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 I₀. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:

Question

G1 Physics · Accepted Answer

Triangle DEF is similar to ABC with linear scale 1/2. Its mass is therefore 1/4 of the original and, about the common centroid G, its moment of inertia scales as mass × length² = (1/4)(1/4)=1/16. Thus removed moment of inertia = I₀/16 and remaining moment of inertia = I₀-I₀/16 = 15I₀/16. Hence option D.