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An aluminium rod of length l1 (linear expansion coefficient alphaₐ) and a steel rod of length l2 (coefficient alphaₛ) are joined end to end. For a given temperature change, both rods expand by the same amount. Find the value of l1/(l1 + l2).

1. alphaₛ/(alphaₐ + alphaₛ)
2. alphaₛ/(alphaₐ - alphaₛ)
3. (alphaₐ + alphaₛ)/alphaₛ
4. None of these

Correct answer: alphaₛ/(alphaₐ + alphaₛ)

Solution

Equal expansions give l1*alphaₐ = l2*alphaₛ, leading to l1/(l1+l2) = alphaₛ/(alphaₐ + alphaₛ).

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