Question

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. $\frac{M{L}^2}{48}$

Answer 1

The correct option is B $\frac{M{L}^2}{9}$

A point at a distance of $L/3$ from one of the ends is at a distance of $\frac{L}{2}-\frac{L}{3}=\frac{L}{6}$ from the center of the rod.

Moment of inertia of uniform rod about and axis passing through the center and perpendicular to it=$=I_{CM}=\frac{M{L}^2}{12}$
Using the parallel axis theorem, $I_d=I_{CM}+M{d}^2$

$=\frac{M{L}^2}{12}+M(\frac{L}{6}{)}^2=\frac{M{L}^2}{9}$