Question

A rocket, set for vertical firing, weighs $50\text{kg}$ and contains $450\text{kg}$ of fuel. It can have maximum exhaust velocity of $2\text{km/s}$. What should be its minimum rate of fuel consumption, to just lift it off the launching pad ?

Take $g=9.8{\text{m/s}}^2$

• A. $2.45\text{kg/s}$
• B. $5.05\text{kg/s}$
• C. $3.50\text{kg/s}$
• D. $6.00\text{kg/s}$

Answer 1

The correct option is A $2.45\text{kg/s}$

To just lift if off the launching pad,

Total weight of the rocket $=$ Upthrust of the rocket engine

$\Rightarrow mg=v_r\left(\frac{dm}{dt}\right)$

$\Rightarrow \frac{dm}{dt}=\frac{mg}{v_r}=\frac{(450+50)\times 9.8}{2000}=2.45\text{kg/s}$

Hence, option $\left(A\right)$ is the correct answer.