question_answer

The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of \[\frac{L}{3}\]from one of its ends and perpendicular to the rod is

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

B)  \[\frac{M{{L}^{2}}}{9}\]

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

D)  \[\frac{M{{L}^{2}}}{3}\]

Correct Answer: B

Solution :

                 The moment of inertia about middle point \[{{I}_{CM}}=\frac{M{{L}^{2}}}{12}\] From theorem of parallel axis theorem \[\therefore \]  \[I={{I}_{CM}}+M{{x}^{2}}=\frac{M{{L}^{2}}}{12}+M{{\left( \frac{L}{6} \right)}^{2}}\]                                                 \[=\frac{M{{L}^{2}}}{9}\]