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  4. A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind. The moment of inertia about the z-axis is then <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/f3ea0bd9600e5f4ae8b14d66c3fc6044-.png />

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Q. A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the centre of the plate leaving a hole behind. The moment of inertia about the $z$-axis is then
image

System of Particles and Rotational Motion

Solution:

cording to the theorem of perpendicular axes
$I_z = I_x +I_y$
With the hole, $I_x$ and $I_y$ both decrease. Gluing the removed piece at the centre of square plate does not affect $I_z$. Hence, $I_z$ decrease overall.