Which mechanical principle is represented by Hooke's law?

Hooke's law describes the relationship between the force exerted on an elastic material and the resulting displacement or deformation of that material. Specifically, it states that the force needed to extend or compress a spring by some distance is proportional to that distance, as long as the limit of elasticity is not exceeded. This principle is foundational in understanding how materials behave when subjected to stress and is widely applicable in fields such as mechanical engineering, materials science, and physics. Understanding this relationship is crucial when designing systems that involve springs or other elastic materials, ensuring that they operate safely within their elastic limits.

The other options pertain to different principles in physics. The first option deals with Newton's second law of motion, the third addresses Boyle's law in thermodynamics, and the fourth relates to the work-energy principle. These concepts are distinct and do not relate to the specific behavior of elastic materials as described by Hooke's law.