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  4. Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB . The moment of inertia of the plate about the axis CD is then equal to <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-ukkm9hubxfstazzm.jpg />

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Q. Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta $ with $AB$ . The moment of inertia of the plate about the axis $CD$ is then equal to
Question

NTA AbhyasNTA Abhyas 2022

Solution:

From symmetry $I_{AB}=I_{A ' B '}$ and $I_{CD}=I_{C ' D '}$
Solution
From theorem of perpendicular axes
$\text{I}_{zz}=\text{I}_{\text{AB}}+\text{I}_{A ' B '}=\text{I}_{\text{CD}}+\text{I}_{\text{C'D'}}$
$I_{zz}=2\text{I}_{\text{AB}}$
$I_{zz}=2\text{I}_{\text{CD}}$
$\therefore I_{CD}=I_{C ' D '}$