Explanation:

Hooke's law states that the extension produced in a body is directly proportional to the applied load, provided the limit of proportionality is not exceeded. This law is valid only within certain limits, and these limits depend on the properties of the material being tested.

Type of Material:

The type of material is an essential factor that determines the validity of Hooke's law. Hooke's law is valid only for elastic materials, i.e., the materials that can regain their original shape after the removal of the applied load. For example, rubber is an elastic material, and Hooke's law is valid for it as long as the load applied is within the limit of proportionality.

Hardness of Material:

The hardness of the material also affects the validity of Hooke's law. Harder materials can withstand larger loads before deforming, and thus, their limit of proportionality is higher. So, the validity of Hooke's law for a material depends on its hardness.

Type of Loading:

The type of loading also affects the validity of Hooke's law. Hooke's law is valid only for the materials subjected to uniaxial stress, i.e., stress applied in one direction. For example, if a material is subjected to shear stress, Hooke's law is not valid.

Area of Cross-Section:

The area of cross-section does not affect the validity of Hooke's law. The extension produced in a body is directly proportional to the applied load, regardless of the area of cross-section.

Conclusion:

In conclusion, Hooke's law is valid only within the limits of proportionality, and these limits depend on the properties of the material being tested. The type of material, hardness, and type of loading are crucial factors that affect the validity of Hooke's law.