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 solve the problem of determining the force exerted by the bullets on the gun, we can follow these steps:

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

### Step 2: Calculate the change in momentum for one bullet
The change in momentum (\( \Delta P \)) for one bullet can be calculated using the formula:
\[ \Delta P = m \cdot v - m \cdot 0 = m \cdot v \]
where \( 0 \) is the initial velocity of the bullet before it is fired.

### Step 3: Calculate the total change in momentum for N bullets
Since the gun fires \( N \) bullets per second, the total change in momentum for all the bullets in one second is:
\[ \Delta P_{\text{total}} = N \cdot (m \cdot v) = N \cdot m \cdot v \]

### Step 4: Use Newton's second law to find the force
According to Newton's second law, the force (\( F \)) can be calculated using the formula:
\[ F = \frac{\Delta P}{\Delta t} \]
Here, \( \Delta t = 1 \) second (since we are considering the change in momentum per second). Therefore, we have:
\[ F = \frac{N \cdot m \cdot v}{1} = N \cdot m \cdot v \]

### Conclusion
The force exerted by the bullets on the gun is:
\[ F = N \cdot m \cdot v \]

Thus, the answer is \( N \cdot m \cdot v \).

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