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 $$2011$$]

Question

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 $$2011$$]

Infinity Learn · Accepted Answer

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 $$bydmdt=Fwin$$ $$v=10000100=100kgs-1$$

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