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 modulus of the materials, then
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$\frac{{{Y_A}}}{{{Y_B}}} = \frac{{\tan \,{\theta _A}}}{{\tan \,{\theta _B}}} = \frac{{\tan \,{{30}^o}}}{{\tan \,{{60}^o}}} = \frac{{1/\sqrt 3 }}{{\sqrt 3 }} = \frac{1}{3} \Rightarrow {Y_B} = 3{Y_A}$
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