Question 11: Properties of Matter

Question

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

Accepted Answer

Young's Modulus (Y) is defined as the ratio of Stress $(\sigma)$ to Strain $(\varepsilon)$ within the elastic limit :
$$ Y=\frac{	ext { Stress }}{	ext { Strain }} $$
For the given graph,
1. Y -axis: $\operatorname{Strain}(\varepsilon)$
2. X -axis: Stress $(\sigma)$
Since Strain is on the Y -axis and Stress is on the X -axis, the slope of the line is given by :
$$ 	ext { Slope }=\frac{\Delta \mathrm{Y}}{\Delta \mathrm{X}}=\frac{	ext { Strain }}{	ext { Stress }} $$
$$ 	ext { Slope }=\frac{1}{\mathrm{Y}} $$
It shows that the slope is inversely proportional to Young's Modulus, i.e., higher slope corresponds to smaller Young's Modulus (material is more elastic) whereas lower slope shows larger Young's Modulus (material is less elastic).
So, the material with the largest Young's modulus will be the line with the smallest slope.
1. Material A has the highest slope Ã¢ÂÂ smallest Y.
2. Material C has the lowest slope Ã¢ÂÂ largest Y.
Therefore, material C has the largest Young's modulus. Hence, the correct option is (D).

Answer

$B$

Answer

$A$

Answer

$D$

Answer

$C$

Properties of Matter

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

Choose the correct answer: