c
                As the system is initially at rest, therefore, initial angular momentum \({L_i} = 0\)

According to the principal of conservation of angular momentum, final angular momentum,

\({L_f} = 0\).

\(\therefore \) Angular momentum \(=\) Angular momentum, of man is in opposite direction of platform.

i.e., \(mvR=I\)\(\omega \)

or \(\omega  = \frac{{mvR}}{I} = \frac{{50 \times 1 \times 2}}{{200}} = \frac{1}{2}\,rad\,{s^{ - 1}}\)

Angular velocity of man relative to platform is 

\({\omega _r} = \omega  + \frac{v}{R} = \frac{1}{2} + \frac{1}{2} = 1\,rad\,{s^{ - 1}}\)

Time taken by the man to complete one revolution is 

\(T = \frac{{2\pi }}{{{\omega _r}}} = \frac{{2\pi }}{1} = 2\pi \,s\)