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. Two
B. Four
C. One
D. Three

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Convert the mass of the bullet from grams to kilograms.
The mass of the bullet is given as 40 g. To convert grams to kilograms, we use the conversion factor \(1 \, \text{kg} = 1000 \, \text{g}\).

\[ \text{Mass of bullet} = 40 \, \text{g} = \frac{40}{1000} \, \text{kg} = 0.04 \, \text{kg} \]

**Hint:** Remember to convert grams to kilograms by dividing by 1000.

### Step 2: Calculate the change in momentum of one bullet.
The change in momentum (\( \Delta p \)) of the bullet can be calculated using the formula:

\[ \Delta p = m(v_f - v_i) \]

Where:
- \( m \) is the mass of the bullet (0.04 kg),
- \( v_f \) is the final velocity (1200 m/s),
- \( v_i \) is the initial velocity (0 m/s).

Substituting the values:

\[ \Delta p = 0.04 \, \text{kg} \times (1200 \, \text{m/s} - 0 \, \text{m/s}) = 0.04 \, \text{kg} \times 1200 \, \text{m/s} = 48 \, \text{kg m/s} \]

**Hint:** The change in momentum is calculated as the product of mass and the change in velocity.

### Step 3: Relate the force exerted to the change in momentum.
According to Newton's second law, the force (\( F \)) 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 \( N \times \Delta p \).

\[ F = N \times \Delta p \]

We know the maximum force exerted is 144 N, so we can set up the equation:

\[ 144 \, \text{N} = N \times 48 \, \text{kg m/s} \]

**Hint:** Use the relationship between force and momentum to set up your equation.

### Step 4: Solve for \( N \).
Rearranging the equation to solve for \( N \):

\[ N = \frac{144 \, \text{N}}{48 \, \text{kg m/s}} = 3 \]

**Hint:** To find \( N \), divide the maximum force by the change in momentum per bullet.

### Conclusion
The maximum number of bullets that can be fired per second is \( N = 3 \).

**Final Answer:** The man can fire a maximum of **3 bullets per second**.