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Q.

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 planet and star is proportional  to R−5/2, then T2 is proportional to-

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a

R3

b

R7/2

c

R5/2

d

R3/2

answer is B.

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Detailed Solution

F∝1R5/2⇒mω2R∞1R5/2; mω2∞1R7/2⇒ω2∞1R7/2 2πT2=1R7/2⇒T2∝R7/2
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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 planet and star is proportional  to R−5/2, then T2 is proportional to-