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Two rods of different materials having coefficients of thermal expansion α1 and α2 and Young's modulii Y1 and Y2 are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided 
 


  1. Y1Y2=α1α2

  2. Y1Y2=α2α1

  3. Y1Y2=α1α2

  4. Y1Y2=α2α1


Solution

The correct option is D

Y1Y2=α2α1


If a rod of length L and coefficient fo thermal expansion α is heated to a temperature t, the increase in the length is given by l=αLt
Strain =lL=αt
and stress =Y×strain=Yαt
Since the value of t is the same for the two rods, the stresses in them will be equal if Y1α1t=Y2α2t, i.e., Y1Y2=α2α1
Hence, the correct choice is (d).
 

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