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

Answer

C

Explanation

Thermal stress `=Yalphat`
In the given problem
`Yalpha=` constant
`(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(1))=3/2`