Two rods, each of length L and cross-sectional area A, are joined end to end and fixed between two rigid supports. On heating, under what condition does the junction between the rods stay in place? (Y1, Y2 are Young's moduli and alpha1, alpha2 the linear expansion coefficients.)

alpha1/Y1 = alpha2/Y2
alpha1*Y1 = alpha2*Y2
alpha1/Y2 = alpha2/Y1
alpha1 = alpha2

Correct answer: alpha1*Y1 = alpha2*Y2

Solution

For zero junction shift each rod's elongation must cancel exactly: F = A*alpha1*Y1*dT = A*alpha2*Y2*dT, hence alpha1*Y1 = alpha2*Y2.

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