A gun of mass 10kg fires 4 bullets per second. The mass of each bullet is 20 g and the velocity of the bullet when it leaves the gun is `300ms^(-1)`. The force required to hold the gun while firing is

Options

A. 6 N
B. 8 N
C. 24 N
D. 240 N

Answer

To solve the problem step by step, we will calculate the force required to hold the gun while firing.

### Step 1: Understand the given data
- Mass of the gun (M) = 10 kg
- Mass of each bullet (m) = 20 g = 0.02 kg (since 1 g = 0.001 kg)
- Velocity of each bullet (v) = 300 m/s
- Number of bullets fired per second (n) = 4

### Step 2: Calculate the momentum of one bullet
The momentum (p) of one bullet can be calculated using the formula:
\[ p = m \cdot v \]
Substituting the values:
\[ p = 0.02 \, \text{kg} \cdot 300 \, \text{m/s} \]
\[ p = 6 \, \text{kg m/s} \]

### Step 3: Calculate the total momentum for 4 bullets
Since the gun fires 4 bullets per second, the total momentum (P_total) imparted by the bullets in one second is:
\[ P_{\text{total}} = n \cdot p \]
Substituting the values:
\[ P_{\text{total}} = 4 \cdot 6 \, \text{kg m/s} \]
\[ P_{\text{total}} = 24 \, \text{kg m/s} \]

### Step 4: Calculate the force required to hold the gun
The force (F) required to hold the gun while firing can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
Where \(\Delta p\) is the change in momentum and \(\Delta t\) is the time interval (1 second in this case).
Substituting the values:
\[ F = \frac{24 \, \text{kg m/s}}{1 \, \text{s}} \]
\[ F = 24 \, \text{N} \]

### Conclusion
The force required to hold the gun while firing is **24 N**.