question_answer

The moment of inertia of a thin uniform rod of length L and mass M about an axis passing through a point at a distance of 1/3 from one of its ends and perpendicular to the rod is

A) \[\frac{M{{L}^{2}}}{12}\]

B) \[\frac{M{{L}^{2}}}{9}\]

C) \[\frac{7M{{L}^{2}}}{48}\]

D) \[\frac{M{{L}^{2}}}{48}\]

Correct Answer: B

Solution :

\[{{I}_{\operatorname{CM}}}=\frac{M{{L}^{2}}}{12}\](about middle point)

\[\therefore \]\[I={{I}_{\operatorname{CM}}}+M{{x}^{2}}\left( x=\frac{L}{6} \right)\]

\[=\frac{M{{L}^{2}}}{12}+M{{\left( \frac{L}{6} \right)}^{2}}I=\frac{M{{L}^{2}}}{9}\]