Question

A rocket of mass 6000kg is fired from earth with speed $1{kms}^{-1}$ . What should be the rate of ejection of gas, so that it moves with acceleration of $20m/s^2$. Take $g=10m/s^2$

• A. $60{kgs}^{-1}$
• B. $180{kgs}^{-1}$
• C. $200{kgs}^{-1}$
• D. $120{kgs}^{-1}$

Answer 1

The correct option is B $180{kgs}^{-1}$

For the rocket to move with acceleration $a$, thrust required is -

$F=m(a+g)$ ...(1)

To provide this thrust, let dm/dt be rate of ejection of gas.

$F=v\left(\frac{dm}{dt}\right)$ ...(2)

From (1) & (2),

$m(a+g)=v\left(\frac{dm}{dt}\right)$

$\frac{dm}{dt}=\frac{m(a+g)}{v}$

$\frac{dm}{dt}=\frac{6000\times (20+10)}{1000}$

$\frac{dm}{dt}=180kg/s$

Therefore, rate of ejection of gas should be $180kg/s$.