Q.

Two rods of different materials having coefficients of linear expansion α1,α2 and Young's moduli Y1 and Y2, respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α1:α2=2:3, the thermal stresses developed in the two rods are equally provided, Y1:Y2 is equal to

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a

2:3

b

1:1

c

3:2

d

4:9

answer is C.

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Detailed Solution

Thermal stress =YαΔθIf thermal stress and rise in temperature are equal, then Y∝1α⇒Y1Y2=α2α1=32
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Two rods of different materials having coefficients of linear expansion α1,α2 and Young's moduli Y1 and Y2, respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α1:α2=2:3, the thermal stresses developed in the two rods are equally provided, Y1:Y2 is equal to