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The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is

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9 T

27 T

12 T

3 T

answer is B.

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Detailed Solution

$\begin{array}{l} T^{2} \propto R^{3} \\ {(\frac{T'}{T})}^{2} = {(\frac{9 R}{R})}^{3} \\ T'^{2} = T^{2} \times 9^{3} \\ T' = T \times 3^{3} \Rightarrow T' = 27 T . \end{array}$

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