Question

The load versus elongation graph for four wires of the same materials shown in the figure. The thinnest wire is represented by the line:

• A. OC
• B. OD
• C. OA
• D. OB

Answer 1

The correct option is C OA

Using $Y=\frac{F/A}{\Delta L/L}$

Cross-section area of the wire $A=\pi R^2$ where $R$ is the radius of the wire

$\therefore$ $Y=\frac{F}{\pi R^2}\times \frac{L}{\Delta L}$ $⟹$ $F=\frac{\pi R^{2}Y}{L}\Delta L$

Thus Slope of load vs elongation graph, $s=\frac{\pi R^{2}Y}{L}$

$⟹$ $s\propto R^2$

Now from the graph shown, OA has the least slope and hence the least radius.

Thus OA represents the thinnest wire.