Question

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is $90^\circ$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

• A. $\frac{ML^2}{6}$
• B. $\frac{\sqrt{2}ML^2}{24}$
• C. $\frac{ML^2}{24}$
• D. $\frac{ML^2}{12}$

Answer 1

Answer: (D)

$\frac{ML^2}{12}$

Answer 2

Total mass = M, total length = L
Moment of inertia of OA about O = Moment of inertia of OB about O.
$\Rightarrow M.I.$ total $=2\times\Bigg(\frac{M}{2}\Bigg)\Bigg(\frac{M}{2}\Bigg)^2 \cdot \frac{1}{3}=\frac{ML^2}{12}$