Question:
The initial mass of a rocket is $1000 \mathrm{~kg}$. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20 \mathrm{~ms}^{-2}$. The gases come out at a relative speed of $500 \mathrm{~ms}^{-1}$ with respect to the rocket :[Use $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ]
Correct Option: , 4
Solution:
$\mathrm{F}_{\text {thrust }}=\left(\frac{\mathrm{dm}}{\mathrm{dt}} \cdot \mathrm{V}_{\mathrm{rel}}\right)$
$\left(\frac{\mathrm{dm}}{\mathrm{dt}} \mathrm{V}_{\mathrm{rel}}-\mathrm{mg}\right)=\mathrm{ma}$
$\Rightarrow\left(\frac{\mathrm{dm}}{\mathrm{dt}}\right) \times 500-10^{3} \times 10=10^{3} \times 20$
$\frac{\mathrm{dm}}{\mathrm{dt}}=(60 \mathrm{~kg} / \mathrm{s})$
Option (4)