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

Answer

C

Explanation

( c) From conservation of angular momentum
`I omega = mvr`
`200 xx omega = 50 xx 2 xx 1`
`omega = (1)/(2) rad//s`
`v = r omega = 1 m//s`
:. `t = (2 pi r)/(1 -(-1)) =(2 pi r)/(2) = pi r = 2 pi s`.