Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² units will be

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(3) 5/4ml². Given: equal masses m at A, B and C of an equilateral triangle of side l; the axis AX passes through A, lies in the plane and is perpendicular to AB. Idea: I=Σ mr², with r the perpendicular distance from each particle to AX — that is, its displacement measured along AB. A lies on the axis: r_A=0. B lies a full side along AB: r_B=l. C sits above the midpoint of AB, so its foot on AB is /l2 from A: r_C=/l2. I=m(0)²+m(l)²+m(/l2)²=ml²+(ml²)/4 I=5/4ml²

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm² units will be

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