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Q.

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be (α1, α2 = linear expansion coefficientA1, A2 = Area of rodsY1, Y2 = Young modulus)

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a

A1A2 = α1Y1α2Y2

b

A1A2 = L1α1Y1L2α2Y2

c

A1A2 = L2α2Y2L1α1Y1

d

A1A2 = α2Y2α1Y1

answer is D.

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Detailed Solution

Y = StressStrain = TA∆llT = Y.∆llA =Y . Aα∆TIn both the rods tension will be same soT1 = T2, Hence Y1A1α1∆T = Y2A2α2∆TA1A2 = Y2α2Y1α1

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Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be (α1, α2 = linear expansion coefficientA1, A2 = Area of rodsY1, Y2 = Young modulus)