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  • A unit scale is to be prepared whose length does not change with temperature and remains , using a bimetallic strip made o

A unit scale is to be prepared whose length does not change with temperature and remains 20 \mathrm{~cm}, 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 40 \mathrm{~cm} and length of iron will be ____________\mathrm{cm.}\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right.$ and $\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} \mathrm{~K}^{-1}\right).

Option: 1

60


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Let,

    \mathrm{l =l_{\text {Brass }}-l_{\text {Iron }} }

\mathrm{\Delta l =\Delta l_{\text {Brass }}-\Delta l_{I r o n} }

\mathrm{0 =l_B\: \alpha_B \: \Delta T-\: l_I\: \alpha_{I} \: \Delta T }

\mathrm{l_B \: \dot{\alpha}_B . = l_I \alpha_I }

\mathrm{40 \times 1.8 =l_I \times 1.2 }

\mathrm{l_I =60 \mathrm{~cm}}

The length of iron will be \mathrm{60 \mathrm{~cm}}






\end{aligned}

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