The stress-strain graph of two wires A and B | vedclass

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(C) The Young's modulus $Y$ is defined as the ratio of stress to strain, which corresponds to the slope of the stress-strain graph.$Y = 	ext{slope} =

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$Y_{B}=3 Y_{A}$

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(C) The Young's modulus $Y$ is defined as the ratio of stress to strain, which corresponds to the slope of the stress-strain graph.$Y = 	ext{slope} = 	an(	heta)$, where $	heta$ is the angle the line makes with the strain axis.For wire $A$, the angle with the strain axis is $	heta_A = 30^{\circ}$.Therefore, $Y_A = 	an(30^{\circ}) = \frac{1}{\sqrt{3}}$.For wire $B$, the angle with the strain axis is $	heta_B = 30^{\circ} + 30^{\circ} = 60^{\circ}$.Therefore, $Y_B = 	an(60^{\circ}) = \sqrt{3}$.Now, calculating the ratio $\frac{Y_B}{Y_A} = \frac{\sqrt{3}}{1/\sqrt{3}} = 3$.Thus, $Y_B = 3 Y_A$.

The stress-strain graph of two wires $A$ and $B$ is shown in the figure. If $Y_{A}$ and $Y_B$ are Young's moduli of materials of wires $A$ and $B$ respectively, then

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