Young's Modulus is defined as which of the following?

Young's Modulus is defined as which of the following?

• A. The measure of resistance to elastic deformation
• B. The energy stored per unit volume
• C. The ratio of stress to strain, or the gradient of the stress-strain graph
• D. The total elongation per unit length

Answer: (C)

Young's Modulus is the stiffness of a material in the elastic region, defined as the ratio of stress to strain: E = σ/ε. In a tensile test, stress is F/A and strain is ΔL/L0, so E = (F/A) / (ΔL/L0) = (F L0) / (A ΔL). This ratio is the slope of the linear portion of the stress–strain curve, meaning it tells you how much stress is needed to produce a given amount of strain. Its units are Pascals. A high modulus means the material is stiff and resists deformation, while a low modulus means it deforms more under the same load. The energy stored per unit volume is strain energy density (not the modulus), and the total elongation per unit length is the strain itself, not the ratio of stress to strain. So the defining characteristic is the ratio of stress to strain, i.e., the gradient of the linear part of the stress–strain graph.

Young's Modulus is the stiffness of a material in the elastic region, defined as the ratio of stress to strain: E = σ/ε. In a tensile test, stress is F/A and strain is ΔL/L0, so E = (F/A) / (ΔL/L0) = (F L0) / (A ΔL). This ratio is the slope of the linear portion of the stress–strain curve, meaning it tells you how much stress is needed to produce a given amount of strain. Its units are Pascals. A high modulus means the material is stiff and resists deformation, while a low modulus means it deforms more under the same load. The energy stored per unit volume is strain energy density (not the modulus), and the total elongation per unit length is the strain itself, not the ratio of stress to strain. So the defining characteristic is the ratio of stress to strain, i.e., the gradient of the linear part of the stress–strain graph.