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

Options

A. `nK^(2)`
B. `(K)/(n)`
C. `n^(2)K`
D. nk

Explanation

To solve the problem, we need to determine the power of a machine gun that fires \( n \) bullets per second, each with a kinetic energy \( K \).

### Step-by-Step Solution:

1. **Understanding Power**:
Power is defined as the rate at which work is done or energy is transferred. The formula for power \( P \) is given by:
\[ P = \frac{\text{Total Work Done}}{\text{Time Taken}} \]

2. **Total Work Done**:
In this scenario, the work done by the machine gun can be related to the kinetic energy of the bullets fired. When the gun fires \( n \) bullets, the total kinetic energy imparted to these bullets is:
\[ \text{Total Kinetic Energy} = n \times K \]
where \( K \) is the kinetic energy of each bullet.

3. **Time Taken**:
The problem states that the bullets are fired at a rate of \( n \) bullets per second. Therefore, the time taken for this operation is:
\[ \text{Time} = 1 \text{ second} \]

4. **Calculating Power**:
Now, substituting the total work done (in terms of kinetic energy) and the time into the power formula:
\[ P = \frac{n \times K}{1} \]
Simplifying this, we find:
\[ P = nK \]

5. **Final Answer**:
Therefore, the power of the machine gun is:
\[ P = nK \]

### Conclusion:
The power of the machine gun that fires \( n \) bullets per second, each with kinetic energy \( K \), is given by \( P = nK \).

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