Question

The Hooke’s law defines:
A .Modulus of elasticity
B. Stress
C. Strain
D. Elastic limit

Answer 1

The word Hooke itself gives a hint which means that “As the extension, so the force”. This law states that, within the elastic limit of body stress is directly proportional to strain. The proportionality constant can be defined by using Hooke’s law. Unit of proportionality is $\dfrac{N}{{{M}^{2}}}$.

Complete answer:
Robert Hooke was the inventor, and has given fundamental law of elasticity. In our life, we come across Hooke’s law behavior in many cases of bending, twisting, stretching, compression, in short are varieties of deformation. Hooke’s law states that within the elastic limit, stress is directly proportional to strain. Thus,
$\begin{aligned} & \text{Stress = A strain} \\\ & \text{Stress = M strain} \\\ \end{aligned}$
$\therefore M=\dfrac{\text{stress}}{\text{strain}}$
The constant of proportionality (m) is called the modulus of elasticity. Unit of proportionality is $\dfrac{N}{{{M}^{2}}}$.
Therefore we can define modulus of elasticity as ration of stress, strain of the material.

Thus, the modulus of elasticity of a material is defined as the slope of the stress-strain curve in the elastic deformation region. Therefore, Hooke’s law defines modulus of elasticity.

Hence option (A) is the correct option.

Note: The material which obeys Hooke’s law is called linear elastic or Hooke’s material modulus of elasticity depends on the nature of material. The maximum value of stress is directly proportional to the strain which is nothing but elastic limit. As you can define the modulus of elasticity i.e. option (A) and elastic limit i.e. option (B) seems similar but it is not. The term maximum value of stress in elastic limit makes difference.