How is Hooke's Law expressed mathematically?

The correct mathematical expression of Hooke's Law is represented through the relationship between stress, strain, and the modulus of elasticity. Hooke's Law states that the deformation (strain) of an elastic material is directly proportional to the applied stress, within the limits of elasticity.

In terms of the formula, stress (σ) is defined as the force (P) applied per unit area (A), or σ = P / A. Strain (ε), which is the deformation per unit length, is proportional to the stress applied (σ) times the modulus of elasticity (E). When these relationships are combined using the definition of strain, you can conclude that ε = σ / E = (P / A) / E.

When you rearrange these relationships, specifically considering the deformation under a load which relates back to the original given option, you derive that the extension or deformation in terms of the original length (L) is directly influenced by the variables expressed in Option A: P * L / (A * E). This equation essentially derives from rearranging the overall force relationship in a linearly elastic material.

Thus, Option A correctly depicts Hooke's Law in its mathematical form where the deformation is proportional to the applied load and inversely proportional