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Q.

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:

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(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.

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a

(ii, iii)

b

(i, ii)

c

(i, iv)

d

(i, ii, iii)

answer is D.

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Detailed Solution

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

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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 + I4where I1 ,I2, I3 and l4 are respectively the moments of inertiaabout axes 1,2,3 and 4 which are in the plane of the plate.