Question

The mass of a rocket is $2400\text{kg}$. The nozzle of the rocket is designed to give velocity of $200\text{m/s}$ to the gases produced after combustion of the fuel. If the rocket has to achieve an acceleration of $15{\text{m/s}}^2$, what should be the rate of burning of the fuel? (Take $g=10{\text{m/s}}^2$)

• A. $200\text{kg/s}$
• B. $250\text{kg/s}$
• C. $400\text{kg/s}$
• D. $300\text{kg/s}$

Answer 1

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

Mass of rocket, $M=2400\text{kg}$
Acceleration required, $a=15{\text{m/s}}^2$

Velocity of exhaust gases, $v=200\text{m/s}$
$F$ is the force generated by exhaust gases.

Applying Newton's laws of motion, we get,
$F-Mg=Ma$

$\Rightarrow v.\frac{dm}{dt}-Mg=Ma$
where $\frac{dm}{dt}$ is the rate of consumption of fuel.

$\Rightarrow 200\times \frac{dm}{dt}-2400\times 10=2400\times 15$

$\Rightarrow 200\times \frac{dm}{dt}=2400\times (15+10)$

$\Rightarrow \frac{dm}{dt}=300\text{kg/s}$
Hence the correct option is (d).