A material is said to be perfectly elastic when which of the following statements best describes its behavior under loading and unloading?

Introduction / Context:
Elasticity measures a material's ability to recover its original dimensions after the applied load is removed. Perfect elasticity is an idealization used in fundamental mechanics to simplify analysis and define the linear portion of stress–strain behavior.

Given Data / Assumptions:

• Material is homogeneous and isotropic in the ideal model.
• Loading remains within the elastic limit.
• No time-dependent effects (creep, relaxation) are considered.

Concept / Approach:
For a perfectly elastic material, strain is entirely recoverable upon unloading: there is no plastic (permanent) deformation, and the unloading path coincides with the loading path. Hooke's law (stress proportional to strain) typically models this regime for small deformations.

Step-by-Step Solution:
Define perfect elasticity: zero permanent set after full unloading.Relate to stress–strain curve: linear reversible behavior below yield point.Choose the option that explicitly states complete recovery.

Verification / Alternative check:
In tensile tests, if the specimen returns exactly to its original gauge length after removal of load within the elastic range, the behavior matches perfect elasticity.

Why Other Options Are Wrong:

• Partial recovery: Indicates viscoelastic or elastoplastic behavior.
• No recovery: Represents plastic or damaged state.
• None of these: Incorrect because a precise correct statement exists.

Common Pitfalls:
Confusing perfect elasticity with high elasticity; believing linearity is required at all strains (the idealization usually concerns small strains).

Final Answer:
It regains its original shape completely upon removal of load (no permanent set).