The real force $F$ acting on a particle of mass $m$ performing circular motion acts along the radius of a circle of radius $r$ and is directed towards the center of the circle. If the square root of the magnitude of such force is given by $\sqrt{F} = \frac{2 \pi}{T} \sqrt{m r}$,where $T$ is the periodic time,find the expression for the force $F$.

• A
  $\frac{4 \pi^2 m r}{T^2}$
• B
  $\frac{T m r}{4 \pi}$
• C
  $\frac{2 \pi T}{\sqrt{m r}}$
• D
  $\frac{T^2 m r}{4 \pi}$