A machine gun of mass 10 kg fires 20 g bullets at the rate of 10 bullets per second with a speed of 500 `ms^(-1)`. What force is required to hold the gun in position ?

Answer

To find the force required to hold the machine gun in position while it fires bullets, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the mass of the bullets and the firing rate**:
- The mass of each bullet is given as 20 grams.
- Convert this mass into kilograms:
\[ m = 20 \, \text{g} = \frac{20}{1000} \, \text{kg} = 0.02 \, \text{kg} \]

2. **Determine the number of bullets fired per second**:
- The gun fires at a rate of 10 bullets per second.

3. **Calculate the total mass flow rate**:
- The mass flow rate (\( \dot{m} \)) can be calculated as:
\[ \dot{m} = \text{number of bullets per second} \times \text{mass of each bullet} \]
\[ \dot{m} = 10 \, \text{bullets/s} \times 0.02 \, \text{kg/bullet} = 0.2 \, \text{kg/s} \]

4. **Identify the velocity of the bullets**:
- The speed of each bullet is given as 500 m/s.

5. **Calculate the force exerted by the bullets**:
- The force (\( F \)) required to hold the gun in position can be calculated using the formula:
\[ F = v \cdot \dot{m} \]
where \( v \) is the velocity of the bullets and \( \dot{m} \) is the mass flow rate.
- Substituting the values:
\[ F = 500 \, \text{m/s} \times 0.2 \, \text{kg/s} = 100 \, \text{N} \]

6. **Conclusion**:
- The force required to hold the gun in position is \( 100 \, \text{N} \).

### Final Answer:
The force required to hold the gun in position is **100 N**.