Two wires, A and B, are made of the identical material. Wire A has a length L and radius r , while wire B has a length 2L and radius r 2 . If the stress-strain curves for both wires are plotted on the same axes, what is the ratio of the slopes of the curves for wire A to wire B in the elastic region?

Step-by-step solution

The slope of a stress-strain curve in the elastic region represents the Young's modulus ( Y ) of the material. Young's modulus is an intrinsic property of the material and is independent of the geometric dimensions (length and radius) of the wire. Since both wires A and B are made of the identical material, their Young's modulus is exactly the same, i.e., Y_A = Y_B . Therefore, the ratio of the slopes of their stress-strain curves is 1:1 . Answer: 1:1