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A particle P of mass m is tied to a vertical axis by two strings AP and BP, each of length L, with the points A and B on the axis separated by AB = L. P rotates about the axis with angular velocity omega, and the tensions in the strings are T1 (upper, AP) and T2 (lower, BP). Which statement is correct?

1. T1 = T2
2. T1 + T2 = m omega² L
3. T1 - T2 = 2mg
4. BP will remain taut only if omega >= sqrt(2g/L)

Correct answer: BP will remain taut only if omega >= sqrt(2g/L)

Solution

With the equilateral-triangle geometry, vertical balance gives (T1 - T2)cos(angle) = mg and horizontal gives (T1+T2)sin(angle) = m omega² r. T2 >= 0 requires omega >= sqrt(2g/L).

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