Question 64 - 2019 (11 Jan Shift 1)

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. Then:

(1) $I = \frac{15}{16}I_0$

(2) $I = \frac{3}{4}I_0$

(3) $I = \frac{9}{16}I_0$

(4) $I = \frac{I_0}{4}$