Question

For smaller deformations, stress is directly proportional to the strain for any material. Then the constant of proportionality is called as its

• A. modulus of elasticity
• B. Poisson's ratio
• C. compressibility
• D. coefficient of deformation
• E. mechanical strength

Hint:

For materials under small deformations, the modulus of elasticity is the proportional constant between stress and strain.

Answer 1

The Correct Option is A

The modulus of elasticity, also known as Young's modulus, is the constant of proportionality in Hooke’s law that relates stress and strain for materials under elastic deformation. This law states that for small deformations (in the elastic range), the stress applied to a material is directly proportional to the strain produced. The modulus of elasticity (E) represents the stiffness of a material. It can be defined as the ratio of stress to strain: \[ E = \frac{\text{stress}}{\text{strain}} \] - Poisson’s ratio (B): Poisson's ratio is the ratio of lateral strain to longitudinal strain when a material is subjected to stress. It is not the constant of proportionality between stress and strain. - Compressibility (C): Compressibility refers to the measure of a material's ability to decrease in volume under pressure, not related to stress-strain proportionality. - Coefficient of deformation (D): This term is not typically used in relation to stress-strain relationships. - Mechanical strength (E): Mechanical strength is the ability of a material to withstand an applied force without breaking or deforming. It is not directly related to the proportionality of stress and strain. Thus, the correct answer is (A) modulus of elasticity.