A steel wire of cross-sectional area `0.5mm^2` is held between two fixed supports. If the wire is just taut at `20^@C`, determine the tension when the temperature falls to `0^@C`. Coefficient of linear expansion of steel is `1.2 xx 10^(-5)C^(-1)` and its Young's modulus is `2.0 xx 10^11 N m^(-2).`

Explanation

To solve the problem, we need to determine the tension in a steel wire when the temperature drops from \(20^\circ C\) to \(0^\circ C\). Here’s a step-by-step solution:

### Step 1: Identify the parameters given in the problem
- Cross-sectional area of the wire, \(A = 0.5 \, \text{mm}^2 = 0.5 \times 10^{-6} \, \text{m}^2\)
- Coefficient of linear expansion of steel, \(\alpha = 1.2 \times 10^{-5} \, \text{C}^{-1}\)
- Young's modulus of steel, \(E = 2.0 \times 10^{11} \, \text{N/m}^2\)
- Initial temperature, \(T_1 = 20^\circ C\)
- Final temperature, \(T_2 = 0^\circ C\)
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