Units of Stress, Strain, and Young's Modulus in Mechanics

Steps:

• Stress is defined as force per unit area, with units of newtons per square meter (N/m²), or pascal (Pa).
• Strain is the ratio of extension to original length, a dimensionless quantity with no units.
• Young's modulus is the ratio of stress to strain, so its units match those of stress: pascal (Pa).

Why D is correct:

• Young's modulus E = stress / strain; since strain is dimensionless, E inherits stress units (Pa), as per Hooke's law.

Why the others are wrong:

• A: Stress units are Pa (force/area), not newton (force alone).
• B: Young's modulus units are Pa, not newton (force).
• C: Strain is dimensionless (not metre); Young's modulus is Pa, not newton-metre (torque).

Final answer: D