Show dimensionally that the expression , `T = (MgL)/(pi r^(2)l` is dimensionally correct , where T is Young 's modulus of the length of the wire ,Mg is the weight applied in the wire and L is the original length of the wire ,and l is the increase in the length of the wire .

Explanation

To show that the expression \( T = \frac{MgL}{\pi r^2 l} \) is dimensionally correct, we need to analyze the dimensions of both sides of the equation.

### Step 1: Identify the dimensions of Young's Modulus \( T \)

Young's modulus \( T \) is defined as the ratio of stress to strain.

- **Stress** is defined as force per unit area. The dimension of force is given by:
\[
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