Centripetal Force String Tension

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

Two masses M of the same amount are tied to two stings of length L and 2L. If both masses are swung in unison faster and faster, which string will break first?

2. Relevant equations

The formula I’ve been using is Tension = mv^2/r.

3. The attempt at a solution

My understanding is that when the string breaks, tension will be 0. If I plug that into the formula the radius/length of the string will not matter. What am I doing wrong here?

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