I was learning about stress and strain and my text book suddenly mentions about this law so called hooke's law. It states that $$\text{stress}\propto \text{strain}$$ Or, $$ \text{stress}=k \times \text{strain}$$ Where $k$ is the constant of proportionality. I have basic knowledge of strain and stress.
My question:-
How to prove the hooke's law?
Physical laws do not necessarily need to be proved mathematically, but are generalizations of the results of physical experiment. In other words a physical law is 'proven' not by math and logic, but experiment and observation.
It is possible to derive the results from other assumptions, and @Chemomechanics posted a link to a good derivation. The wikipedia page also adds a significant amount of additional sources and reading material. This quote from the wikipedia page is relevant.
"Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached."
