A bucket containing water is tied to one end of a rope of length 2.5 m and rotated about the other end in a vertical circle so that water does not spill even when bucet is upside down . What is the maximum velocity of the bucket at which this happens ? How many rotations per minute is it making `g = 10 m//s^(2) ` .

Explanation

To solve the problem of finding the maximum velocity of the bucket so that the water does not spill when the bucket is upside down, we can follow these steps:

### Step 1: Understand the Forces Acting on the Bucket
When the bucket is at the top of the vertical circle, the forces acting on it are:
1. The gravitational force (weight) acting downward, which is \( W = mg \).
2. The centripetal force required to keep the bucket moving in a circular path, which is provided by the tension in the rope and the weight of the water.

### Step 2: Set Up the Equation for Forces
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