Question

Hooke’s law is valid up to:

• A. Breaking point
• B. Yield point
• C. Elastic limit
• D. Ultimate stress

Hint:

Always remember: {Hooke’s law works only in the elastic region} of the stress–strain curve.

Answer 1

The Correct Option is C

Step 1: Understanding Hooke’s law.
Hooke’s law states that within certain limits, stress is directly proportional to strain. Mathematically, it is expressed as: \[ \text{Stress} \propto \text{Strain} \] or \[ \text{Stress} = E \times \text{Strain} \] where $E$ is the modulus of elasticity.
Step 2: Meaning of elastic limit.
The elastic limit is the maximum stress a material can withstand without undergoing permanent deformation. Up to this point, the material returns to its original shape once the load is removed.
Step 3: Relationship between Hooke’s law and elastic limit.
Hooke’s law is valid only in the region where stress and strain remain proportional. This proportional behavior exists only up to the elastic limit. Beyond this limit, the stress–strain relationship becomes non-linear.
Step 4: Analysis of options.
(A) Breaking point: Incorrect — At this point, the material fractures, and Hooke’s law no longer applies.
(B) Yield point: Incorrect — Plastic deformation begins near the yield point, violating Hooke’s law.
(C) Elastic limit: Correct — Hooke’s law holds true only up to the elastic limit.
(D) Ultimate stress: Incorrect — This corresponds to maximum stress before failure, far beyond the elastic region.
Step 5: Conclusion.
Since Hooke’s law requires proportionality between stress and strain, it is valid only up to the elastic limit.