A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T . If the force of attraction between planet and star is proportional to R - 3 / 2 then c

Question

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T . If the force of attraction between planet and star is proportional to R - 3 / 2 then choose the correct option :

TestHub · Accepted Answer

Let the gravitational force of attraction be $F = \frac{G M m}{R^{3 / 2}}$ .

Now, this gravitational force will provide the required centripetal force. Therefore,

$\frac{G M m}{R^{3 / 2}} = m ω^{2} R$

$\Rightarrow ω^{2} \propto \frac{1}{R^{5 / 2}} ∵ T = \frac{2 π}{ω}$

$\Rightarrow T^{2} \propto R^{5 / 2}$

Physics - Gravitation Question with Solution | TestHub

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