A B C is a plane lamina of the shape of an equilateral triangle. D ,   E are mid-points of A B ,   A C and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane A B C is I 0 . If part A D E is removed, the moment of inertia of the remaining part about the same axis is N I 0 16 where N is an integer. Value of N is:

Step-by-step solution

Let mass of lamina = m , and length of side = l , then moment of inertila of lamina about an axis passing through G and perpendicular to the plane. I 0 ∝ m l 2 I 0 = k m l 2 Let moment of inertila of D E F = I 1 about G then, I 1 = I 0 16 then, I A D E = I B D F = I E F C = I 2 3 I 2 + I 1 = I 0 3 I 2 + I 0 16 = I 0 ⇒ I 2 = 5 I 0 16 So, Moment of inertila of D E C B = 2 I 2 + I 1 2 5 I 0 16 + I 0 16 = 11 I 0 16