A wire 2 mm in diameter is just stretched in between two fixed points at a temperature of `50^(@)C`. Calculate the tension in the wire, when the temperature falls to `30^(@)C`. Coefficient of linear expansion is `11 xx 10^(-4) l^(@)C` and Young modulus is `2.1 xx 10^(11) N m^(2)`

Explanation

To solve the problem of calculating the tension in a wire when the temperature falls, we can follow these steps:

### Step 1: Understand the Given Data
- Diameter of the wire, \( d = 2 \, \text{mm} = 2 \times 10^{-3} \, \text{m} \)
- Radius of the wire, \( r = \frac{d}{2} = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Initial temperature, \( T_1 = 50^\circ C \)
- Final temperature, \( T_2 = 30^\circ C \)
- Coefficient of linear expansion, \( \alpha = 11 \times 10^{-4} \, \text{°C}^{-1} \)
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