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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-on2 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-on2 units will bePhysics Question Image

MGIMS WardhaMGIMS Wardha 2008

Solution:

Moment of inertia c $ ={{I}_{A}}+{{I}_{B}}+{{I}_{C}} $ $ ={{m}_{A}}{{({{r}_{A}})}^{2}}+{{m}_{B}}{{({{r}_{B}})}^{2}}+{{m}_{C}}{{({{r}_{C}})}^{2}} $ $ =m{{(0)}^{2}}+m{{(l)}^{2}}+m{{(l\cos 60)}^{2}} $ $ =m{{l}^{2}}+\frac{m{{l}^{2}}}{4}=\frac{5m{{l}^{2}}}{4} $

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