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Question

A wire of mass M and length L is bent in form of a square. Calculate the MI of the square about the central axis perpendicular to the plane.

A
ML22
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B
ML224
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C
ML236
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D
ML248
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Solution

The correct option is D ML248
Each side of the square can be considered as rod of length m=M4 and mass m=M4
Moment of inertia of rod about center of square is
I=[ml212+m(l2)2]

Moment of inertia due four sides of square
4I=[ml212+m(l2)2]×4
Here, l=L4 and m=M4
=4ml23=43×ML264=ML248

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