Two metal rods are fixed end to end between two rigid supports as shown in figure. Each rod is of length l and area of cross - section is A. When the system is heated up, determine the condition when the junction between rods does not shift ? (Given : Y_(1) and Y_(2) are Young.s modulus of materials of the rods, alpha_(1) and alpha_(2) are coeffi-cients of linear expansion)

Two metal rods are fixed end to end between two rigid supports as show

1.	Two metal rods are fixed end to end between two rigid supports as shown in figure. Each rod is of length l and area of cross - section is A. When the system is heated up, determine the condition when the junction between rods does not shift ? (Given : Y_(1) and Y_(2) are Young.s modulus of materials of the rods, alpha_(1) and alpha_(2) are coeffi-cients of linear expansion)
Answer» Solution :Since, each rodis PREVENTED from EXPANSION so, they are under compression and mechanical strain. The net strain in each rod. `epsilon_(1)=alpha_(1)lDeltaT-(Fl)/(AY_(1)), epsilon_(2)=alpha_(2)lDeltaT-(Fl)/(AY_(2)) rArr epsilon_(1)=epsilon_(2)=0` `alpha_(1)l DeltaT-(Fl)/(AY_(1))=0 and alpha_(2)lDeltaT-(Fl)/(AY_(2))=0, alpha_(1)lDeltaT-(Fl)/(AY_(1))=0 and alpha_(2)lDeltaT-(Fl)/(AY_(2))=0` Solving, we get`alpha_(1)Y_(1)=alpha_(2)Y_(2)`