The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plate is:
(i) I₁ + I₂
(ii) I₃ + I₄
(iii) I₁+ I₃
(iv) I₁ + I₂+ I₃ + I₄
where I₁ ,I₂, I₃ and l₄ are respectively the moments of inertia
about axes 1,2,3 and 4 which are in the plane of the plate.

Question

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plate is:

(i) I₁ + I₂
(ii) I₃ + I₄
(iii) I₁+ I₃
(iv) I₁ + I₂+ I₃ + I₄
where I₁ ,I₂, I₃ and l₄ are respectively the moments of inertia
about axes 1,2,3 and 4 which are in the plane of the plate.

Infinity Learn · Accepted Answer

It is a square plate so by symmetry, $$I3$$ $$=$$ $$I4$$ and $$I1$$ $$=$$ $$I2By$$ perpendicular axis theorem, $$I0$$ $$=$$ $$I1$$ $$+$$ $$I2$$ $$+$$ $$I3$$ $$+$$ $$I4$$

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