Two Rods Of Different Materials Having Coefficients Of Thermal Expansion  and Young’s Modulii Y1, 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 The Rods. If  the Thermal Stresses Developed In The Two Rods Are Equal Provided Y1 : Y2 is Equal To:

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Question

Two rods of different materials having coefficients of thermal expansion  and Young’s modulii Y1Y2 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 the rods. If  the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to:

Solution

Correct option is

3 : 2

 

Let l be the original length of the rods. Let them be heated so that the increase in temperature is toC.

Increase in length = 

Where  is the coefficient of linear expansion of the rod

                    Strain = 

                     Stress = 

Stresses are equal for the two rods if

                   

or                     

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