A uniform disc of radius \( R \) has a round disc of radius \( R / 3 \) cut as shown in figure. ...

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A uniform disc of radius \( R \) has a round disc of radius \( R / 3 \) cut as shown in figure. The mass of the remaining (shaded) portion of the disc equals \( M \). Find the moment of inertia of such a disc relative to the axis passing through geometrical centre of original disc and perpendicular to the plane of the disc. Consider surface mass density as \( \sigma \).
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