#2015_12 My class test problem -Part 3

A uniform disc of radius $$4R$$ has a circular cavity of radius $$R$$ as shown. The surface mass density of the disc is $$\sigma$$. The disk is held vertically on a rough horizontal such that the line joining the geometrical center $$O$$ of the disc and center of the cavity $$C$$ is horizontal. If the angular acceleration of the disc just when it is released, assuming that it starts pure rolling motion and does not topple, is $$\dfrac { Ng }{ 717R }$$, then find $$N$$.

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