Two rods of different materials having coefficient of linear expansion `alpha_(1)` and `alpha_(2)` and Young's modulus `Y_(1)` and `Y_(2)` respectively are fixed between two rigid walls. The rods are heated to same high temperature. If `alpha_(1): alpha_(2)` :: 2 : 3 the thermal stress in two rods is the same. Then the rate `Y_(1)//Y_(2)` is :

Options

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

Answer

C

Explanation

Here stress is same for the two
Now stress = Y `xx` strain
`thereforeY_(1)xxalpha_(1)xxt_(1)=Y_(2)xxalpha_(2)xxt_(2)`
But `t_(1)=t_(2)`
`thereforeY_(1)alpha_(1)=Y_(2)alpha_(2)` or `(Y_(1))/(Y_(2))=(alpha_(2))/(alpha_(2))=3/2`
Correct choice is (c).