Three point masses m₁, m₂ and m₃ are located at the vertices of an equilateral triangle of side ‘a’. What is the moment of inertia of the system about an axis along the altitude of the triangle passin

Question

Three point masses m₁, m₂ and m₃ are located at the vertices of an equilateral triangle of side ‘a’. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through m₁?

Accepted Answer

Answer: (m₂ + m₃)a²/4 — Axis passes through m₁, so its perpendicular distance is zero. Distances of m₂ and m₃ from the altitude are each a/2. Hence I = m₂(a/2)² + m₃(a/2)² = (m₂ + m₃)a²/4

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