Question

Figure 9.11 shows the strain-stress curve for a given material. What is Young's modulus.

Answer 1

Hello champ!!

Well Young's modulus is nothing but an elastic constant. It is used to determine the extent up-to which a given material can undergo the change in its length

Mathematically it is given as

$\textbf{Young's modulus}$ = $\frac{longtitudinal stress}{longitudinal strain}$

Where ,

Stress = $\frac{force}{area}$

Hence it has unit Nm^-2

Strain= $\frac{change in dimension}{original dimension}$ hence it is dimension less quantity

In graph the slope of the line is constant...

Let us consider two point (0,0) and (0.002,150) on the graph

Therefore the slope would be :-

= $\frac{y2-y1}{x2-x1}$

=150/0.002

= 75,000

Hence the young's modulus of given material is 75,000 Nm^-2