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

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

Solution:

$\Delta L =\Delta L _{1}+\Delta L _{2}$
$\alpha_{\text{mix}}(3 L ) \Delta T = L \alpha \Delta T +2 L (2 \alpha) \Delta T$
$\alpha_{\text{ mix }}=\frac{5}{3} \alpha$