The initial mass of a rocket is $1000 k g$ . Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20 m s^{- 2}$ . The gases come out at a relative speed of $500 m s^{- 1}$ with respect to the rocket: $[U s e g = 10 m / s^{2}]$

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$10 k g s^{- 1}$

$60 k g s^{- 1}$

$500 k g s^{- 1}$

$6.0 \times 10^{2} k g s^{- 1}$

answer is D.

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Detailed Solution

$\begin{array}{r} F_{thust} = (\frac{dm}{dt} \cdot V_{rel}) \\ (\frac{dm}{dt} V_{rel} - mg) = ma \\ \Rightarrow (\frac{dm}{dt}) \times 500 - 10^{3} \times 10 = 10^{3} \times 20 \\ \frac{dm}{dt} = (60 kg / s) \end{array}$

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