A small planet is revolving around a very massive star in a circular orbit of radius r with a period of revolution T . If the gravitational force between the planet and the star is proportional to r - 5 / 2 , then T will be proportional to

Question

A small planet is revolving around a very massive star in a circular orbit of radius r with a period of revolution T . If the gravitational force between the planet and the star is proportional to r - 5 / 2 , then T will be proportional to, r 3 / 2, r 5 / 3, r 7 / 4, r 3

MARKS App · Accepted Answer

Gravitational force provides the necessary centripetal force required by the given planet for circular motion. So mv 2 r ∝ r - 5 / 2 ⇒ mv 2 r = kr - 5 / 2 , k = constant ∴ v = kr - 3 / 2 m T = 2 π r v = 2 π r × m k r - 3 / 2 i.e., T ∝ r 7 / 4 .

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