A uniform disc of mass M and radius R is smoothly pivoted at ' O '. A light inextensible strings wrapped over the disc hangs a particle of mass m. If the system is released from rest, assuming string does not slide. What will be the angular speed of the disc as a function of time.

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TestHub · Accepted Answer

For the falling mass, mg-T=ma and for the disc TR=(MR²/2)(a/R). Hence a=2mg/(M+2m). With no slip, α=a/R, so ω=αt=2mgt/[(M+2m)R].

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