Which of the following defines Young's modulus of elasticity?

Young's modulus of elasticity is defined as the ratio of stress to strain in a material within the elastic limit, which means it quantifies how much a material will deform under a given load. Stress is defined as the force applied per unit area, while strain is the measure of the deformation of the material — specifically, the change in length divided by the original length.

Thus, the correct definition involves the relationship between stress (force per unit area) and strain (the relative change in shape). This relationship is crucial for understanding how materials behave under different loads, and it helps engineers determine the suitability of materials for various applications, particularly in structural engineering.

In contrast, other choices do not correctly reflect the definition of Young's modulus. Load over material volume might relate to material density but does not consider strain. Extension over time does not define elasticity; it rather implies a dynamic aspect that isn’t relevant to the static definition of Young's modulus. Lastly, force applied over strain does not provide the necessary context of the cross-sectional area, failing to encompass the foundational concept of stress.