A rocket of mass 1000 kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity 100 ms-1 with respect to the rocket. What is the minimum rateof burning of fuel, so as to just lift the rocket upwards against the gravitational attraction?(Take, g = 10 ms-2) [AMU 2011]
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a
50 kg s-1
b
200 kg s-1
c
100 kg s-1
d
400 kg s-1
answer is B.
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Detailed Solution
The velocity of exhaust gases with respect to the rocket=100 ms-1The minimum force on the rocket to lift it,Fmin=mg=1000×10=10000 NHence. minimum rate of burning of fuel is given bydmdt=Fwin v=10000100=100kgs-1