Heat and Thermal ExpansionHard

Question

Two metal rods of the same length and area of cross - section are fixed  ends to end between rigid supports. The materials of the rods have Young moduli Y1 and Y2, and coefficients of linear  expansion α1 and α2 . When rods are cooled the junction between the rods does not shift if :-

Options

A.Y1α1 = Y2α2
B.Y1α2 = Y2α1
C.Y1α12 = Y2α22
D.Y21α1 = Y21α2

Solution

ᐃL = ᐃ Lthermal - ᐃLcontact force = 0 ⇒α1Lθ = (rod - 1)

α2Lθ = (rod - 2) ⇒ Y1α1 = Y2α2

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