Question

A rocket which is ejecting gas with a speed of $100\text{m/s}$ and the rate of ejection of the gas from the rocket is $800\text{kg/s}$. If the mass of the rocket is $4000\text{kg}$, find out the initial acceleration of the rocket. Take $(g=10{\text{m/s}}^2)$

• A. $8{\text{m/s}}^2$
• B. $6{\text{m/s}}^2$
• C. $12{\text{m/s}}^2$
• D. $10{\text{m/s}}^2$

Answer 1

The correct option is D $10{\text{m/s}}^2$

Mass of rocket, $m=4000\text{kg}$
Relative velocity of gases w.r.t rocket ;$v=100\text{m/s}$
Rate of ejection of gas, $=800\text{kg/s}=\frac{dM}{dt}$

As we know,
$v.\frac{dM}{dt}-mg=ma$
$100\times 800-4000\times 10=4000\times a$
$a=10{\text{m/s}}^2$