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. $\frac{M{L}^2}{9}$
• C. $\frac{M{L}^2}{12}$
• D. $\frac{M{L}^2}{3}$

Answer 1

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

$\begin{array}{c}\text{know -}\\ \text{moment of Inertia of a rod about an axis}\\ \text{passing through its centre-}\\ I=\frac{M{L}^2}{12}\end{array}$

$\begin{array}{c}\text{Therefore moment of Inertia about the given}ax\text{is}\\ \text{by parallel axis theorem-}\\ I^{\prime }=I+M{d}^2=\frac{M{L}^2}{12}+M{\left(\frac{L}{6}\right)}^2\\ I^{\prime }=\frac{M{L}^2}{9}\end{array}$