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A unifrom square plate has a small piece...

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.

Text Solution

Verified by Experts

The correct Answer is:
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.
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