Unit check: since Young’s modulus E is defined as stress divided by strain (and strain is dimensionless), is the unit of E the same as the unit of stress?

Introduction / Context:Dimensional consistency is crucial in mechanics. Young’s modulus quantifies stiffness as the ratio of stress to strain and therefore inherits the units of stress.

Given Data / Assumptions:

• E = stress / strain.
• Strain is dimensionless (change in length / original length).
• Any coherent unit system (SI, CGS, U.S. customary) is acceptable.

Concept / Approach:Because strain has no dimensions, the dimensions of E are exactly those of stress. In SI units, stress is in pascals (Pa = N/m^2), so E is also in pascals. In practice, engineers use MPa or GPa for convenience.

Step-by-Step Solution:

Verification / Alternative check:Check typical values: steels have E ≈ 200 GPa, which is a stress unit magnitude, confirming the reasoning.

Why Other Options Are Wrong:“False”: contradicts the definition.Conditions like “only in SI” or “only for metals” are irrelevant; the dimensional reasoning is universal.

Common Pitfalls:Confusing modulus units with material-dependent numbers; the unit type is always the same as stress, regardless of the material.

Final Answer:

True