Three particles having equal masses are placed at the three corne… - Vidyadip

Question

Three particles having equal masses are placed at the three corners of an equilateral triangle of side a. Find the moment of inertia of the system relative to the axis passing through any one particle and perpendicular to the plane of the triangle.

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Answer

Let the mass of each particle at the vertex of the equilateral traingle be. The moment of inertia of a particle at a vertex through which the required axis is passing will be zero because its distance from the axis is zero. And there will be moment of inertia due to the particles on the remaining two vertices since the particles placed at the other two vertices have equal mass and are at equal distances from the axis, the moment of inertia of both the particles will be equal. Moment of inertia of one particle $=m(a)^2=m a^2$

Moment of inertia of both particles $=2 ma ^2$ Hence, moment of inertia of the system
$=0+2 m a^2=2 m a^2 .\quad \text { Ans. }$

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