Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius 'R' around the sun will be proportional to

Options

A. `R^((n+1)/2)`
B. `R^((n-1)/2)`
C. `R^(n)`
D. `r((n-2)/2)`

Answer

A

Explanation

`(mv^(2))/r = k/r^(n) rArr v = sqrt(k/(mr^(n-1))`
`T = (2pir)/v = (2pir)/(sqrt(k/(mr^(n-1)))` or `T propto r^((n-1)/2)`