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Kepler's Law

Two satellite...

Question

Two satellites of masses 400 kg, 500 kg are revolving around earth in different circular orbits of radii $r_{1}$ , $r_{2}$ such that their kinetic energies are equal. The ratio of $r_{1}$ , $r_{2}$ is

A

4 : 5

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B

16 : 25

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C

5 : 4

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D

25 : 16

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Solution

The correct option is A $4 : 5$
Kinetic energy of a satellite is given by: $K E = \frac{G M m}{r}$
$∴ \frac{K E_{1}}{K E_{2}} = \frac{r_{2}}{r_{1}} \frac{m_{1}}{m_{2}}$
Given: $K E_{1} = K E_{2}$
$\Rightarrow \frac{r_{1}}{r_{2}} = \frac{m_{1}}{m_{2}} = \frac{400}{500}$
$∴ r_{1} : r_{2} = 4 : 5$

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