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  4. The moment of inertia of semicircular plate of radius R and mass M about axis AA' in its plane passing through its centre is, <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-stphjos6ll1vlo0h.jpg />

Q. The moment of inertia of semicircular plate of radius and mass about axis in its plane passing through its centre is,

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Solution:


Moment of inertia of disk w.r.t. principle axis (1) =
Moment of inertia of disk w.r.t. diametrical axis (2) -

From perpendicular axes theorem
here , because both are diametrical axis,
So here and
So from eq.

For half disk also, it is applicable, So

(It does not depend on given in diagram, because given axis is also similar to diametrical axis)

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