Edge Case Of Rolling!

On the edge of a cuboidal plank of mass M=8 kgM = 8\text{ kg}, a uniform solid spherical ball of mass m=12 kgm = 12\text{ kg} and radius RR is kept. The ball is given a very slight push towards right. There is no\underline{\text{no}} friction between plank and ground and friction between ball and plank is sufficient to prevent slipping\underline{\text{prevent slipping}}. The plank won't topple during the journey.

If when ball just loses contact with plank, the angle made by Center of Mass ball with vertical is θ\theta, then cosθ=ab3 where a,bI+\displaystyle \cos\theta = \frac{\sqrt{a} - b}{3} \text{ where } a, b \in I^+ Enter your answer as a+ba + b.


Inspiration Aniket Sanghi

All of my problems are original.

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