question_answer

Inertia of a thin rod of mass M and length L about an axis making an angle\[90{}^\circ \]with its length is \[\frac{M{{L}^{2}}}{9}.\] The distance of this axis from the midpoint of rod will be

A)  \[\frac{L}{6}\]      

B)  \[\frac{L}{3}\]    

C)  \[\frac{L}{4}\]    

D)  \[\frac{L}{2}\]

Correct Answer: A

Solution :

 \[{{I}_{CM}}=\frac{M{{L}^{2}}}{12}\] where L = length of rod. According to theorem of parallel axis, moment of inertia about axis MM' \[\frac{M{{L}^{2}}}{9}=\frac{M{{L}^{2}}}{12}+M{{r}^{2}}\] \[r=\frac{L}{6}\]