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A composite bar of length $L = L_{1} + L_{2}$ is made up from a rod of material 1and of length $L_{1}$ attached to a rod of material 2 and of length $L_{2}$ as shown. If $α_{1} a n d α_{2}$ are their respective coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is

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$\frac{α_{1} L_{2} + α_{2} L_{2}}{L}$

$\frac{α_{1} α_{2} (L_{1}^{2} + L_{2})}{α_{1} L_{1} + α_{2} L_{2}}$

$\frac{α_{1} L_{2} + α_{2} L_{1}}{L}$

$\frac{α_{1} L_{1} + α_{2} L_{2}}{L}$

answer is C.

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Detailed Solution

$α_{e f f} = \frac{α_{1} L_{1} + α_{2} L_{2}}{L_{1} + L_{2}}$

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