Two rods of different materials having coefficients of thermal expansion `alpha_1`, `alpha_2` and Young's modulii `Y_1`, `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 the rods. If `alpha_1:alpha_2=2:3`, the thermal stresses developed in the two rods are equal provided `Y_1:Y_2` is equal to

Options

A. (a) 2:3
B. (b) 1:1
C. (c) 3:2
D. (d) 4:9

Answer

C

Explanation

`Deltal=lalphaDeltaTimplies(Deltal)/(l)=alphaDeltaT`
Stress =Y x stain
`:.` `Stress=YalphaDeltaT`
For first rod stress `=Y_1alpha_1DeltaT`
For second rod stress `=Y_2alpha_2DeltaT`
Since, stresses are equal
`:.Y_1alpha_1DeltaT=Y_2alpha_2T`
or, `Y_1/Y_2=alpha_2/alpha_1=3/2`