One end of a steel rod of radius \(10.0 \mathrm{~mm}\) and length \(50.0 \mathrm{~cm}\) is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude \(10.0 \times \pi \mathrm{kN}\). This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (Use Young's modulus \(=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.