Two satellites of masses m and 3m revolve around the earth in circular orbit of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is k, then the value of k is ___

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Two satellites of masses m and 3m revolve around the earth in circular orbit of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is $\sqrt{k}$ , then the value of $k$ is ____

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answer is 3.

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Detailed Solution

Orbital speed = $V = \sqrt{\frac{G M}{r}} ∝ \frac{1}{\sqrt{r}}$

$\frac{V_{1}}{V_{2}} = \sqrt{\frac{r_{2}}{r_{1}}} = \sqrt{\frac{3 r}{r}} = \sqrt{3}$

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