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Question

The mass of a rocket is 2400 kg. The nozzle of the rocket is designed to give velocity of 200 m/s to the gases produced after combustion of the fuel. If the rocket has to achieve an acceleration of 15 m/s2, what should be the rate of burning of the fuel? (Take g=10 m/s2)

A
200 kg/s
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B
250 kg/s
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C
400 kg/s
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D
300 kg/s
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Solution

The correct option is D 300 kg/s
Mass of rocket, M=2400 kg
Acceleration required, a=15 m/s2

Velocity of exhaust gases, v=200 m/s
F is the force generated by exhaust gases.

Applying Newton's laws of motion, we get,
FMg=Ma

v.dmdtMg=Ma
where dmdt is the rate of consumption of fuel.

200×dmdt2400×10=2400×15

200×dmdt=2400×(15+10)

dmdt=300 kg/s
Hence the correct option is (d).

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