Two wires 1 and 2 made of the same material have their Load ( F ) on the y-axis versus Elongation ( L ) on the x-axis graphs plotted as straight lines. Wire 1 has length L and radius 2r . Wire 2 has length 2L and radius r . The ratio of the slope of the graph for wire 1 to the slope of the graph for wire 2 is _____.

Step-by-step solution

The slope of a Load ( F ) versus Elongation ( L ) graph represents the stiffness of the wire. From Hooke's law, F = YA L L , so the slope is k = YA L = Y r^2 L . For wire 1, the length is L and radius is 2r : k₁ = Y (2r)^2 L = 4 Y r^2 L For wire 2, the length is 2L and radius is r : k₂ = Y r^2 2L The ratio of their slopes is: k₁ k₂ = 4 Y r^2 / L Y r^2 / 2L = 4 2 = 8 Answer: 8