A machine gun is mounted on a 2000kg car on a harizontal frictionless surface. At some instant the gun fires bullets of mass 10gm with a velocity of `500m/sec` with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is

Options

A. `550 N`
B. `50 N`
C. `250 N`
D. `300 N `

Answer

To find the average thrust on the system when the machine gun fires bullets, we can follow these steps:

### Step 1: Identify the given data
- Mass of the car (m_car) = 2000 kg (not directly needed for thrust calculation)
- Mass of each bullet (m_bullet) = 10 g = 10 x 10^(-3) kg = 0.01 kg
- Velocity of each bullet (v_bullet) = 500 m/s
- Number of bullets fired per second (n) = 10 bullets/s

### Step 2: Calculate the mass flow rate (m_dot)
The mass flow rate (m_dot) is the mass of bullets fired per second. Since 10 bullets are fired per second, we can calculate it as follows:

\[ m_{\text{dot}} = n \times m_{\text{bullet}} = 10 \, \text{bullets/s} \times 0.01 \, \text{kg/bullet} = 0.1 \, \text{kg/s} \]

### Step 3: Use the thrust formula
The thrust (T) can be calculated using the formula:

\[ T = m_{\text{dot}} \times v_{\text{bullet}} \]

Substituting the values we have:

\[ T = 0.1 \, \text{kg/s} \times 500 \, \text{m/s} \]

### Step 4: Calculate the thrust
Now we calculate the thrust:

\[ T = 0.1 \times 500 = 50 \, \text{N} \]

### Conclusion
The average thrust on the system is **50 Newtons**.

---