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A particle is attached by two equal strings to two points A and B lying in the same vertical line (A above B), with AB = h. The particle describes a horizontal circle with uniform angular speed omega = 2*sqrt(2g/h). Find the ratio of the tension in the upper string to that in the lower string.

1. 5: 3
2. 3: 5
3. 2: 1
4. 5: 1

Correct answer: 5: 3

Solution

With omega² = 8g/h the equations give T1 + T2 = 8mgl/h and T1 - T2 = 2mgl/h, so T1 = 5mgl/h and T2 = 3mgl/h, a ratio of 5: 3.

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