Question

A rocket of mass $1000kg$ is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity $100m/s$ with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upwards against the gravitational attraction? (Take $g=10m/s^2$ ).

• A. 50 kg/s
• B. 100 kg/s
• C. 200 kg/s
• D. 400 kg/s

Answer 1

Answer: (B)

The force $(F)$ lifting the rocket is given by
$F=v_r\left(\frac{\Delta m}{\Delta t}\right)$
where $v_r$ is velocity of the gas relative to rocket,
$\frac{\Delta m}{\Delta t}$ is rate of change of mass.
Given, $F=Mg=1000\times 10=10,000N$
$v_r=100m/s$
$\therefore \frac{\Delta m}{\Delta t}=\frac{F}{v_r}$
$=\frac{10,000}{100}=100kg/s$