Question

If the force on a rocket is $400\text{N}$ and relative velocity of mass emission is $500\text{m/s}$, then the rate of combustion of the fuel will be

• A. $0.8\text{kg/s}$
• B. $0.6\text{kg/s}$
• C. $0.4\text{kg/s}$
• D. $0.2\text{kg/s}$

Answer 1

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

The mass ejected develops the upward thrust force on the rocket.
Thrust force,
$F_t=-v_r\frac{dm}{dt}$
$\Rightarrow 400=-500\times \frac{dm}{dt}$
$\Rightarrow \frac{dm}{dt}=-0.8\text{kg/s}$
The negative sign shows that mass is being ejected.
$$\begin{array}{c}\text{Why this question?}\\ \text{Tips: Ejection of fuel leads to change in momentum}\\ \text{of rocket on account of change in its mass.}\end{array}$$