A brass wire `1.8 m` long at `27^(@)C` is held taut with little tension between two rigid supports. If the wire cooled to a temperature of `-39^(@)C`, what is the tension developed in the wire, if its diameter is `2.0 mm`? Coefficient of linear expansion of brass `= 2.0 xx 10^(-5)//^(@)C`, Young's modulus of brass `= 0.91 xx 10^(11) Pa`.

Explanation

To solve the problem of finding the tension developed in a brass wire when it is cooled from 27°C to -39°C, we can follow these steps:

### Step 1: Identify the given data
- Length of the wire, \( L = 1.8 \, \text{m} \)
- Initial temperature, \( T_1 = 27 \, \text{°C} \)
- Final temperature, \( T_2 = -39 \, \text{°C} \)
- Diameter of the wire, \( d = 2.0 \, \text{mm} = 2.0 \times 10^{-3} \, \text{m} \)
- Coefficient of linear expansion of brass, \( \alpha = 2.0 \times 10^{-5} \, \text{°C}^{-1} \)
...