Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R−3/2, then T2 is proportional to

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R5/2

R3/2

R7/2

answer is C.

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Detailed Solution

Gravitational force =GMmR3/2 provides the necessarycentripetal force (i.e., mRω2 ) So GMmR3/2=mRω2=mR2πT2=4π2mRT2or T2=4π2R3/4GMe,i, T2∝R3/2

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