Units of modulus of elasticity (Young's modulus) Modulus of elasticity has the same dimensional units as which of the following quantities?

Introduction / Context:Understanding units helps cross-check formulas and prevents design mistakes. Young's modulus E quantifies stiffness by relating stress to strain within the elastic range.

Given Data / Assumptions:

• Stress = force/area; strain = dimensionless.
• Pressure has the same units as normal stress.
• Modulus of rigidity G relates shear stress to shear strain.

Concept / Approach:Because strain is dimensionless, E has the same units as stress: pascal (Pa) = N/m^2. Pressure p is also in pascal. Modulus of rigidity G shares the same units as E because it relates shear stress to shear strain.

Step-by-Step Solution:E = σ / ε → units(E) = units(σ)/units(ε).units(σ) = N/m^2; units(ε) = 1 → units(E) = N/m^2.Pressure p has units N/m^2; modulus G has units N/m^2.Therefore, E shares units with stress, pressure, and modulus of rigidity.

Verification / Alternative check:Dimensional analysis confirms [E] = [F][L]^-2. Any correct grouping must include only quantities with pascal units, not strain (dimensionless) or force alone (newton).

Why Other Options Are Wrong:(a) incorrectly includes strain; (b) includes force (newton) which is not consistent; (c) includes strain and force; (e) includes displacement which has units of length.

Common Pitfalls:Confusing stress with force; forgetting that strain is unitless; mixing SI and non-SI units without conversion.

Final Answer:stress, pressure, and modulus of rigidity