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Question

A rocket of mass 20 kg has 180 kg fuel. The exhaust velocity of the fuel is 1.6 km/s. Calculate the minimum rate of ejection of fuel so that the rocket may rise from the ground. (Take g=9.8 m/s2)

A
1.225 kg/s
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B
1.725 kg/s
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C
2.125 kg/s
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D
2.425 kg/s
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Solution

The correct option is A 1.225 kg/s
Given, mass of rocket without fuel =20 kg
Mass of fuel in rocket =180 kg
Total mass of rocket initially
m=20+180=200 kg
Relative exhaust velocity of the fuel (Vr)=1.6 km/s

Minimum thrust force applied should counter the weight of the rocket so that the rocket may just rise from the ground.
i.e Fthrust=mg
Vr(dmdt)=mg
dmdt=mgVr=200×9.81.6×103=1.225 kg/s
is the rate of ejection of fuel

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