Question

A rocket of mass $20\text{kg}$ has $180\text{kg}$ fuel. The exhaust velocity of the fuel is $1.6\text{km/s}$. Calculate the minimum rate of ejection of fuel so that the rocket may rise from the ground. (Take $g=9.8{\text{m/s}}^2$)

• A. $1.225\text{kg/s}$
• B. $1.725\text{kg/s}$
• C. $2.125\text{kg/s}$
• D. $2.425\text{kg/s}$

Answer 1

The correct option is A $1.225\text{kg/s}$

Given, mass of rocket without fuel $=20\text{kg}$
Mass of fuel in rocket $=180\text{kg}$
$\Rightarrow$ Total mass of rocket initially
$m=20+180=200\text{kg}$
Relative exhaust velocity of the fuel $\left(V_r\right)=1.6\text{km/s}$

Minimum thrust force applied should counter the weight of the rocket so that the rocket may just rise from the ground.
i.e $F_{thrust}=mg$
$\Rightarrow V_r\left(\frac{-dm}{dt}\right)=mg$
$\Rightarrow \left|\frac{dm}{dt}\right|=\frac{mg}{V_r}=\frac{200\times 9.8}{1.6\times {10}^3}=1.225\text{kg/s}$
is the rate of ejection of fuel