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Two metal rods A and B have lengths $L_{1} and L_{2}$ and same radius. The coefficients of linear expansions of the materials of A and B are $α_{1}$ and $α_{2}$ respectively. If the two rods are joined to form a longer rod of length $L_{1} + L_{2}$ , the equivalent coefficient of linear expansion of the composite rod will be

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$\frac{L_{1} α_{1} + L_{2} α_{2}}{L_{1} + L_{2}}$

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

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

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

answer is A.

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