Two cars of masses \(\mathrm{m}_1\) and \(\mathrm{m}_2\), joined back to back by a massless compressed spring are at rest on a horizontal rough road. When the compression of the spring is suddenly removed, the cars move away from each other and come to rest due to friction. If the frictional force is same on them, their stopping times are in the ratio

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.