Question

A $6000$kg rocket is set for vertical firing. The exhaust speed is $900$ m$/$s. To give an upward acceleration of $20$ $m/s^2$ the amount of gas ejected per second to supply the needed thrust is (Take $g=10m/s^2$).

• A. $225$ $kg{s}^{-1}$
• B. $200$ $kg{s}^{-1}$
• C. $275$ $kg{s}^{-1}$
• D. $100$ $kg{s}^{-1}$

Answer 1

The correct option is B $200$ $kg{s}^{-1}$

Given, $m=6000$kg
$v=900m/s$
$a=20m/s^2$
$\frac{dm}{dt}=?$
Here, upward thrust $=F_{th}=\frac{dm}{dt}v$
Also, $m(g+a)=F_{th}=v\frac{dm}{dt}$
$\therefore \frac{dm}{dt}=\frac{m(g+a)}{v}$
$=\frac{6000(10+20)}{900}$
$=\frac{60\times 30}{9}$
$=20\times 10$
$\therefore \frac{dm}{dt}=200kg/s$.