Modulus of Elasticity is Defined as the Ratio of Linear Stress to Linear Strain

The correct answer to this question is option 'B' - modulus of elasticity is defined as the ratio of linear stress to linear strain. In order to understand why this is the correct answer, let's break down the definitions of stress and strain, and how they relate to each other.

Understanding Stress and Strain:
- Stress: Stress is a measure of the internal force experienced by a material when an external force is applied to it. It is defined as the force per unit area and is represented by the symbol σ (sigma). Stress can be categorized into different types such as tensile stress, compressive stress, shear stress, etc.
- Strain: Strain is a measure of the deformation experienced by a material when an external force is applied to it. It is defined as the change in length per unit length and is represented by the symbol ε (epsilon). Strain can also be categorized into different types such as tensile strain, compressive strain, shear strain, etc.

Modulus of Elasticity:
The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness of a material. It quantifies how much a material deforms under a certain amount of stress. Mathematically, it is defined as the ratio of stress to strain:

Modulus of Elasticity (E) = Stress (σ) / Strain (ε)

Linear Stress and Linear Strain:
Linear stress and linear strain specifically refer to the stress and strain that occur in the longitudinal direction of a material. In other words, they describe the deformation of a material along its length.

Why Option B is the Correct Answer:
- Option A (Shear stress to shear strain): Shear stress and shear strain describe the deformation of a material when a force is applied parallel to its surface. They do not relate to the modulus of elasticity.
- Option B (Linear stress to linear strain): This is the correct answer. The modulus of elasticity is specifically defined as the ratio of linear stress to linear strain. It quantifies the deformation of a material in the longitudinal direction when a force is applied along its length.
- Option C (Linear stress to lateral strain): Lateral strain refers to the deformation of a material perpendicular to its length. This does not relate to the modulus of elasticity.
- Option D (Lateral stress to linear strain): Lateral stress refers to the stress that occurs perpendicular to the length of a material. This does not relate to the modulus of elasticity.

In conclusion, the correct answer to the question is option 'B' - the modulus of elasticity is defined as the ratio of linear stress to linear strain. This definition specifically relates to the deformation of a material in the longitudinal direction when a force is applied along its length.