Moment of inertia of an equilateral triangular plate of side length a , about an axis passing through one of its vertices perpendicular to its plane is equal to I 0 . If the following symmetric stru

Question

Moment of inertia of an equilateral triangular plate of side length $a$ , about an axis passing through one of its vertices perpendicular to its plane is equal to $I_{0}$ . If the following symmetric structure is made from the same material, then its moment of inertia about the axis OO' is found to be equal to $NI_{0}$ . Find $N$ .

CT42 n3 diagram

TestHub · Accepted Answer

The structure contains eight equilateral plates of side $2a$ arranged symmetrically about OO'.

Using each plate moment about its centroid and the parallel-axis theorem, the total is $32I_0$.

Therefore $N=32$.

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