Question

Three balls of masses 4kg, 3 kg and 5 kg are arranged at the corners of an equilateral triangle ΔABC of side 2 m. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle is

(a) 16 kg-m²

(b) 4\(\sqrt3\) kg-m²

(c) 4 kg-m²

(d) 16\(\sqrt3\) kg-m²

Answer 1

Correct option: (a) 16 kg-m²

Let G be the centroid of ΔABC

Moment of inertia about an axis through centroid G and perpendicular to plane of ΔABC is

l = 4 x AG² + 3 x BG² + 5 x CG²

= (4 + 3 + 5) CG² = 12 x \(\cfrac{4}{3}\) = 16 kg-m²