Two rods of different materials having coefficients of linear expansion \[{{\alpha }_{1}},\,{{\alpha }_{2}}\] 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 \[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\], the thermal stresses developed in the two rods are equally provided \[{{Y}_{1}}:{{Y}_{2}}\] is equal to [IIT 1989]

Two rods of different materials having coefficients of linear expansio

1.	Two rods of different materials having coefficients of linear expansion \[{{\alpha }_{1}},\,{{\alpha }_{2}}\] 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 \[{{\alpha }_{1}}:{{\alpha }_{2}}=2:3\], the thermal stresses developed in the two rods are equally provided \[{{Y}_{1}}:{{Y}_{2}}\] is equal to [IIT 1989]
A.	2 : 3
B.	1 : 1
C.	3 : 2
D.	4 : 9
Answer» D. 4 : 9