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  4. Three point masses m1 , m2 ,m3 are located at the vertices of an equilateral triangle of length a. The moment of inertia of system about an axis along the altitude of the triangle passing through m1 is

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Q. Three point masses $m_1 , m_2 ,m_3 $ are located at the vertices of an equilateral triangle of length $a$. The moment of inertia of system about an axis along the altitude of the triangle passing through $m_1$ is

System of Particles and Rotational Motion

Solution:

$m_1$ becomes insignificant because it lies on the axis of rotation
M.O.I = $m_2 \left(\frac{a}{2} \right)^2 + m_3 \left( \frac{a}{2} \right)^2$
= $\frac{a^2}{4}(m_2 + m_3)$

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