Uniform circular motion and angular momentum?

1. The problem statement, all variables and given/known data

A sphere on top of a table is attached to a rope which goes through a hole in the table and is attached to a bucket at the other end. The sphere moves in a uniform circular motion with radius R.

Water is then added to the bucket and the radius for the sphere’s circular motion is changed. Find an expression for the new radius.

The mass of the sphere (m) and bucket (M) is known. The mass of the water added to the bucket is known as well. The initial radius of the circular motion is known and the initial speed of the sphere is known. Angular momentum is conserved.

Friction can be neglected.

2. Relevant equations
Angular momentum?

3. The attempt at a solution
I have no idea how to start on this?


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