Question

Two satellites of masses $400\text{kg}$ and $500\text{kg}$ are revolving around earth in different circular orbits of radii $r_1$ and $r_2$ such that their kinetic energies are equal. The ratio of $r_1$ to $r_2$ is

• A. $4:5$
• B. $16:25$
• C. $5:4$
• D. $25:16$

Answer 1

The correct option is A $4:5$

Given:

$m_1=400\text{kg};m_2=500\text{kg}$

Kinetic energy of a satellite in an orbit or radius $r$ is given by

$K=\frac{GMm}{2r}$

As per the equation, $K_1=K_2$

$\therefore \frac{GM{m}_1}{2r_1}=\frac{GM{m}_2}{2r_2}$

$\Rightarrow \frac{GM\times 400}{2r_1}=\frac{GM\times 500}{2r_2}$

$\Rightarrow \frac{r_1}{r_2}=\frac{4}{5}$

Hence, option $\left(a\right)$ is correct.

$\begin{array}{c}\text{Why this question: To make students}\\ \text{practice and remember the result}\\ K=\frac{GMm}{2r}\text{. it is helpful to remember}\\ \text{this apart from}K=\frac{1}{2}m{v}^2.\end{array}$