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)

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
$I=I_{C M}+M d^{2}$
where $I_{C M}$ 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, $I_{C M}=I_{0}, d=\frac{L}{2}$
$\therefore I=I_{0}+M\left(\frac{L}{2}\right)^{2}=I_{0}+\frac{M L^{2}}{4}$