Question

$GSLV$ launched a rocket with a ejection speed of $200\text{m/s}$ and with $20{\text{m/s}}^2$ acceleration. Mass of the rocket is $2000\text{kg}$. What will be the rate of consumption of the fuel? (Take $g=10{\text{m/s}}^2$)

• A. $400\text{kg/s}$
• B. $300\text{kg/s}$
• C. $500\text{kg/s}$
• D. $600\text{kg/s}$

Answer 1

The correct option is B $300\text{kg/s}$

Given, Mass of the rocket $M=2000\text{kg}$
Ejection speed, $v=200\text{m/s}$
Acceleration of the rocket $a=20{\text{m/s}}^2$
As we know, for variable mass system with constant rate of ejection $\mu$
$M\frac{dv}{dt}=F_{ext}-\mu u$
Here, $F_{ext}=-Mg$ (downward) and relative velocity of ejection $u=-v$ (downward)
$\Rightarrow Ma=-Mg+v\frac{dM}{dt}$
$\Rightarrow 2000\times 20=-2000\times 10+200\cdot \frac{dM}{dt}$
$\Rightarrow \frac{dM}{dt}=300\text{kg/s}$ is the rate of consumption of fuel.