Question

If the force on a rocket, moving with a velocity $500\text{m/s}$ is $400N$, then the rate of combustion of the fuel will be:

• A. $0.8\text{kg/sec}$
• B. $10.8\text{kg/sec}$
• C. $8\text{kg/sec}$
• D. $1.6\text{kg/sec}$

Answer 1

The correct option is A $0.8\text{kg/sec}$

We know that Force $=\frac{\text{dp}}{\text{dt}}=\frac{\text{d}\left(\text{mv}\right)}{\text{dt}}=\text{v}\frac{\text{dm}}{\text{dt}}$[When $\text{v}$ is constant]

In the given case force $=400N;\text{v}=500\text{m/sec}$.

We are required to calculate $\frac{\text{dm}}{\text{dt}}$ or rate of change of mass of the rocket.

In normal cases, force creates change in momentum. Here force is created due to change in momentum of the rocket by emission of fuel (a part of rocket).

So, $\frac{\text{dm}}{\text{dt}}=\frac{\text{force}}{\text{v}}=\frac{400}{500}=0.8\text{kg/sec}$