Question

What is the nature of relation betweenthe kinetic energy $\left(E_k\right)$ and their orbitalradius $\left(r\right)$ of the satellites revolvingaround the Earth?

• A. $E_k\propto 1$
• B. $E_k\propto \frac{1}{r}$
• C. $E_k\propto r^2$
• D. $E_k\propto \frac{1}{r^2}$

Answer 1

The correct option is B $E_k\propto \frac{1}{r}$

$\begin{array}{c}\frac{GMm}{r^2}=\frac{m{v}^2}{r}\\ \Rightarrow \frac{m{v}^2}{2}=\frac{GMm}{2r}\\ \therefore K_E\propto \frac{1}{r}\end{array}$

$\therefore$ Option $B$ is correct .