A classical mechanics problem by Arpita Karkera

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

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

What is the value of \(a+b\)?

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