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

Explanation

`(GM m)/(R^(n)) = m R ((2 pi)/(T))^(2)`
or `T^(2) = (R xx 4 pi^(2) xx R^(n))/(GM) = (4 pi^(2)R^((n + 1)))/(GM)`
or `T = (2 pi)/(sqrt(GM)). R^((n + 1)//2)` or `T prop R^((n + 1)//2)`