Question

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 Youngs modulus of the materials, then:

• A. $ {{Y}_{B}}=2{{Y}_{A}} $
• B. $ {{Y}_{A}}={{Y}_{B}} $
• C. $ {{Y}_{B}}=3{{Y}_{A}} $
• D. $ {{Y}_{A}}=3{{Y}_{B}} $
• E. $ {{Y}_{B}}=\frac{1}{3}{{Y}_{A}} $

Answer 1

Answer: (D)

$ Y=\frac{stress}{strain}= $ slope of the graph
$ =\tan \theta $
$ \therefore $ $ \frac{{{Y}_{A}}}{{{Y}_{B}}}=\frac{\tan 60{}^\circ }{\tan 30{}^\circ }=\frac{\sqrt{3}}{1/\sqrt{3}}=3 $
$ \Rightarrow $ $ {{Y}_{A}}=3{{Y}_{B}} $