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: (2008)
Solution:
Treat the bent rod as two rods of length $L/2$ and mass $M/2$ connected at the origin. Using the moment of inertia formula for a rod about its end $I = \frac{m l^2}{3}$, total $I = 2 \times \frac{(M/2)(L/2)^2}{3} = \frac{ML^2}{12}$.
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