GO = \frac{(\frac{1}{2}w + \frac{1}{2}B)d^2 - \frac{1}{2}w(a d + a^2)}{(\frac{1}{2}w + B)a - \frac{1}{2}dw}; or, if we consider the weight of the thread as an unit, and the weight of the ball as its multiple (or as expressed by the number of times it contains the weight of the thread),
GO = \frac{(\frac{1}{2}w + \frac{1}{2}B)d^2 - \frac{1}{2}w(a d + a^2)}{(\frac{1}{2}w + B)a - \frac{1}{2}dw}; or
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