Moment Of Inertia

We are given that three particles of mass are placed at the vertices of an equilateral triangle with side length . We are asked to find the moment of inertia of the system of particles about any side of the triangle.
Step 1: Moment of inertia formula. The moment of inertia of a system of point masses is given by: where is the mass of the -th particle and is the perpendicular distance from the axis of rotation.
Step 2: Geometry of the problem. The particles are placed at the vertices of an equilateral triangle. The distance from each particle to the axis (side of the triangle) is .
Step 3: Moment of inertia calculation. The moment of inertia of the two particles not on the axis is:
Step 4: Final answer. Thus, the moment of inertia is , corresponding to Option 3.