#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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