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Question

The moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of the square plate is given by:

A
Ml212
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B
Ml2
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C
Ml26
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D
23Ml2
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Solution

The correct option is D 23Ml2
Moment of inertia of the square plate about an axis passing through its center of mass and perpendicular to its plane is :
Icom=Ml26
According to the parallel axis theorem, moment of inertia of the plate about the axis passing from the corner and perpendicular to its plane is :
I=Icom+Mx2
Here, the distance between this axis from com is equal to half the length of the diagonal of the square.
i.e.x=l22=l2
I=Ml26+Ml22
Or, I=2Ml23

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