In a rocket of mass 1000 kg fuel is consumed at a rate of 40 kg/s. The velocity of the gases ejected from the rocket is 5 x 10⁴ m /s . The thrust on the rocket is

The correct option is 2 x 10⁶ N.

Step-by-Step Explanation:
Thrust on a rocket is the force exerted on the rocket by the escaping exhaust gases. According to Newton's second law of motion in terms of variable mass systems, the thrust force ($F$) is given by the formula:
$F=v\cdot \frac{dm}{dt}$
where:
• $v$ is the velocity of the ejected gases.
• $\frac{dm}{dt}$ is the rate at which fuel is consumed (rate of change of mass).

Given Data:
• Rate of fuel consumption, $\frac{dm}{dt}=40\text{ kg/s}$
• Velocity of ejected gases, $v=5\times {10}^4\text{ m/s}$
• Mass of the rocket, $M=1000\text{ kg}$ (Note: The mass of the rocket is extra information and is not required to calculate the thrust).

Calculation:
Substitute the given values into the thrust formula:
$F=\left(5\times {10}^4\text{ m/s}\right)\times \left(40\text{ kg/s}\right)$
$F=200\times {10}^4\text{ N}$
$F=2\times {10}^6\text{ N}$

Therefore, the thrust acting on the rocket is $2\times {10}^6\text{ N}$.