Ncert Exercises & Solutions

A uniform square plate has a small piece \(Q\) of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The moment of inertia about the \(\mathrm{z}\)-axis is then

1.	increased
2.	decreased
3.	the same
4.	changed in an unpredictable manner

Hint: The moment of inertia depends on mass distribution.

Explanation: In the given diagrams, when the small piece \(Q\) is removed and glued to the center of the plate, the mass comes closer to the \(\mathrm{z}\)-axis, hence, the moment of inertia decreases. Therefore, the moment of inertia about the \(\mathrm{z}\)-axis is decreased.
Hence, option (2) is the correct answer.

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