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

`Y=(F*L)/(A*l)` and
`Y prop (L)/(l), (Y_(1))/(Y_(2)) =(l_(2))/(l_(1)) = (alpha_(2)l DeltaT)/(alpha_(1)l DeltaT) = (alpha_(2))/(alpha_(1))=(3)/(2)`