State the limit up to which Hooke's law (stress is directly proportional to strain) is valid for a typical ductile metal tested in tension under standard laboratory conditions.

Introduction:
Hooke's law states that stress is proportional to strain (σ ∝ ε) in the initial portion of a material's stress–strain curve. Knowing the boundary of this linear relationship is crucial for elastic analysis and modulus determination.

Given Data / Assumptions:

• Metallic specimen tested in monotonic tension.
• Quasi-static loading; room temperature.
• Linearly elastic behavior at small strains.

Concept / Approach:
The linear proportionality holds only up to the material's proportional limit. In many educational contexts and basic MCQs, the proportional limit is taken as very close to the elastic limit; hence Hooke's law is said to be valid up to the elastic limit for practical purposes. Beyond this, nonlinearity and yielding begin, invalidating σ ∝ ε.

Step-by-Step Solution:
1) Identify linear region on the stress–strain curve.2) Note the end of linearity ≈ proportional limit.3) Elastic limit closely coincides with proportional limit in many metals; MCQ convention uses "elastic limit".4) Therefore, Hooke's law validity is taken up to the elastic limit for typical problems.

Verification / Alternative check:
Laboratory curves show deviation from linearity just before yield; the elastic domain ends at the elastic limit, consistent with Hooke's law applicability.

Why Other Options Are Wrong:
Yield point: plastic flow begins; σ–ε is no longer linear.

Plastic limit / breaking point: far beyond elastic behavior.

Creep limit: relates to time-dependent deformation, not monotonic linearity.

Common Pitfalls:
Confusing proportional limit with yield point; using Hooke's law in plastic range.

Final Answer:
elastic limit