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The moment of inertia is additive: if we have two objects having moments of inertia `I_1` and `I_2` with respect to the same axis, then the moment of inertia of the compound object (with respect to the same axis) will be `I_1+I_2.`
Therefore the moment of inertia of a semicircular disk (which I think is a half of a circular disk) is a half of the entire disk's moment of inertia.
Also, it is well known (or may be easily obtained by integration) that the moment of inertia of a circular disk or mass M and radius r (about a line perpendicular to the plane of disc through its center) is equal to
So for the semidisk the moment of inertia is `(M*r^2)/4,` option C.
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