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A bucket of water tied to one end of a rope of length 3 m is rotated in a vertical circle about the other end in such a way that water in it dows not spill . Calculate the minimum velocity of the bucket at which this happens .

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To solve the problem of finding the minimum velocity of a bucket of water tied to a rope of length 3 meters, which is rotated in a vertical circle without spilling the water, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Problem**: - We have a bucket of water tied to a rope of length \( r = 3 \, \text{m} \). - The bucket is rotated in a vertical circle about the fixed end of the rope. - We need to find the minimum velocity at the top of the circular path to ensure the water does not spill out. ...
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