Consider an elliptically shaped rail PQ in the vertical plane with $\mathrm{O}\mathrm{P}\mathrm{}=\mathrm{}3\mathrm{}\mathrm{m}$ and $\mathrm{O}\mathrm{Q}\mathrm{}=\mathrm{}4\mathrm{}\mathrm{m}$ . A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is $(\mathrm{n}\times 10)$ Joules. The value of n is (take acceleration due to gravity = $10\mathrm{}\mathrm{m}{\mathrm{s}}^{–2}$ )

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.