Let 'I' be the moment of inertia of a uniform square plate about an axis AB that

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

Options:

A . I

B . Isin2θ

C . Icos2θ

D . Icos2(θ2)

Answer: Option A
:
A

I_{A B} = I_{A^{'} B^{'}} = I a n d I_{C D} = I_{C^{'} D^{'}}

I_{0}

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

I_{0} = I_{A B} + I_{A^{'} B^{'}} = 2 I_{A B} . . . . (1)

I_{0} = I_{C D} = I_{C^{'} D^{'}} = 2 I_{C D} . . . . (2)

From ((1) and (2))

I_{C D} = I_{A B} = I .

Let 'I' Be The Moment Of Inertia Of A Uniform Square Plate A...

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