Three point masses m,, m, and m, are located at the vertices of an equilateral triangle of side length a. What is the moment of inertia about an axis along the altitude of the triangle passing through $m_1$?
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The masses are arranged as shown below. AB is the axis about which moment of inertia is to be found. Since $m_1$ is on the axis and $m_2, m_3$ are at a distance $\frac{\text{a}}{2}$ from it, the moment of inertia is, $\text{I}=(\text{m}_2+\text{m}_3)\Big(\frac{\text{a}}{2}\Big)^2$
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