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 :

Two rods of different materials having coefficient of linear expansion

1.	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 :
Answer» `2/3` `1/1` `3/2` `4/9` SOLUTION :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).

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