A planet of mass m revolve around the sun of mass M in an elliptical orbit. The minimum and maximum distance of the planet from the sun are r and 3r respectively. The time period of the planet is proportional to

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${(4 r)}^{2 / 3}$

${(2 r)}^{2 / 3}$

${(2 r)}^{3 / 2}$

${(4 r)}^{5 / 2}$

answer is C.

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Detailed Solution

$r_{\min} = r$
$r_{\max} = 3 r$
$∴$ length of major a x is $= 4 r = 2 a \Rightarrow a = 2 r$
And $T^{2} α a^{3} \Rightarrow T^{2} α {(2 r)}^{3} \Rightarrow T α {(2 r)}^{3 / 2}$

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