Rolling on a Plane and a Loop!

A plane inclined at an angle of $\displaystyle \frac{\pi}{6}$ ends in a circular loop of radius $\displaystyle R=2m$ . The plane and the loop join smoothly. A marble (a solid sphere) of negligible radius and mass $\displaystyle m=20g$ is released from the slope at height $\displaystyle h=3R$ . What is the lowest value of the coefficient of friction if the marble rolls along the path without sliding?

The answer is in the form of $\displaystyle \frac{\alpha}{\sqrt{\beta}}$ where $\displaystyle \alpha$ and $\displaystyle \beta$ are positive coprime integers. Find $\displaystyle \alpha+\beta$