A machine gun fires bullets of 50gm at the speed of 1000m/sec. If an average force of 200N is exerted on the gun, the maximum number of bullets fired per minute is:

Options

A. 240
B. 120
C. 60
D. 30

Explanation

To solve the problem, we need to determine the maximum number of bullets that can be fired per minute by the machine gun given the force exerted and the properties of the bullets.

### Step-by-Step Solution:

1. **Convert the mass of the bullet to kilograms**:
- The mass of each bullet is given as 50 grams. To convert this to kilograms:
\[ \text{mass} = 50 \, \text{g} = 0.05 \, \text{kg} \]

2. **Identify the speed of the bullet**:
- The speed of the bullet is given as 1000 m/s.

3. **Identify the average force exerted on the gun**:
- The average force is given as 200 N.

4. **Use the formula for force in terms of momentum**:
- The force can be expressed as the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} \]
- Where \(\Delta p\) is the change in momentum and \(\Delta t\) is the time interval. The momentum \(p\) of one bullet is given by:
\[ p = mv \]
- Therefore, for \(N\) bullets fired in time \(T\):
\[ \Delta p = N \cdot (m \cdot v) \]

5. **Set up the equation**:
- Substituting into the force equation:
\[ F = \frac{N \cdot (m \cdot v)}{T} \]
- For our case, we can consider \(T = 1 \, \text{s}\) (to find bullets per second):
\[ F = N \cdot (m \cdot v) \]

6. **Substitute the known values**:
- Substituting \(F = 200 \, \text{N}\), \(m = 0.05 \, \text{kg}\), and \(v = 1000 \, \text{m/s}\):
\[ 200 = N \cdot (0.05 \cdot 1000) \]
- Simplifying:
\[ 200 = N \cdot 50 \]

7. **Solve for \(N\)**:
- Rearranging gives:
\[ N = \frac{200}{50} = 4 \, \text{bullets per second} \]

8. **Convert bullets per second to bullets per minute**:
- To find the number of bullets fired in one minute:
\[ \text{Bullets per minute} = N \cdot 60 = 4 \cdot 60 = 240 \, \text{bullets per minute} \]

### Final Answer:
The maximum number of bullets fired per minute is **240 bullets per minute**.

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