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Suppose the gravitational force varies i...

Suppose the gravitational force varies inversely as the `n^(th) `power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to-

A

`R^(((n+1)/(2)))`

B

`R^(((n-1)/(2)))`

C

`R^(n)`

D

`R^(((n-2)/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(GMm)/(R^(n))=(mv^(2))/(R)`
`impliesv=sqrt((GM)/(R^(n-1)))`
`T=(2piR)/(v)impliesT^(2)=(4pi^(2)R^(n+1))/(GM)`
`implies TpropR^(((n+1))/(2))`
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