Question

A $3000\text{kg}$ rocket has to be fired vertically. Calculate the rate of ejection of gas required at an exhaust speed $450\text{m/s}$ in order to provide necessary support to the weight of the rocket.
(Take $g=10m/s^2$)

• A. $50\text{kg/s}$
• B. $56.66\text{kg/s}$
• C. $60.88\text{kg/s}$
• D. $66.66\text{kg/s}$

Answer 1

The correct option is D $66.66\text{kg/s}$

Let rate of ejection of gas is $\frac{dm}{dt}$.
In order to support the weight of the rocket, the acceleration is zero.
The weight of the rocket, $Mg=3000\times 10$
$\Rightarrow w=30000\text{N}$
Force generated by the combustion of exhaust gases to balance weight of rocket $;F=v.\frac{dm}{dt}=w$

$\Rightarrow v.\frac{dm}{dt}=30000$
$\Rightarrow 450\times \frac{dm}{dt}=30000$
$\Rightarrow \frac{dm}{dt}=66.66\text{kg/s}$
The correct option is (d).