Show that moment of inertia of a solid body

Question:

Show that moment of inertia of a solid body of any shape changes with temperature as $I=I_{0}(1+2 \alpha \theta)$ where $I_{0}$ is the moment of inertia at $0^{\circ} \mathrm{C}$ and $\alpha$ is the coefficient of linear expansion of the solid.

Solution:

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