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Two rods made of different materials are sandwiched between two rigid massive walls as shown. The cross-sectional area of both rods is A. Their Young's moduli are E1 and E2, their lengths are l1 and l2, and their coefficients of linear expansion are alpha1 and alpha2 respectively. When the system is heated through T degrees, which of the following statements is/are correct?

1. The thermal strain produced in both rods is equal
2. The thermal stress produced in both rods is equal
3. The compressive force exerted by one rod on the other is A*(alpha1*l1 + alpha2*l2)*T / (l1/E1 + l2/E2)
4. The compressive force exerted is A*(alpha1 + alpha2)*T / (1/E1 + 1/E2)

Correct answer: The compressive force exerted by one rod on the other is A*(alpha1*l1 + alpha2*l2)*T / (l1/E1 + l2/E2)

Solution

Since the walls are rigid, the free thermal expansion of both rods combined must be exactly offset by the compressive elastic deformation. Setting these equal gives the compressive force; stress differs between rods (since E1 and E2 differ) but strain also differs, only force is the same.

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