A circular platform is mounted on a frictionless vertical axle, its radius R = 2m and its moment of inertia about the axle is $200 k g m^{2}$ . It is initially at rest. A 50kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1m/s relative to the ground. Time taken by the man to complete one revolution is $k π \sec .$ Find ‘k’

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Detailed Solution

MI of plat form $= 200 k g m^{2}$
MI of man $= m R^{2} = 200 k g m^{2}$
For system (plat form + man) by using COAM $I p ω_{0} = m v R$
$ω_{0} = \frac{50 \times 1 \times 2}{200} = \frac{1}{2} r a d / s$
Angular velocity of man w.r.t platform $= \frac{V}{R} + ω_{0}$ $\frac{1}{2} + \frac{1}{2} = 1 r a d / \sec$
$= \frac{2 π r a d}{1 r a d / \sec} = 2 π$ s
Time taken by the man to complete one revolution