A thin rod of length L and mass M is bent at its midpoint into two… | NEET 2008 (AIPMT)

Q188NEET 2008 · AIPMTMedium

Moment of Inertia & Radius of Gyration

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°. 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

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Answer: (d)

Each half: mass $\frac{M}{2}$ , length $\frac{L}{2}$ , rotating about its end (the bend point).
Each half: $\frac{1}{3}\cdot\frac{M}{2}\cdot\frac{L^2}{4} = \frac{ML^2}{24}$ . The angle between halves does not matter.
$I = 2 \times \frac{ML^2}{24} = \frac{ML^2}{12}$
So the answer is (d) $\frac{ML^2}{12}$ .

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