question_answer

The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end, is

A)  \[\frac{M{{L}^{2}}}{3}\]

B)  \[\frac{M{{L}^{2}}}{12}\]

C)  \[\frac{M{{L}^{2}}}{2}\]

D)  \[\frac{M{{L}^{2}}}{13}\]

Correct Answer: A

Solution :

 From theorem of parallel axis \[{{I}_{A}}={{I}_{C}}+M{{\left( \frac{L}{2} \right)}^{2}}\] \[=\frac{M{{L}^{2}}}{12}+\frac{M{{L}^{2}}}{4}\] \[{{I}_{A}}=\frac{M{{L}^{2}}}{3}\]