Question

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. $\frac{M{L}^2}{6}$
• C. $\frac{M{L}^2}{9}$
• D. $\frac{M{L}^2}{3}$

Answer 1

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

The MI of rod about axis passing through its center is $M{L}^2/12$.

The distance of new axis from center is $L/2-L/3=L/6$

Using parallel axis theorem, the MI about this axis is $M{L}^2/12+M(L/6{)}^2=M{L}^2/12+M{L}^2/36=M{L}^2/9$