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  4. Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be

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

AIPMTAIPMT 2004System of Particles and Rotational Motion

Solution:

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$I _{ AX }= m \ell^{2}+ m \left(\frac{\ell}{2}\right)^{2}$
$= m \ell^{2}+\frac{ m \ell^{2}}{4}=\frac{5}{4} m \ell^{2}$