A vertical spring of spring constant \(24 \mathrm{Nm}^{-1}\) is fixed on a table. A ball of mass 0.5 kg at a height 2 m above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance of 50 cm . The net work done in the process is:

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.