\[\begin {array} {1 1} (a)\;\frac{17MR^2}{32} & \quad (b)\;\frac{13MR^2}{32} \\ (c)\;\frac{11}{32}MR^2 & \quad (d)\;\frac{MR^2}{2} \end {array}\]

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Moment of inertia of the cut disc portion about $0=I_1$

Moment of inertia of remaining portion about $0=I_2$

$M.I$ of the full disc about $O=I$

$I=I_1+I_2$

Mass of out disc $=\large\frac{M}{R^2}. \bigg(\large\frac{R}{2}\bigg)^2$

$\qquad= \large\frac{M}{4}$

$I_1$ about $O^{1}=\large\frac{1}{2} \bigg( \large\frac{M}{4} \bigg) \bigg( \frac{R}{2} \bigg)^2$

$\qquad = \large\frac{MR^2}{32}$

$I_1$ about $O=\large\frac{MR^2}{32}+\frac{M}{4} \bigg( \frac{R}{4} \bigg)$

$\qquad= \large\frac{MR^2}{32}+\frac{MR^2}{16}$

$\qquad= \large\frac{3 MR^2}{32}$

$I_2= I-I_1$

$\qquad= \large\frac{MR^2}{2} -\frac{3MR^2}{32}$

$\qquad= \large\frac{13 MR^2}{32}$

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