A circular platform is mounted on a frictionless vertical axle. Its radius $R=2\text{m}$ and its moment of inertia $I=200{\text{kg m}}^2$. It is initially at rest. A $50\text{kg}$ man stands on the edge and begins to walk along the edge at a speed of $1{\text{ms}}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is:

1. A
   $\frac{\pi }{2}\text{s}$
2. B
   $\pi \text{s}$
3. C
   $\frac{3\pi }{2}\text{s}$
4. D
   $2\pi \text{s}$