A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $n^{th}$ power of $R$. If the period of rotation of the particle is T, then :

Question

( A ) $T \propto R^{{n+1}/2}$
( B ) $T \propto R^{\frac{n}{2} + 1}$
( C ) $T \propto R^{n/2}$
( D ) $T \propto R^{3/2}$ for any $n$