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Question

A uniform thin rod of length L and mass M is bent at the middle point O as shown in figure. Consider an axis passing through its middle point O and perpendicular to the plane of the bent rod. Then moment of inertia about this axis is :


A
23mL2
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B
13mL2
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C
112mL2
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D
dependent on θ
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Solution

The correct option is C 112mL2


Moment of inertia of rod about O is sum of moment of inertia of both halfs.

I0=I1+I2
using moment of inertia of rod about corner, we get
I0=(m/2)(L2)23+(m/2)(L2)23=mL212

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