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

The correct option is 500N.

To find the initial upthrust (thrust force) on the rocket when it just starts moving, we can use the concept of thrust force in variable mass systems. The thrust force ($F_t$) exerted on a rocket due to the ejection of fuel is given by the formula:
$F_t=v_{\mathrm{rel}}·\frac{dm}{dt}$
where:
- $v_{\mathrm{rel}}$ is the relative velocity of the ejected fuel with respect to the rocket.
- $\frac{dm}{dt}$ is the rate at which mass is ejected (rate of fuel consumption).

From the given problem, we have the following values:
- The relative velocity of the fuel vapors, $v_{\mathrm{rel}}=500\text{m/sec}$.
- The rate of fuel ejection, $\frac{dm}{dt}=1\text{kg/sec}$.

Substituting these values into the thrust formula:
$F_t=500·1$
$F_t=500\text{N}$

Therefore, the initial upthrust on the rocket when it just starts moving upwards is 500N.