Question

A rocket, set for vertical launching, has a mass of $50$ kg and contains $450$ kg of fuel. It can have a maximum exhaust speed of $2$ km $s^{-1}$. If $g=10$ m$s^{-2}$, what should be the minimum rate of fuel consumption to just lift it off the launching pad?

• A. $2.5$ kg $s^{-1}$
• B. $5$ kg $s^{-1}$
• C. $7.5$ kg $s^{-1}$
• D. $10$ kg $s^{-1}$

Answer 1

The correct option is A $2.5$ kg $s^{-1}$

We have mass of rocket = $50$ kg and mass of fuel = $450$ kg

Thus total mass = $500$ kg

Exhaust speed of rocket $v_r$= $2$ km/s = $2\times {10}^3$m/s

$Force$ = $mass\times gravity$ = $500\times 10m/s=5000$ N

Also we know force of an object = $mass\times \frac{v}{t}$ as initial velocity = $0$

So $F=v_r\times \frac{dm}{dt}$ where $\frac{dm}{dt}$ is the rate of fuel burn.

$\frac{dm}{dt}$ =$\frac{F}{v_r}=\frac{5000}{2000}=2.5$ kg /s