Q.State Hooke's law of elasticity.

HOOKE'S LAW states that, for a small deformation within the elastic limit, the strain produced in a body is directly proportional to the stress that produces it: $\text{stress}\propto\text{strain}$, or $\sigma=(\text{constant})\times\varepsilon$, where the constant of proportionality is the modulus of elasticity for that particular kind of stress-strain pair. EXPERIMENTAL VERIFICATION: a thin, straight wire of uniform cross-sectional area A and natural length L is suspended from a rigid support, with a pan (for adding weights) and a pointer attached at its free lower end; the pointer's position is read off against a fixed graduated scale (using a vernier arrangement) so the extension produced by each load can be measured precisely. As weights are added to the pan in steps, the corresponding stretching force F and the resulting elongation $\Delta L$ are recorded for each load. Plotting F (horizontal axis) against $\Delta L$ (vertical axis) yields a straight line through the origin -- direct experimental confirmation that, within the elastic limit, elongation is directly proportional to the applied force. Algebraically, since $\Delta L=(\text{slope})F$, and using $V=AL$ to rewrite the slope in terms of A and L, this reduces exactly to $\sigma\propto\varepsilon$: stress proportional to strain, i.e. Hooke's law. Hooke's law holds only within the elastic limit; beyond it (the region OA on the stress-strain graph ends and region AB begins), stress and strain are no longer strictly proportional even though the material may still recover its shape up to the elastic limit at B, and beyond B the material enters permanent (plastic) deformation.