A steel rod of length 50 cm has a cross–sectional area of `0.4 cm^(2) `. What force would be required to stretch this rod by the same amount as the expansion produced by heating it through `10^(@)C` .
(`alpha = 10^(-5) k^(-1)` and `Y = 2 xx 10^(11) N//m^(2))`

Explanation

To solve the problem, we need to find the force required to stretch a steel rod by the same amount as the expansion produced by heating it through \(10^\circ C\). We will use the concepts of thermal expansion and Young's modulus.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Length of the rod, \(L = 50 \, \text{cm} = 0.5 \, \text{m}\)
- Cross-sectional area, \(A = 0.4 \, \text{cm}^2 = 0.4 \times 10^{-4} \, \text{m}^2 = 4 \times 10^{-5} \, \text{m}^2\)
- Coefficient of linear expansion, \(\alpha = 10^{-5} \, \text{K}^{-1}\)
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