Two rods of different materials having coefficient 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 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. `2 : 3`
B. `1 : 1`
C. `3 : 2`
D. `4 : 9`

Answer

C

Explanation

Stress developed `=Yxx` strain
`=Y(Deltal)/(l_(0))=(Y(l_(0)alphaDeltaT))/(l_(0))=YalphaDeltaT`
So , `Y_(1)alpha_(1)DeltaT=Y_(2)alpha_(2)DeltaT`
So , `(Y_(1))/(Y_(2))=(3)/(2)`