Q 11-04-174JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
The initial mass of a rocket is $1000$ kg. 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: [Use $g = 10$ m s$^{-2}$]
Answer: (B) $60$ kg s$^{-1}$
Thrust $u\dfrac{dm}{dt}$ must overcome gravity and provide the acceleration:
$$u\frac{dm}{dt} - mg = ma \Rightarrow \frac{dm}{dt} = \frac{m(g + a)}{u} = \frac{1000\times30}{500} = 60\ \text{kg s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics