A steel wire of corss sectional area `0.5mm^(2)` is held between two rigid clamps so that it is just taut at `20^(@)C`. Find the tension in the wire at `0^(@)C`. Given that Young's Modulus of steel is `Y_(st)=2.1xx10^(12)` dynes/`cm^(2)` and coefficient of linear expansion of steel is `alpha_(st)=1.1xx10^(-5).^(@)C^(-1)`

Explanation

To find the tension in the steel wire at \(0^\circ C\), we will use the relationship between Young's modulus, stress, strain, and the coefficients of linear expansion. Here’s a step-by-step solution:

### Step 1: Convert the area of cross-section
The area of cross-section is given as \(0.5 \, mm^2\). We need to convert this to \(cm^2\) because Young's modulus is given in dynes/cm².

\[ 0.5 \, mm^2 = 0.5 \times 10^{-2} \, cm^2 = 0.00005 \, cm^2 \]
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