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

Two ,netal rods are fixed end to end between two rigid supports as sho

1.	Two ,netal rods are fixed end to end between two rigid supports as shown in figure. Each rod is of length land area of cross -section is A. When the system is heated up, detennine the condition when the junction between rods does not shift ? (Given : Y_(1) and Y_(2) are Young's modulus of ,naterials of the rods, alpha_(1) and alpha_(2) are coefficientsof linear expansion )
Answer» SOLUTION :Since, each ROD is prevented from expansion so, they are under compression and mechanical strain The net strain in each rod. `epsilon_(1) = alpha_(1) 1 Delta T - (Fl)/(A Y_(1)) , epsilon_(2) = alpha_(2) l Delta T - (Fl)/(A Y_(2))` ` epsilon_(1) = epsilon_(2) = 0` `alpha_(1) 1 Delta T - (Fl)/(A Y_(1)) = 0 and alpha_(2) l Delta T - (Fl)/(A Y_(2))= 0 ` `alpha_(1) l Delta T - (Fl)/(A Y_(1)) = 0 and alpha_(1) 1 Delta T - (Fl)/(A Y_(2)) = 0 ` Solving , we GET `"" alpha_(1) Y_(1) = alpha_(2) Y_(2)`