The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

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40 hours

30 hours

25 hours

36 hours

answer is B.

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Detailed Solution

$\begin{array}{l} T = \frac{2 π}{\sqrt{GM}} r^{3 / 2} \\ \frac{T_{1}}{T_{2}} = {(\frac{r_{1}}{r_{2}})}^{3 / 2} = {(\frac{1}{3})}^{3 / 2} \\ T_{2} = T_{1} 3 \sqrt{3} = 21 \sqrt{3} hours \\ \approx 36 hours \end{array}$

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