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 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
Updated On: May 25, 2022
- $\frac{ML^2}{6}$
- $\frac{\sqrt{2}ML^2}{24}$
- $\frac{ML^2}{24}$
- $\frac{ML^2}{12}$
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The Correct Option is D
Solution and Explanation
Total mass = M, total length = L
Moment of inertia of OA about O = Moment of inertia of OB about O.
$\Rightarrow M.I.$ total $=2\times\Bigg(\frac{M}{2}\Bigg)\Bigg(\frac{M}{2}\Bigg)^2 \cdot \frac{1}{3}=\frac{ML^2}{12}$
Moment of inertia of OA about O = Moment of inertia of OB about O.
$\Rightarrow M.I.$ total $=2\times\Bigg(\frac{M}{2}\Bigg)\Bigg(\frac{M}{2}\Bigg)^2 \cdot \frac{1}{3}=\frac{ML^2}{12}$
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