The load versus elongation graph for four wires is shown. The thinnest wire is

Using \(\quad \mathrm{Y}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}\) Cross-section area of the wire \(\quad \mathrm{A}=\pi \mathrm{R}^{2}\) where \(\quad \mathrm{R}\) is the radius of the wire \(\therefore \quad \mathrm{Y}=\frac{\mathrm{F}}{\pi \mathrm{R}^{2}} \times \frac{\mathrm{L}}{\Delta \mathrm{L}}\) \(\Longrightarrow \mathrm{F}=\frac{\pi \mathrm{R}^{2} \mathrm{Y}}{\mathrm{L}} \Delta \mathrm{L}\) Thus Slope of load vs elongation graph, \(\mathrm{s}=\frac{\pi \mathrm{R}^{2} \mathrm{Y}}{\mathrm{L}}\) \(\Longrightarrow \quad \mathrm{s} \propto \mathrm{R}^{2}\) Now from the graph shown, OA has the least slope and hence the least radius. Thus \(\mathrm{OA}\) represents the thinnest wire.