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

Question

$$(a)\;r^{\bigg(\Large\frac{n+1}{2}\bigg)} \quad (b)\;r^{\bigg(\Large\frac{n-1}{2}\bigg)} \quad (c)\;r^n \quad (d)\;r^{\bigg(\Large\frac{n-2}{2}\bigg)}$$