A machine gun fires n bullets per second and the mass of each bullet is m. If v is the speed of each bullet, then the force exerted on the machine gun is

Options

A. m n g
B. m n v
C. m n v g
D. (m n v )/g

Explanation

To find the force exerted on the machine gun when it fires bullets, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- A machine gun fires \( n \) bullets per second.
- Each bullet has a mass \( m \).
- Each bullet travels at a speed \( v \).

2. **Calculate the Change in Momentum of One Bullet**:
- The change in momentum (\( \Delta P \)) of one bullet can be calculated using the formula:
\[ \Delta P = m \cdot v - m \cdot 0 = m \cdot v \]
- Here, the initial momentum is zero (since the bullet starts from rest) and the final momentum is \( m \cdot v \).

3. **Calculate the Total Change in Momentum in One Second**:
- Since the machine gun fires \( n \) bullets per second, the total change in momentum (\( \Delta P_{total} \)) in one second is:
\[ \Delta P_{total} = n \cdot \Delta P = n \cdot (m \cdot v) = n \cdot m \cdot v \]

4. **Calculate the Force Exerted on the Machine Gun**:
- The force (\( F \)) exerted on the machine gun is equal to the rate of change of momentum. This can be expressed as:
\[ F = \frac{\Delta P_{total}}{\Delta t} \]
- Since we are considering the change in momentum over one second (\( \Delta t = 1 \) second), we have:
\[ F = \Delta P_{total} = n \cdot m \cdot v \]

5. **Final Result**:
- Therefore, the force exerted on the machine gun is:
\[ F = n \cdot m \cdot v \]

### Conclusion:
The force exerted on the machine gun is given by the formula:
\[ F = n \cdot m \cdot v \]