Question

The stress-strain graphs for materials A and B are shown in Figure.

The graphs are drawn to the same scale. 

1. Which of the materials has the greater Young’s modulus? 

2. Which of the two is the stronger material?

Answer 1

(a) Young’s modulus is given by the equation,

Y = stress strain

At a particular strain, Young’s modulus is directly proportional to the stress.

The stress strain curve for material A has greater stress at particular strain. Therefore, the material A has greater Young’s modulus than the material B.

(b) The strength of the material depends upon the stress at the fracture point or the rupture point. The fracture strength of material A is more than that of B. Hence, material A is stronger.

Answer 2

1. Material A has greater Young’s modulus as the slope of the graph of material A is greater than material B. 

Young’s Modulus = Y = Slope = \(\frac {stress}{strain}\)

∴ Material A has greater Young’s Modulus. 

2. From the graph it can be approximated that the stress at the fracture point for material A is higher than material B, thus material A is stronger.