A machine gun fires a bullet of mass 65 g with a velocity of 1300 m/s. The main holding it can exert a maximum force of 169 N on the gun. The number of bullets he can fire per second will be

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to find out how many bullets can be fired per second by the machine gun, given the mass of each bullet, its velocity, and the maximum force that can be exerted by the man holding the gun.

### Step-by-Step Solution:

1. **Convert the Mass of the Bullet to Kilograms**:
- The mass of the bullet is given as 65 grams. We need to convert this to kilograms since the standard unit of mass in physics is kilograms.
\[ \text{Mass of bullet} = 65 \text{ g} = \frac{65}{1000} \text{ kg} = 0.065 \text{ kg} \]

2. **Calculate the Momentum of One Bullet**:
- Momentum (p) is calculated using the formula:
\[ p = mv \]
- Where \( m \) is the mass and \( v \) is the velocity of the bullet.
- Given that the velocity of the bullet is 1300 m/s, we can calculate the momentum:
\[ p = 0.065 \text{ kg} \times 1300 \text{ m/s} = 84.5 \text{ kg m/s} \]

3. **Relate Force to Momentum Change**:
- The force exerted by the man holding the gun is related to the rate of change of momentum:
\[ F = \frac{dp}{dt} \]
- Here, \( F \) is the maximum force (169 N) and \( dp \) is the change in momentum.

4. **Determine the Number of Bullets Fired per Second**:
- If \( n \) is the number of bullets fired per second, then the total change in momentum per second when firing \( n \) bullets is:
\[ dp = n \times p \]
- Therefore, we can write:
\[ F = n \times p \]
- Rearranging gives:
\[ n = \frac{F}{p} \]
- Substituting the values we have:
\[ n = \frac{169 \text{ N}}{84.5 \text{ kg m/s}} \approx 2 \]

5. **Conclusion**:
- The number of bullets the man can fire per second is approximately 2.

### Final Answer:
The number of bullets he can fire per second is **2**.