An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D , E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G

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An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D , E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I ₀ . If the smaller triangle DEF is removed from ABC , the moment of inertia of the remaining figure about the same axis is I .

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Correct answer: A. I = 15 16 I ₀

Let mass of the larger triangle = M Side of larger triangle = Moment of inertia of larger triangle = ma ² Mass of smaller triangle = M 4 Length of smaller triangle = 2 Moment of inertia of removed triangle = M 4 ( a 2 )² I _ removed I _ original = M 4 M ( a 2 )² ( a )² I_ removed = I₀ 16 So , I = I ₀- I ₀ 16 = 15 I ₀ 16

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