Question

Hooke's Law is valid only in :

• A. Plastic Region
• B. Elastic Region
• C. Necking Region
• D. Fracture Point

Hint:

Remember the sequence on a stress-strain curve: Proportional Limit (end of Hooke's Law) $\rightarrow$ Elastic Limit (end of reversible deformation) $\rightarrow$ Yield Point (start of plastic deformation) $\rightarrow$ Ultimate Tensile Strength (start of necking) $\rightarrow$ Fracture.

Answer 1

The Correct Option is B

Step 1: Concept:
Hooke's Law is a principle of physics stating that the force required to stretch or compress a spring (or a solid material) by some distance is strictly proportional to that distance. We must identify which region of a standard stress-strain curve supports this linear behavior.

Step 2: Key Formula or Approach:
Mathematically, Hooke's Law is expressed as:
\[ \sigma = E \cdot \epsilon \]
where $\sigma$ is stress, $E$ is Young's Modulus, and $\epsilon$ is strain. This indicates a direct, linear relationship between stress and strain.

Step 3: Step-by-step Explanation:

• Elastic Region (B): In the initial portion of a material's stress-strain curve, the material deforms reversibly. More specifically, within the very early part of this region (up to the proportional limit), stress is directly proportional to strain, creating a straight line on the graph. Hooke's Law is fully valid here.

• Plastic Region (A): Once the yield strength is surpassed, the material undergoes permanent, irreversible deformation. The stress-strain relationship is no longer linear, so Hooke's Law completely fails.

• Necking Region (C): This occurs deep within the plastic region just before failure, where the material's cross-sectional area begins to rapidly decrease locally. Hooke's Law is invalid here.

• Fracture Point (D): This is the terminal point where the material breaks. Hooke's Law does not apply.

Step 4: Final Answer:
Hooke's Law is only valid in the linear portion of the elastic region, matching option (B).