The general definition of elastic modulus is

Analyze the question: You are asked for the general definition of elastic modulus, which is a measure of how stiff a material is.

Concept: Within the elastic limit, Hooke's law says that stress is directly proportional to strain. The constant of proportionality is the elastic modulus:

• Stress = force per unit area (F/A), measured in N/m² (Pa)
• Strain = change in dimension divided by original dimension (e.g. e/L), which has no unit

Solution:

Stress ∝ Strain

Stress = (constant) × Strain

Elastic modulus = Stress / Strain

Checking the options:

• A. stress/strain is correct. This is the general definition.
• B. strain/stress is the inverse, which is called compliance, not the modulus.
• C. stress × strain has no meaning as a modulus.
• D. √(stress/strain) is not a standard definition.

Examples of this definition:

• Young's modulus: E = (F/A)/(e/L) = FL/(Ae)
• Bulk modulus: stress is pressure change, strain is volume change divided by original volume
• Shear (rigidity) modulus: shear stress divided by shear strain

Exam tip: Remember "modulus = stress over strain." The unit of the modulus is the same as the unit of stress (N/m² or Pa), because strain has no unit. If an option has a different unit, it cannot be a modulus.