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 the planet and the star is proportional to R+5/2, then

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a

T2∝R3

b

T2∝R7/2

c

T2∝R3/2

d

T2∝R3/76

answer is B.

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Detailed Solution

The gravitational force  F  ∝ 1R52  givenF=CR52−−−−−1here C is constantThe centripetal force for the planet  =mRω2=mR2πT2−−−−−2Centripetal force is provided from gravitational force  (1) = (2)F=CR52=mR2πT2⇒T2 ∝ R52R⇒T2 ∝ R72Therefore, the correct answer is  (B)
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