A classical mechanics problem by Arpita Karkera

In the figure shown a ring AA is initially rolling without sliding with a velocity vv on the horizontal surface of the body BB (of same mass as AA). All surfaces are smooth. BB has no initial velocity. Find the maximum height reached by AA on BB. (gg is acceleration due to gravity).

Answer comes out as av2bg\frac{av^{2}}{bg} where a and b are coprime integers

What is the value of a+ba+b?

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