A machine gun has a mass of `20kg` It fires `30g` bullets at the rate of 400 bullets/s with a sped of `400m//s` What force must be applied on the gun to keep it in position ?

Explanation

To solve the problem, we need to find the force that must be applied to the machine gun to keep it in position while it is firing bullets. The force can be calculated using the concept of momentum.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the machine gun (M_g) = 20 kg
- Mass of each bullet (m_b) = 30 g = 30 × 10^(-3) kg = 0.03 kg
- Rate of fire (N) = 400 bullets/s
- Speed of bullets (v) = 400 m/s

2. **Calculate the Momentum of One Bullet:**
- Momentum (p) of one bullet = mass × velocity
\[ p = m_b \times v = 0.03 \, \text{kg} \times 400 \, \text{m/s} = 12 \, \text{kg m/s} \]

3. **Calculate the Rate of Change of Momentum:**
- The rate of change of momentum when firing N bullets per second is given by:
\[ \text{Rate of change of momentum} = N \times p \]
\[ = 400 \, \text{bullets/s} \times 12 \, \text{kg m/s} = 4800 \, \text{kg m/s}^2 \]

4. **Determine the Force Required:**
- According to Newton's second law, the force (F) required to keep the machine gun in position is equal to the rate of change of momentum:
\[ F = \text{Rate of change of momentum} = 4800 \, \text{N} \]

### Final Answer:
The force that must be applied to keep the machine gun in position is **4800 N**.

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