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

• A

  $\mathrm{\pi } \sec$

• B

  $\frac{3\mathrm{\pi }}{2} \sec$

• C

  2$\mathrm{\pi }$ sec

• D

  $\frac{\mathrm{\pi }}{2}\sec$