What law states that the stress in an elastic body is directly proportional to the strain within the elastic limit?

The statement refers to Hooke's Law, which establishes the fundamental relationship between stress and strain in elastic materials. According to Hooke's Law, stress (which is the force applied per unit area) is directly proportional to strain (the deformation caused by that force) as long as the material remains within its elastic limit. This means that if a material is deformed within this limit, it will return to its original shape once the load is removed, reflecting the characteristic behavior of elastic materials.

Hooke's Law is mathematically represented as σ = Eε, where σ is the stress, E is the modulus of elasticity (Young's modulus), and ε is the strain. This law is critical in engineering and material science as it allows for the prediction of how materials will behave under various loads.

Additionally, while Young's Modulus and Modulus of Elasticity refer to the specific proportionality constant in Hooke's Law, they do not encapsulate the relationship itself; instead, they quantify the stiffness of a material. The yield point signifies the point beyond which the material will no longer return to its original form, leading to permanent deformation, which is outside the realm of elastic behavior defined by Hooke's Law.