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Intuition for COM

Three point m...

Question

Three point masses $m_{1}, m_{2}, m_{3}$ 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 atitude of the triangle passing through $m_{1}$ ?

(m_{1} + m_{2}) \frac{a^{2}}{4}

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(m_{2} + m_{3}) \frac{a^{2}}{4}

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(m_{1} + m_{3}) \frac{a^{2}}{4}

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(m_{1} + m_{2} + m_{3}) \frac{a^{2}}{4}

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Solution

The correct option is B $(m_{2} + m_{3}) \frac{a^{2}}{4}$

So, $μ . I$ about $m_{1} = 0$
So, eqn should contain $m_{2}, m_{3}$ terms so, B satisfies or other wise by solving $(m_{2} + m_{3}) \frac{a^{2}}{4} .$
Hence, the answer is $\frac{a^{2}}{4} (m_{2} + m_{3}) .$

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