A steel wire and a copper wire, both possessing equal length and equal cross-sectional area, are joined end to end and the combination is subjected to a tension. Determine the ratio of the strain developed in the copper wire to the strain developed in the steel wire. Let Y of steel = 2 10¹¹ N/m ^2 and Y of copper = 1.3 10¹¹ N/m ^2 .

Step-by-step solution

Let F be the tension applied to the combination of the wires. Since the wires are joined end to end, the tension F is the same in both wires. The cross-sectional area A is also the same for both wires. Therefore, the stress = F A is equal for both the steel and copper wires. Young's modulus is given by Y = Stress Strain , which implies Strain = Stress Y . Let _c and _s be the strains developed in the copper and steel wires, respectively. _c = Y_c _s = Y_s Taking the ratio of the strain in copper to the strain in st