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Two rods of lengths L and 2L have linear expansion coefficients alpha and 2alpha respectively. They are joined end to end to form a composite rod of length 3L. Find the effective (average) coefficient of linear expansion of the composite rod.

1. alpha
2. 3 alpha / 2
3. 5 alpha / 3
4. 2 alpha

Correct answer: 5 alpha / 3

Solution

Equating total expansion, alpha_eff = (L*alpha + 2L*2alpha)/(3L) = 5alpha/3.

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