Question

$PSLV$ launches a rocket which is ejecting gas with a speed of $100\text{m/s}$ w.r.t the rocket and the rate of ejection of gas from the rocket is $400\text{kg/s}$. If the mass of the rocket is $2000\text{kg}$, calculate the initial acceleration of the rocket. [Take $g=10{\text{m/s}}^2$]

• A. $10{\text{m/s}}^2$
• B. $20{\text{m/s}}^2$
• C. $5{\text{m/s}}^2$
• D. $15{\text{m/s}}^2$

Answer 1

The correct option is A $10{\text{m/s}}^2$

Given,
Mass of the rocket = $2000\text{kg}$
Relative speed of gas ejected from the rocket
$v=-100\text{m/s}$
(Taking downward direction -ve)
Rate of ejection of gas $=400\text{kg/s}=\frac{dM}{dt}$
As we know,
$Ma=F_{ext}+v\frac{dM}{dt}=-Mg-v\frac{dM}{dt}$
$\Rightarrow 2000\times a=-2000\times 10-(-100)\times 400$
$\Rightarrow a=10{\text{m/s}}^2$