find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion `alpha`) about its perpendicular bisector when its temperature is slightly increased by `Delta T.`

Explanation

To find the increase in the moment of inertia \( I \) of a uniform rod about its perpendicular bisector when its temperature is slightly increased by \( \Delta T \), we can follow these steps:

### Step 1: Define the initial moment of inertia
The moment of inertia \( I \) of a uniform rod of length \( L \) about its perpendicular bisector is given by the formula:
\[ I = \frac{1}{12} M L^2 \]
where \( M \) is the mass of the rod.
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