Question

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its midpoint and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :

• A. $I_0+M{L}^2/2$
• B. $I_0+M{L}^2/4$
• C. $I_0+2M{L}^2$
• D. $I_0+M{L}^2$

Answer 1

The correct option is B $I_0+M{L}^2/4$

Here, we apply theorem of parallel axis

$I_0$ moment of inertia of Red length $L$ about its axis

$I_B$ moment of inertia of Rod at its end

$\begin{array}{c}{I}_B=I_0+M{\left(\frac{L}{2}\right)}^2\\ I_B=I_0+\frac{M{L}^2}{4}\end{array}$