Question

A rocket of initial mass $m=2000\text{kg}$ is burning fuel at the rate of $20\text{kg/s}$ and ejecting burnt matter with a constant speed of $1000\text{m/s}$ w.r.t the rocket. Find the acceleration of the rocket at $t=10\text{sec}$.
[Take $g=10{\text{m/s}}^2$]

• A. $0$
• B. $0.55{\text{m/s}}^2$
• C. $1.11{\text{m/s}}^2$
• D. $2.3{\text{m/s}}^2$

Answer 1

The correct option is C $1.11{\text{m/s}}^2$

Given, initial mass of rocket = $2000\text{kg}$


Rate of burning fuel $\mu =\frac{dM}{dt}=20\text{kg/s}$
and relative velocity of ejection of fuel
$V_r=-1000\text{m/s}$
(downwards -ve)

We know, for a variable mass system with constant rate of ejection:
$F_{ext}-V_r\frac{dm}{dt}=ma$

Here $\left(\frac{-dm}{dt}\right)\text{and}{V}_r$ will be constant through out the journey.
$\Rightarrow -mg-(-1000\times 20)=ma$

Mass at $t=10\text{sec}$
$m=2000-20\times 10=1800$ kg

$\Rightarrow 1000\times \left(20\right)-1800\times 10=1800\times a$
$\Rightarrow a=1.11{\text{m/s}}^2$