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  4. If two rods of length L and 2L having coefficients of linear expansion α and 2α , respectively, are connected such that total length becomes 3L, the average coefficient of linear expansion of the composition rod equals

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Q. If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha $ and $2\alpha $ , respectively, are connected such that total length becomes $3L,$ the average coefficient of linear expansion of the composition rod equals

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
$\Delta l=\Delta l_{1}+\Delta l_{2}$
$\alpha _{e q}3L\Delta T=\alpha L\Delta T+2\alpha \times 2L\Delta T$
$3\alpha _{e q}=5\alpha $
$\Rightarrow \, \, \alpha _{e q}=\frac{5}{3}\alpha $