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/sMass 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, F−Mg=Ma ⇒v.dmdt−Mg=Ma where dmdt is the rate of consumption of fuel. ⇒200×dmdt−2400×10=2400×15 ⇒200×dmdt=2400×(15+10) ⇒dmdt=300 kg/s Hence the correct option is (d).

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