Two satellites,S₁ and,S₂ describe circular orbits of radii r and 2r respectively around a planet. If the orbital angular velocity of S₁ is $ω$ , what is that of S₂?

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$\frac{ω \sqrt{2}}{3}$

$ω \sqrt{2}$

$\frac{ω}{\sqrt{2}}$

$\frac{ω}{2 \sqrt{2}}$

answer is A.

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Detailed Solution

$A c c o r d i n g t o K e p l e r' s l a w T^{2} \propto r^{3} ω^{2} \propto r^{- 3} \frac{ω_{1}}{ω_{2}} = {(\frac{r_{2}}{r_{1}})}^{\frac{3}{2}} = 2^{\frac{3}{2}} ω_{2} = \frac{ω}{2 \sqrt{2}}$

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