Laws of Motion

JEE Main level, single correct, medium

33 of 210

Question 33 of 210

The initial mass of a rocket is 1000kg1000kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of, 20ms−220{ms}^{-2}. The gases come out at a relative speed of 500ms−1500{ms}^{-1}, with respect to the rocket:
[Useg=10ms−2]\left[\text{Use}g=10m{s}^{-2}\right]

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Answer: (B) 60kgs−160kg{s}^{-1}

Here we are applying the equation, Fr−mg=ma{F}_{r}-mg=ma
From Newton's second law, Fr=dmdtvr{F}_{r}=\dfrac{dm}{dt}{v}_{r}⇒dmdtvr=mg+ma\Rightarrow \dfrac{dm}{dt}{v}_{r}=mg+ma
Put the given values in the above equations,
⇒dmdt500=1000(10+20)\Rightarrow \dfrac{dm}{dt}500=1000(10+20)⇒dmdt=60kgs−1\Rightarrow \dfrac{dm}{dt}=60kg{s}^{-1}.

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