Two rods of different materials having coefficient of thermal expansion `alpha_(1) and alpha_(2)` and Young's modulues `Y_(1) and Y_(2)` respectively are fixed betwee two rigid massive walls. The rods are heated such that these undergo same increase in temperature. there is no bending of the rods. if `alpha_(1):alpha_(2)=2:3`, the thermal stress developed in the two rods are equal, provided `Y_(1):Y_(2)` is

Options

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

Answer

D

Explanation

From the formula for thermal stress
`((F)/(A))_(1) = alpha_(1) Y_(1) Delta T` …(i)
`((F)/(A))_(2) = alpha_(2) Y_(2) Delta T` …(ii)
(since, temperature `Delta T` is same)
Dividing (i) by (ii) we get
`((F//A)_(1))/((F//A)_(2)) = (alpha_(1) Y_(1))/(alpha_(2) Y_(2))`
For thermal stress to be equal, `alpha_(1) Y_(1) = alpha_(2) Y_(2)`
or `(Y_(1))/(Y_(2)) = (alpha_(2))/(alpha_(1)) = (3)/(2) ( "As " (alpha_(1))/(alpha_(2)) = (2)/(3))`