A hole of radius \( R / 2 \) is cut from a thin circular plate of radius \( R \) and mass \( M \...

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A hole of radius \( R / 2 \) is cut from a thin circular plate of radius \( R \) and mass \( M \). The moment of inertia of the plate about an axis through \( O \) perpendicular to the \( x y \)-plane (i.e. about the \( z \)-axis) is
(a) \( \frac{5}{7} M R^{2} \)
(b) \( \frac{7}{12} M R^{2} \)
(c) \( \frac{13}{32} M R^{2} \)
(d) \( \frac{13}{24} M R^{2} \)
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