A linear force–deformation relation is obtained in materials:
Try it first: pick an option, then read the explanation.
Correct answer: C. following Hooke's law
Asked in SSC JE 2014 (Morning)
Detailed Explanation
‘Elastic’ only means the material returns to its shape after unloading; it does not have to be linear. ‘Linear’ is the extra condition in Hooke's law.
Why “following Hooke's law” Is Correct
In a material following Hooke's law, stress is proportional to strain, so force is proportional to deformation (P = (AE/L)δ). Some elastic materials, such as rubber, are elastic but not linear — so option (c) is the precise answer.
Why the Other Options Are Wrong
- A. having elastic stress–strain property: Elastic materials can be non-linear (e.g. rubber).
- B. having plastic stress–strain property: Plastic behaviour is non-linear and permanent.
- D. which are rigid elastic materials: A rigid material does not deform at all.
Key Point
Linear force–deformation ⇔ Hooke's law.
Key Concepts for Students
- Stiffness of a bar k = AE/L.
- Hooke's law holds up to the limit of proportionality.
- Superposition needs linear-elastic behaviour.
Practice more: this is question 20 in Stress and Strain MCQs – Part 2. Try the whole set and check every answer instantly.