Three particles, each having a mass of 200 g , are placed at the corners of an equilateral triangle with a side length of 10 cm . Determine the moment of inertia of the system about an axis passing through one of the particles and perpendicular to the plane of the particles.

Step-by-step solution

Let the three particles be placed at the vertices A, B, and C of the equilateral triangle. Mass of each particle, m = 200 g = 0.2 kg Side length of the triangle, a = 10 cm = 0.1 m The axis of rotation passes through one of the particles (say, at vertex A) and is perpendicular to the plane of the triangle. The perpendicular distance of the particle at A from the axis is r_A = 0 . The perpendicular distances of the particles at B and C from the axis are r_B = a and r_C = a . The moment of inertia of the system about