The critical speed below which the rope would become slack when the bucket reaches the highest point in the circle is determined by the length of the rope and the radius of the circle.
When the bucket is at the highest point in the circle, it is momentarily at rest and the tension in the rope must be zero.
The formula for calculating the critical speed at which the rope becomes slack is:
v = √(gr)
where v is the critical speed, g is the acceleration due to gravity, and r is the radius of the circle.
For example, if the radius of the circle is 2 meters and the acceleration due to gravity is 9.8 m/s², the critical speed would be:
v = √(9.8 × 2) = 4.4 m/s
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