A unit scale is to be prepared whose length does not change with temperature and remains $20\ \text{cm}$, using a bimetallic strip made of brass and iron each of different length. The lengths of both components would change in such a way that the difference between their lengths remains constant. If the length of brass is $40\ \text{cm}$, the length of iron will be ______ cm. ($\alpha_{\text{iron}} = 1.2\times10^{-5}\ \text{K}^{-1}$ and $\alpha_{\text{brass}} = 1.8\times10^{-5}\ \text{K}^{-1}$)
Numerical value type. Enter your answer.
Answer: 60
The difference stays constant if both expand by the same amount: $L_b\alpha_b = L_i\alpha_i$.
$$L_i = \frac{40\times1.8\times10^{-5}}{1.2\times10^{-5}} = 60\ \text{cm}$$
(Check: $60 - 40 = 20\ \text{cm}$.)
Solution by Sreeraj P, M.Sc Physics