Maximum Tension Question

1. The problem statement, all variables and given/known data
The maximum tension the string can have without breaking is Tmax. Derive an expression for Vmax, the maximum speed the ball can have at point Q without breaking the string.

2. Relevant equations
F=ma
Vc=(mv^2)/r
T=mg+ma
3. The attempt at a solution
I thought I could do T+mg=mv^2/r because mv^2/r-mg would give you the max speed to keep the same tension and anything great would produce a greater tension that the string doesn’t have causing it to break. So, I pulled out a common factor in m and got a common denominator giving me m((v^2-gr)/r)=T

Attachment 66448

Attached Images
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