Q.State Hooke's law and verify it with the help of an experiment.

Step 1. Statement. 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: $\text{stress}\propto\text{strain}$.

Step 2. Apparatus. A thin, straight wire of uniform cross-sectional area A and natural length L is suspended from a rigid support. A pan (to hold weights) and a pointer are attached at the wire's free lower end, with the pointer's position read against a fixed graduated scale using a vernier arrangement, so that the extension produced by each load can be measured precisely.

Step 3. Procedure. Weights are added to the pan in a series of equal steps. For each load, the corresponding stretching force F and the resulting elongation $\Delta L$ (read from the pointer's shift on the scale) are recorded.

Step 4. Graph. Plotting F on the horizontal axis against $\Delta L$ on the vertical axis produces a set of points that lie on a single STRAIGHT LINE passing through the origin.

Step 5. Interpretation. Since $\Delta L=(\text{slope})F$, and using $V=AL$ to rewrite the slope in terms of A and L, algebra reduces this directly to $\dfrac{F}{A}\propto\dfrac{\Delta L}{L}$, i.e. $\sigma\propto\varepsilon$ -- exactly Hooke's law. The straight-line, origin-passing nature of the graph is the direct experimental verification: as long as the elastic limit is not exceeded, the elongation (and hence the strain) stays strictly proportional to the applied force (and hence the stress).

Describe the suspended-wire apparatus, the loading procedure, and show algebraically that the resulting straight-line F-vs-Delta-L graph is equivalent to stress proportional to strain.

• Describing only the statement of Hooke's law without the experimental verification the question specifically asks for.
• Forgetting to note the graph passes through the ORIGIN, which is essential to the proportionality (not just linearity).