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Question

Let 'I' be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to


A
I
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B
Isin2θ
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C
Icos2θ
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D
Icos2(θ2)
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Solution

The correct option is A I
IAB=IAB=IandICD=ICD
If I0 be the moment of inertia of the square plate about an axis passing through O and perpendicular to the plate, then by the perpendicular axis theorem
I0=IAB+IAB=2IAB....(1)
or I0=ICD=ICD=2ICD....(2)
From ((1) and (2))
ICD=IAB=I.

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