Three particles, each of mass M are situated at the vertices of an equilateral triangle ABC of side L. Find moment of Inertia of system about an axis passing through the centroid and perpendicular to plane of the triangle ABC.

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$M L^{2}$

$2 M L^{2}$

$4 M L^{2}$

$3 M L^{2}$

answer is A.

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Detailed Solution

Distance of centroid from all the particles is $\frac{L}{\sqrt{3}}$ . MOI about an axis and passing through centroid perpendicular to plane of triangle ABC $I_{c} = 3 \times m {[\frac{L}{\sqrt{3}}]}^{2} = m L^{2}$

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