Question

The following figure shows stress-strain graphs of two metals A and B. From the graphs it can be concluded that

• A. A has greater Young's modulus and more ductility than B
• B. B has greater Young's modulus and more ductility than A
• C. A has greater Young's modulus and less ductility than B
• D. B has greater Young's modulus and less ductility than A

Answer 1

Answer: (C)

A has greater Young's modulus and less ductility than B

Answer 2

Young's modulus ($Y$) is a measure of a material's stiffness and is represented by the slope of the stress-strain curve in the elastic region. Mathematically, $Y = \frac{\text{Stress}}{\text{Strain}}$. In the given graph, stress is plotted on the vertical axis and strain on the horizontal axis. The slope of the linear portion of the curve for metal A is steeper than that for metal B. Therefore, metal A has a greater Young's modulus than metal B ($Y_A > Y_B$).

Ductility is the ability of a material to deform plastically under tensile stress without fracturing. This is indicated by the extent of strain in the plastic region of the stress-strain curve. Metal A's curve is a straight line, suggesting it breaks with little or no plastic deformation, making it less ductile. Metal B's curve shows a significant extension in the plastic region (the curved part after the linear elastic region) before reaching its fracture point. Thus, metal B is more ductile than metal A.

Combining these observations, metal A has a greater Young's modulus and less ductility than metal B.