Two rods of different materials having coefficients of linear expansion `alpha_(1)` and `alpha_(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

`"Stress"/"Strain"` and `/_\lpropl//A`
`:.` Strain `(/_\l)/lalpha/_\Timplies` Stress `=Yalpha/_\T`
For first rod, stress `=gamma_(1)alpha_(1)/_\T`. For the second rod, stress
`=gamma_(2)alpha_(2)/_\T`. Since stresses are equal. Therefore,
`gamma_(1)alpha_(1)/_\T`
`implies(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=3/2`