Question

The Hooke’s law defines
A. modulus of elasticity
B. stress
C. strain
D. elastic limit

Answer 1

Recall the statement of the Hooke’s law which is an accurate assumption for most of the solid bodies. You may find all the given quantities in the statement of the law. But what we have to look for is that quantity that is being introduced by the Hooke’s law. It obviously is the proportionality constant in the expression because the elastic limit just refers to the limit for which the Hooke’s law is valid for a solid.

Complete answer:
Hooke’s law which is one among the prominent laws of physics states that, the force that is required to extend or compress a spring by a distance x is known to be directly proportional to this distance. That is,
${{F}_{s}}\propto x$
$\Rightarrow F=-kx$
Where, k is the elastic constant of the spring.
Otherwise, you may state the law as, within the elastic limits of a body, the stress applied is directly proportional to the strain developed in the body. Mathematically,
$stress\propto strain$
$\Rightarrow stress=k\times strain$
Or,
$\dfrac{stress}{strain}=k$
Where, k is the modulus of elasticity.
Therefore, we could say that Hooke's law defines the modulus of elasticity.

Hence, option A is the right answer.

Note:
We have used the general form of the Hooke’s law to answer the question. By using this generalized version of Hooke’s law you could also deduce the relation between strain and stress for complex objects in terms of the intrinsic properties of the materials it is made of. Like, you could even deduce that the behavior of a homogeneous rod with uniform cross section resembles that of simple spring when stretched.