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A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 m s⁻¹, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of the rocket is

Asked in CBSE PMT 1990 · Rockets, jets and variable mass

Answer: (3) 6 kg s⁻¹

Step-by-step solution

Given: M=600 kg, exhaust speed u=1000 m s⁻¹; the thrust need only match the weight, so the rocket just hovers.

Required thrust: F=Mg=600×9.8=5880 N.

Idea: thrust is F=u (dm)/(dt).

(dm)/(dt)=F/u=(5880)/(1000).

=5.88 kg s⁻¹.

To the nearest option, 6 kg s⁻¹. (With g=10 it would be exactly 6.)

Why the other options are wrong

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