A rocket has a mass of 100 kg . `90%` of this is fuel. It ejects fuel vapours at the rate of `1 kg//sec` with a velocity of 500 `m//sec` relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is

Options

A. Zero
B. 500 N
C. 1000 N
D. 2000 N

Answer

To find the initial upthrust on the rocket when it just starts moving upwards, we can use the thrust formula derived from Newton's laws of motion. The thrust force (F_th) can be calculated using the formula:

\[ F_{th} = v_e \cdot \frac{dm}{dt} \]

Where:
- \( v_e \) is the velocity of ejection of the fuel,
- \( \frac{dm}{dt} \) is the rate of change of mass (the rate at which fuel is ejected).

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the rocket (m) = 100 kg
- Percentage of fuel = 90%
- Rate of fuel ejection (\( \frac{dm}{dt} \)) = 1 kg/s
- Velocity of ejection (\( v_e \)) = 500 m/s

2. **Calculate the thrust force using the formula:**
Substitute the values into the thrust formula:
\[ F_{th} = v_e \cdot \frac{dm}{dt} \]
\[ F_{th} = 500 \, \text{m/s} \cdot 1 \, \text{kg/s} \]

3. **Perform the multiplication:**
\[ F_{th} = 500 \, \text{N} \]

4. **Conclusion:**
The initial upthrust on the rocket when it just starts moving upwards is **500 Newtons**.