for one minute, we can calculate the power:
\[ \text{Power} = \frac{\text{Total KE}}{\text{Time in seconds}} \]
Since 1 minute = 60 seconds:
\[ \text{Power} = \frac{36000}{60} = 600 \text{ Watts} \]

### Final Answer
The power of the gun is **600 Watts**.

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