Moment of inertia

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Question

A massless equilateral triangle EFG of side ‘a’ (as shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $\frac{N}{20} {ma}^{2}$ where N is an integer. The value of N is ___

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Solution

$\begin{array}{l} I = m {(\frac{a}{2})}^{2} + {ma}^{2} \\ = \frac{5}{4} {ma}^{2} \\ I = \frac{25}{20} {ma}^{2} \\ ∴ N = 25 \end{array}$

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