An massless equilateral triangle EFG of side

Question:

An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass $\mathrm{m}$ situated at its vertices. The moment of intertia of the system about the line EX perpendicular

to $\mathrm{EG}$ in the plane of $\mathrm{EFG}$ is $\frac{\mathrm{N}}{20} \mathrm{ma}^{2}$ where $\mathrm{N}$

is an integer. The value of $\mathrm{N}$ is__________.

Solution:

$\mathrm{I}=0+\mathrm{m}\left(\frac{\mathrm{a}}{2}\right)^{2}+\mathrm{ma}^{2}$

$=\frac{5}{4} \mathrm{ma}^{2}$

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