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Two rods of different materials are rigidly clamped at both ends. On heating them through the same temperature rise, equal thermal stresses develop in both. If their Young's moduli are in the ratio x: y, what is the ratio of their coefficients of linear expansion?

1. x: y
2. y: x
3. x²: y²
4. y²: x²

Correct answer: y: x

Solution

Since stress = Y*alpha*dT is equal and dT is common, Y1*alpha1 = Y2*alpha2, so alpha1: alpha2 = Y2: Y1 = y: x.

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