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

Question

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" /> (A) increased (B) decreased (C) the same (D) changed in unpredicted manner

Tardigrade Admin · Accepted Answer

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

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

increased

decreased

the same

changed in unpredicted manner

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.

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