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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 `T^(2)` is proportional to

A

`R^(3)`

B

`R^(3//2)`

C

`R^(5//2)`

D

`R^(7//2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Centripetal force `=mRomega^(2)=mR((2pi)/(T))^(2)`
`=(4pi^(2)mR)/(T^(2))`
Gravitational force `=KR^(-5//2)`(Given)
`KR^(-5//2)=(4pi^(2)mR)/(T^(2))`
`rArrT^(2)K=4pi^(2)m.R^(7//2)`
`thereforeT^(2)propR^(7//2)`
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