Show that moment of inertia of a solid body of any shape changes with temperature as `I=I_0(1+2 alphatheta).` Where `I_0` is the moment of inertia at `0^@C ` and `alpha ` is the coefficient of linear expansion of the solid.

Explanation

To show that the 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 \( 0^\circ C \) and \( \alpha \) is the coefficient of linear expansion of the solid, we can follow these steps:

### Step 1: Define the Moment of Inertia at \( 0^\circ C \)
The moment of inertia \( I_0 \) at \( 0^\circ C \) is defined as:
\[ I_0 = \sum m_i r_i^2 \]
where \( m_i \) is the mass of the \( i^{th} \) particle and \( r_i \) is its distance from the axis of rotation.
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