Question

A unifrom square plate has a small piece `Q` of an irregular shape removed and glued to the centre of the plate leaving a hole behind [Fig.] The moment of inertia about the z-axis is than

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

Answer 1

Correct Answer - B
According to the theorem of perependicular 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)` decreases, overall.