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

• A. increased
• B. decreased
• C. the same
• D. changed in unpredicted manner

Answer 1

Answer: (B)

decreased

Answer 2

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.