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

The correct option is A $60{\text{kg s}}^{-1}$
From the question it is clear that we have to calculate the rate of change of mass with respect to time. The rocket thrust is equal to the burnt mass times relative velocity of the rocket.

So, $F_{\text{thurst}}=\frac{dm}{dt}{v}_{\text{rel}}$

The net force acting on the rocket is given by,

$F_{\text{thurst}}-mg=ma$

i.e. $\frac{dm}{dt}{v}_{\text{rel}}-mg=ma$

$\frac{dm}{dt}\times 500-1000\times 10=1000\times 20$

Therefore, $\frac{dm}{dt}=60{\text{kg s}}^{-1}$

Hence, option $\left(\text{A}\right)$ is correct.