Moment of inertia of an equilateral triangular lamina A B C , about the axis passing through its centre O and perpendicular to its plane is I 0 as shown in the figure. A cavity D E F is cut out from t

Question

Moment of inertia of an equilateral triangular lamina $A B C$ , about the axis passing through its centre $O$ and perpendicular to its plane is $I_{0}$ as shown in the figure. A cavity $D E F$ is cut out from the lamina, where $D, E, F$ are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is:

TestHub · Accepted Answer

Given, A B = B C = A C = l Moment of inertia of a triangular lamina A B C I 0 = k m l 2 D E = E F = D F = 1 2 , A B = l 2 ∴ Moment of inertia of ∆ D E F I D E F = k m 4 l 2 2 I D E F = k 16 m l 2 . I D E F = I 0 16 Moment of inertia of the remaining part I r e m a i n = I 0 - I 0 16 = 15 I 0 16

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