The stress versus strain graphs for wires of | vedclass

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(D) 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 = \frac{	ext{Str

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${Y_A} = 3{Y_B}$

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(D) The Young's modulus $Y$ is defined as the ratio of stress to strain,which corresponds to the slope of the stress-strain graph.$Y = \frac{	ext{Stress}}{	ext{Strain}} = 	an 	heta$For material $A$,the angle with the strain axis is $	heta_A = 60^\circ$. Thus,$Y_A = 	an 60^\circ = \sqrt{3}$.For material $B$,the angle with the strain axis is $	heta_B = 30^\circ$. Thus,$Y_B = 	an 30^\circ = \frac{1}{\sqrt{3}}$.Taking the ratio of the Young's moduli:$\frac{Y_A}{Y_B} = \frac{	an 60^\circ}{	an 30^\circ} = \frac{\sqrt{3}}{1/\sqrt{3}} = 3$Therefore,$Y_A = 3Y_B$.

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young's moduli of the materials,then

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