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

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, I, Isin 2 θ, Icos 2 θ, Icos 2 θ 2

MARKS App · Accepted Answer

From symmetry I AB = I A ' B ' and I CD = I C ' D ' From theorem of perpendicular axes I zz = I AB + I A ' B ' = I CD + I C'D' I zz = 2 I AB I zz = 2 I CD ∴ I CD = I C ' D '

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