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Q.

A planet is revolving around the sun in a circular orbit with a radius r. The time period is T. If the force between the planet and star is proportional to r-3/2 , then the square of time period is  proportional to [AIMS 2018]

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a

r3/2

b

r2

c

r

d

r5/2

answer is D.

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Detailed Solution

As force,   F=GMmr3/2=mω2r⇒  GMmr3/2=4π2mrT2             ∵ω=2πT⇒  T2=4π2GM·r5/2⇒T2∝r5/2
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