A gun fires N bullets per second, each of mass m with velocity v. The force exerted by the bullets on the gun is :

Options

A. vNm
B. `(mv)/(N)`
C. `mvN^(2)`
D. `(mv^(2))/(N)`

Explanation

To find the force exerted by the bullets on the gun, we can follow these steps:

### Step 1: Understand the problem
We have a gun that fires \( N \) bullets per second, each with a mass \( m \) and a velocity \( v \). We need to determine the force exerted by these bullets on the gun.

### Step 2: Calculate the momentum of one bullet
The momentum \( P \) of a single bullet can be calculated using the formula:
\[ P = m \cdot v \]
where \( m \) is the mass of the bullet and \( v \) is its velocity.

### Step 3: Calculate the total momentum of \( N \) bullets
If \( N \) bullets are fired in one second, the total momentum of these bullets is:
\[ P_{\text{total}} = N \cdot P = N \cdot (m \cdot v) = Nmv \]

### Step 4: Use the principle of conservation of momentum
According to the conservation of momentum, the total momentum before firing (which is zero) must equal the total momentum after firing. Therefore, the momentum of the gun must equal the momentum of the bullets:
\[ P_{\text{gun}} = P_{\text{bullets}} = Nmv \]

### Step 5: Calculate the change in momentum
The change in momentum \( \Delta P \) of the gun over the time interval \( \Delta t \) (which is 1 second in this case) is given by:
\[ \Delta P = P_{\text{final}} - P_{\text{initial}} = Nmv - 0 = Nmv \]

### Step 6: Calculate the average force exerted on the gun
The average force \( F \) exerted on the gun can be calculated using the formula:
\[ F = \frac{\Delta P}{\Delta t} \]
Substituting the values we have:
\[ F = \frac{Nmv}{1} = Nmv \]

### Conclusion
Thus, the force exerted by the bullets on the gun is:
\[ F = Nmv \]