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A stone of mass 0.25 kg attached to a string is whirled in a horizontal circle of radius 1.5 m at 40 rev/min. Find the tension in the string. Also, if the string can sustain a maximum tension of 200 N, what is the maximum speed of the stone? (Take pi² approx 9.87)

1. Tension approx 6.6 N; max speed approx 34.6 m/s
2. Tension approx 3.3 N; max speed approx 20 m/s
3. Tension approx 6.6 N; max speed approx 20 m/s
4. Tension approx 13.2 N; max speed approx 34.6 m/s

Correct answer: Tension approx 6.6 N; max speed approx 34.6 m/s

Solution

omega = 40*2pi/60 = 4.19 rad/s, T = m*omega²*r = 0.25*(4.19)²*1.5 approx 6.6 N; max speed from 200 = 0.25*v²/1.5 gives v = sqrt(1200) approx 34.6 m/s.

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