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. $I_0+ML^2/2$
• B. $I_0+ML^2/4$
• C. $I_0+2ML^2$
• D. $I_0+ML^2$

Answer 1

Answer: (B)

$I_0+ML^2/4$

Answer 2

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 $I=I_{CM}+Md^2$ 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, $I_{CM}=I_0, d=\frac{L}{2}$ $\therefore I=I_0+M\Bigg(\frac{L}{2}\Bigg)^2=I_0+\frac{ML^2}{4}$