Q.State Hooke's law. Draw a labeled graph of tensile stress against tensile strain for a metal wire up to the breaking point. In this graph show the region in which Hooke's law is obeyed.

Step 1. Statement of Hooke's law. Within the elastic limit, stress is directly proportional to strain: $\dfrac{\text{Stress}}{\text{Strain}} = \text{constant}$, and this constant is the modulus of elasticity of the material — geometrically the slope of the straight-line portion of the stress-strain graph.

Step 2. Setting up the graph. Plot tensile strain along the x-axis and tensile stress along the y-axis, for a metal wire loaded in gradually increasing steps until it fractures (as obtained from the standard wire-loading experiment of Q.iii above).

Step 3. Labelling the graph. The graph starts at the origin $O$ and rises as a straight line to point $A$ (the proportional limit); from $A$ it bends but remains reversible up to point $B$ (the yield point/elastic limit); from $B$ it enters plastic flow, passing through $C$ (where unloading would leave a permanent set along line $CE$) and continuing to point $D$, where the wire fractures. …

State Hooke's law, sketch the standard O-A-B-C-D stress-strain curve, and mark the OA seg …

Marking the entire elastic region O to B as obeying Hooke's law — Hooke's law (direct proportionality) holds strictly only up to the proportional limit A; the region A to B is still elastic (fully recoverable) …