Mechanical Properties of Solids

JEE Main level, single correct, medium

18 of 118

Question 18 of 118

The strain-stress plot for materials A,B,CA, B, C and DD is shown in the figure. Which material has the largest Young's modulus ?

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Answer: (C) CC

Young's modulus (YY) is defined as the ratio of stress to strain: Y=stressstrainY = \frac{\text{stress}}{\text{strain}}.
In the given graph, the y-axis represents strain and the x-axis represents stress.
The slope of the line in a strain-stress graph is given by m=strainstressm = \frac{\text{strain}}{\text{stress}}.
Therefore, Y=1slopeY = \frac{1}{\text{slope}}.
To have the largest Young's modulus, the material must have the smallest slope in the strain-stress plot.
From the figure, line CC has the smallest angle with the stress axis (x-axis), meaning it has the minimum slope.
Since Y∝1slopeY \propto \frac{1}{\text{slope}}, material CC has the largest Young's modulus.

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