Modulus of elasticity is defined as the ratio of
- AShear stress to Shear Strain
- BLinear stress to linear strainCorrect
- CLateral strain/linear strain
- DLinear strain/lateral strain
Solution
Concept
Definition of modulus of elasticity
Formula
E = Stress / Strain
Step-by-step solution
1. Hooke's law states that within the elastic limit, stress is directly proportional to strain. 2. Modulus of elasticity (Young's modulus, E) is the proportionality constant for longitudinal deformation. 3. Therefore, it is defined as the ratio of linear stress to linear strain. Answer: B
Explanation
Modulus of elasticity, also known as Young's modulus, measures a material's stiffness under uniaxial loading. It is defined by Hooke's law as the ratio of linear stress to linear strain within the proportional elastic limit. By contrast, the ratio of shear stress to shear strain defines the modulus of rigidity, and lateral strain to linear strain defines Poisson's ratio.
Why the other options are wrong
A) The ratio of shear stress to shear strain is defined as the modulus of rigidity. C) The ratio of lateral strain to linear strain defines Poisson's ratio. D) Linear strain divided by lateral strain is the reciprocal of Poisson's ratio.
Shortcut
Modulus of Elasticity (E) = Linear Stress / Linear Strain.
Common mistake
Confusing Modulus of Elasticity with Shear Modulus or Poisson's ratio definitions.
Correct answer: B) Linear stress to linear strain