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A particle P of mass m is attached to a fixed vertical axis by two strings AP and BP, each of length l. The points A and B on the axis are separated by distance l (so triangle APB is equilateral). P rotates in a horizontal circle about the axis with angular velocity omega. T1 is the tension in AP (upper string) and T2 is the tension in BP (lower string). Which of the following is correct?
- T1 equals T2
- T1 + T2 = m * omega² * l
- T1 - T2 = 2mg
- The lower string BP remains taut only if omega > sqrt(2g/l)
Correct answer: T1 - T2 = 2mg
Solution
With AB = AP = BP = l the triangle is equilateral, so each string makes 60 deg with the axis. Vertical balance gives T1*cos60 - T2*cos60 = mg, i.e. (T1-T2)/2 = mg, so T1 - T2 = 2mg.
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