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

According to the theorem of perpendicular axes

$I _ { z } = I _ { x } + I _ { y }$

With the hole, $I _ { x }$ and both decreases. Gluing the removed piece at the centre of square plate does not affect Hence, decreases overall.