Two rods of different materials, having coefficients of linear expansion `a_(1) anda_(2)` and Young’s moduli, `Y_(1) and Y_(2)` , 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 `alpha_(1)//alpha_(2)=2//3`, then the thermal stresses developed in the two rods are equal, provided `Y_(1)//Y_(2)` is equal to :

Options

A. `2 : 3`
B. `1 : 1`
C. `3 : 2`
D. `4 : 9`

Answer

C

Explanation

Thermal stress `sigma=YalphaDeltatheta`
But `sigma_(1) =sigma_(2)rArrY_(1)alpha_(1)Deltatheta=Y_(2)alpha_(2)DeltathetarArr(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=(3)/(2)`