A steel wire of length 1m and diameter 0.8 mm is kept stretched between two rigid supports. What additional stretching force the wire will experience when its temperature falls by 30K? Linear expansivity of steel `alpha = 12 xx 10^(-6) //k` . Young's modulus of steel `Y = 20 xx 10^(10) N //m^(2)`.

Explanation

To solve the problem, we need to find the additional stretching force that a steel wire experiences when its temperature decreases by 30 K. We will use the formula that relates Young's modulus, linear expansivity, change in temperature, and the area of cross-section of the wire.

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the wire, \( L = 1 \, \text{m} \)
- Diameter of the wire, \( d = 0.8 \, \text{mm} = 0.8 \times 10^{-3} \, \text{m} \)
- Linear expansivity of steel, \( \alpha = 12 \times 10^{-6} \, \text{K}^{-1} \)
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