Question

A unit scale is to be prepared whose length does not change with temperature and remains $20cm$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40cm$ and length of iron will be ________$cm$.
$({\alpha }_{\text{iron }}=1.2\times 10^{-5}{K}^{-1}$ and ${\alpha }_{\text{brass }}=1.8\times 10^{-5}{K}^{-1})$.

Answer 1

Answer: 60

${\ell }_B\left(1+{\alpha }_B\Delta T\right)-{\ell }_i\left(1+{\alpha }_i\Delta T\right)={\ell }_B-{\ell }_i$
${\alpha }_B{\ell }_B={\ell }_i{\alpha }_i$
$1.8\times 10^{-5}\times 40={\ell }_i\times 1.2\times 10^{-5}$
${\ell }_i=\frac{1.8\times 10^{-5}\times 40}{1.2\times 10^{-5}}=\frac{3\times 40}{2}=60$
${\ell }_i=60cm$