$A$ 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

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