A machine gun fires a bullet of mass 40 g with a velocity `1200 ms^-1`. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can be fire per second at the most?

Options

A. One
B. Four
C. Two
D. Three

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We need to find out how many bullets can be fired per second by a machine gun, given the mass of each bullet, its velocity, and the maximum force that the man can exert on the gun.

### Step 2: Convert Mass to Kilograms
The mass of the bullet is given as 40 g. We need to convert this to kilograms since the standard unit of mass in physics is kg.
\[ \text{Mass of bullet} = 40 \, \text{g} = \frac{40}{1000} \, \text{kg} = 0.04 \, \text{kg} \]

### Step 3: Calculate the Change in Momentum of One Bullet
The change in momentum (\( \Delta P \)) of one bullet can be calculated using the formula:
\[ \Delta P = \text{mass} \times \text{velocity} \]
Substituting the values:
\[ \Delta P = 0.04 \, \text{kg} \times 1200 \, \text{m/s} = 48 \, \text{kg m/s} \]

### Step 4: Relate Force to Change in Momentum
According to Newton's second law, the force exerted is equal to the rate of change of momentum. If \( N \) is the number of bullets fired per second, the total change in momentum per second is:
\[ \Delta P_{\text{total}} = N \times \Delta P \]
Substituting the change in momentum we found:
\[ \Delta P_{\text{total}} = N \times 48 \, \text{kg m/s} \]

### Step 5: Set Up the Equation Using Maximum Force
The maximum force exerted by the man is given as 144 N. According to the relationship between force and change in momentum:
\[ F = \Delta P_{\text{total}} = 144 \, \text{N} \]
Thus, we can write:
\[ 144 = N \times 48 \]

### Step 6: Solve for \( N \)
Now, we can solve for \( N \):
\[ N = \frac{144}{48} = 3 \]

### Conclusion
The maximum number of bullets that can be fired per second is:
\[ \boxed{3} \]

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