We would like to perpare a scale whose length does not change with temperature. It is proposed to prepare a unit scale f this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length (both components) would change in such a way that differnece between theri lenght rermain constant. If `alpha_(iron) = 1.2 xx 10^(-5)//K and alpha_(brass) = 1.8 xx 10^(-5)//K,` what should we take as lenght of each strip ?

Explanation

To solve the problem of preparing a scale whose length remains constant with temperature using a bimetallic strip made of brass and iron, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the lengths of two strips (one of brass and one of iron) such that the difference in their lengths remains constant at 10 cm, regardless of temperature changes. The coefficients of linear expansion are given as:
- \( \alpha_{\text{iron}} = 1.2 \times 10^{-5} \, \text{K}^{-1} \)
- \( \alpha_{\text{brass}} = 1.8 \times 10^{-5} \, \text{K}^{-1} \)

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