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

Options

A. `pi` sec
B. `(3pi)/2` sec
C. `2pi` sec
D. `pi/2 ` sec

Answer

C

Explanation

From conservation of angular momentum
`I omega = mvr rArr 200 xx omega = 50 xx 2xx 1`
`omega = 1/2 "rad/s" , v = romega = 1 m//s`
`:. T = (2pir)/(1-(-1)) = (2pir)/2 = pir = 2 pis `