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Q.

Three point-masses m are placed at the vertices of an equilateral triangle of side L Moment of inertia of the
system about an axis COD passing through a mass m at O and lying in the plane AOB and perpendicular to OA as shown in the figure is

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a

$\frac{2}{3} {mL}^{2}$

b

2mL²

c

$\frac{5}{4} {mL}^{2}$

d

$\frac{7}{4} {mL}^{2}$

answer is C.

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Detailed Solution

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$\begin{array}{l} I_{COD} = {Σmr}^{2} \\ = m_{A} L^{2} + m_{B} {(Lcos 60^{\circ})}^{2} \\ = {mL}^{2} + m (L^{2} / 4) = (5 / 4) {mL}^{2} \end{array}$

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Three point-masses m are placed at the vertices of an equilateral triangle of side L Moment of inertia of thesystem about an axis COD passing through a mass m at O and lying in the plane AOB and perpendicular to OA as shown in the figure is