Three particles, each of mass $m$ gram, are situated at the vertices of an equilateral triangle $\mathrm{ABC}$ of side $\ell \mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to $\mathrm{AB}$ and in the plane of $\mathrm{ABC}$, in gram-cm $^{2}$ units will be

Question

Aicharya · Accepted Answer

$
\begin{aligned}
\mathrm{I}_{\mathrm{AX}} &=\mathrm{m}(\mathrm{AB})^{2}+\mathrm{m}(\mathrm{OC})^{2} \\
&=\mathrm{m} \ell^{2}+\mathrm{m}\left(\ell \cos 60^{\circ}\right)^{2} \\
&=\mathrm{m} \ell^{2}+\mathrm{m} \ell^{2} / 4=5 / 4 \mathrm{~m} \ell^{2}
\end{aligned}
$

Three particles, each of mass $m$ gram, are situated at the vertices of an equilateral triangle…

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