For materials and structural analysis, identify the correct S.I. unit for the Modulus of Elasticity (Young's modulus), noting that only one option is strictly S.I. while others are non-S.I. scaled variants.

Introduction:Modulus of Elasticity (E) relates stress to strain in the linear elastic range. Its unit must match stress units. In the S.I. system, stress is measured in pascals (Pa), which is equivalent to N/m^2. Recognizing the proper unit ensures dimensional consistency in calculations.

Given Data / Assumptions:

• Stress = Force / Area.
• S.I. force unit: newton (N).
• S.I. area unit: square metre (m^2).

Concept / Approach:

E has the same units as stress. Therefore, the S.I. unit is N/m^2 (also written as Pa). Units like N/cm^2 or N/mm^2 are scaled non-S.I. area bases, used in practice but not strictly S.I.

Step-by-Step Solution:

Verification / Alternative check:

Common engineering practice uses MPa (10^6 Pa) or GPa (10^9 Pa) for convenience. These are still S.I.-consistent since they are decimal multiples of Pa.

Why Other Options Are Wrong:

• Newton/cm2, Newton/mm2: Use non-S.I. area units; convertible but not strictly S.I. base area.
• All the above: Over-inclusive; only one is strictly S.I. among the listed.
• Pascal (Pa): Although correct in principle, it is not one of the original four options A–D in the question. Selecting A (N/m2) matches both the strict S.I. unit and the provided options.

Common Pitfalls:

• Mixing practical convenience units (N/mm^2) with strict S.I. definition.
• Forgetting that Pa and N/m^2 are exactly the same.

Final Answer:

Newton/m2