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Horizontal and Vertical Components of Projectile Motion

Three point m...

Question

Three point masses $m_{1}, m_{2}$ 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 $m_{1}$

(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 $(m_{2} + m_{3}) \frac{a^{2}}{4}$
Moment of inertia of particle 1 is 0 about an axis along the altitude of the triangle passing through $m_{1}$
Moment of inertia of $m_{2}$ about an axis along the altitude of the triangle passing through $m_{1}$ = $m_{2} d^{2} = m_{2} {(a / 2)}^{2}$
Moment of inertia of $m_{3}$ about an axis along the altitude of the triangle passing through $m_{1}$ = $m_{3} d^{2} = m_{3} {(a / 2)}^{2}$
Total Moment of inertia about an axis along the altitude of the triangle passing through $m_{1}$ = $m_{2} {(a / 2)}^{2} + m_{3} {(a / 2)}^{2} = (m_{2} + {m_{3}) (a)}^{2} / 4$

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