In a rocket, fuel burns at the rate of 2 kg/s. This fuel gets ejected from the rocket with a velocity of 80 km/s. Force exerted on the rocket is -

Options

A. `16,000 `N
B. `1,60,000` N
C. `1600 `N
D. `16 `N

Answer

To find the force exerted on the rocket, we can use the principle of conservation of momentum and the formula for thrust. The thrust (or force exerted) can be calculated using the equation:

\[ F = \frac{dm}{dt} \times v \]

where:
- \( F \) is the thrust (force exerted on the rocket),
- \( \frac{dm}{dt} \) is the rate of change of mass (mass flow rate of the fuel),
- \( v \) is the velocity of the ejected fuel.

### Step-by-Step Solution:

1. **Identify the given values:**
- Rate of fuel consumption, \( \frac{dm}{dt} = 2 \, \text{kg/s} \)
- Velocity of the ejected fuel, \( v = 80 \, \text{km/s} \)

2. **Convert the velocity from km/s to m/s:**
\[ v = 80 \, \text{km/s} = 80 \times 1000 \, \text{m/s} = 80000 \, \text{m/s} \]

3. **Substitute the values into the thrust formula:**
\[ F = \frac{dm}{dt} \times v = 2 \, \text{kg/s} \times 80000 \, \text{m/s} \]

4. **Calculate the force:**
\[ F = 2 \times 80000 = 160000 \, \text{N} \]

5. **Final result:**
The force exerted on the rocket is \( 160000 \, \text{N} \) or \( 1.6 \times 10^5 \, \text{N} \).