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Four wires made of the same material but with different cross-sectional areas are each tested under load. A load-versus-strain graph is plotted for all four wires on the same axes, giving four straight lines through the origin labelled OA, OB, OC, and OD in order of decreasing slope (OB is steepest, OD is least steep). Which line represents the thickest wire?
- OB
- OA
- OD
- OC
Correct answer: OB
Solution
Young's modulus Y = (Load / A) / strain, so Load = Y * A * strain. On a Load vs Strain graph, all lines through the origin have slope = Y * A. Since Y is the same for all wires (same material), the slope is directly proportional to the cross-sectional area A. The thickest wire has the largest A and thus the steepest slope. OB is the steepest line, so OB represents the thickest wire.
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