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A small planet is revolving around a ver...

A small planet is revolving around a very massive star in a circular orbit of Radius R with a period of revolution T. If the gravitational force between the planet and the star were proportional to `R^(-5//2)`, then T would be proportional to

A

`T^2` is proportioinal to `R^2`

B

`T^2` is proportional to `R^(7/2)`

C

`T^2` is proportional to `R^(3/2)`

D

`T^2` is proportional to `R^(3.75)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(mv^(2))/R propR^(-5//2), :. vpropR(-3//4)`
Now `T=(2piR)/v` or `T^(2)prop(R/v)^(2)`
`T^(2) prop(R/R^(-3/4))^(2)` or `T^(2)propR^(7//2)`
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