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

Answer: (B)

According to the theorem of parallel axes, the moment of inertia of the thin rod of mass $M$ and length $L$ about an axis passing through one of the ends is
$I=I_{CM}+M{d}^2$
where $I_{CM}$ is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and $d$ is the distance between two parallel axes.
Here, $I_{CM}=I_0,d=\frac{L}{2}$
$\therefore I=I_0+M{\left(\frac{L}{2}\right)}^2=I_0+\frac{M{L}^2}{4}$