Two stones of masses \(\mathrm{m}\) and \(3 \mathrm{~m}\) are whirled in horizontal circles, the heavier one in radius \(\left(\frac{\mathrm{r}}{3}\right)\) and lighter one in radius ' \(\mathrm{r}^{\prime}\). The tangential speed of lighter stone is 'n' times that of the value of heavier stone, when they experience same centripetal force. The value of \(\mathrm{n}\) 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.