A machine gun has a mass of 200 kg. It fires 35 g bullets at the rate of 40 bullets per sec with a speed of 400 m/s. Find the horizontal force need to be applied on the gun to keep it in fixed position ?

Options

A. 560 N
B. 56 N
C. 5.6 N
D. 0.56 N

Answer

To solve the problem of finding the horizontal force that needs to be applied on the machine gun to keep it in a fixed position while it fires bullets, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the machine gun, \( M = 200 \, \text{kg} \)
- Mass of one bullet, \( m = 35 \, \text{g} = 0.035 \, \text{kg} \) (conversion from grams to kilograms)
- Rate of fire, \( n = 40 \, \text{bullets/sec} \)
- Speed of the bullets, \( v = 400 \, \text{m/s} \)

2. **Calculate the Total Mass of Bullets Fired per Second:**
- The total mass of bullets fired in one second is given by:
\[ \text{Total mass per second} = n \times m = 40 \, \text{bullets/sec} \times 0.035 \, \text{kg/bullet} = 1.4 \, \text{kg/sec} \]

3. **Calculate the Momentum Change per Second:**
- The momentum of the bullets fired per second can be calculated using the formula:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
- Therefore, the change in momentum per second (which is the momentum of the bullets fired) is:
\[ \text{Change in momentum per second} = \text{Total mass per second} \times v = 1.4 \, \text{kg/sec} \times 400 \, \text{m/s} = 560 \, \text{kg m/s} \]

4. **Determine the Force Required to Counteract the Momentum Change:**
- The force required to keep the machine gun in a fixed position is equal to the rate of change of momentum (Newton's second law):
\[ F = \frac{dp}{dt} = 560 \, \text{N} \]

5. **Conclusion:**
- The horizontal force that needs to be applied on the gun to keep it in a fixed position is \( 560 \, \text{N} \).

### Final Answer:
The horizontal force required to keep the machine gun in a fixed position is **560 N**.

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