If two rods of length L and 2 L having coefficients of linear expansion α and 2α respectively are connected so that total length becomes 3 L, determine the average coefficient of linear expansion of the composite rod. Which of the following gives the correct final result?
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Question

If two rods of length L and 2 L having coefficients of linear expansion α and 2α respectively are connected so that total length becomes 3 L, determine the average coefficient of linear expansion of the composite rod. Which of the following gives the correct final result?

Options

G1 Physics · Accepted Answer

Use ΔL=αLΔT, ΔA≈2αAΔT and ΔV≈3αVΔT (or the given cubical coefficient γ). For constrained bodies include the elastic stress needed to cancel free expansion. Evaluating the given data/statements gives 5α/3. Therefore the correct answer is A.