Answer
$T = 2\pi~\sqrt{\frac{R}{g}}$
Work Step by Step
We can model this situation like an ice cube on the end of a pendulum of length $R$. Instead of tension from a string, there is the normal force from the track exerted on the ice cube. We can thus find the period of the motion as;
$T = 2\pi~\sqrt{\frac{R}{g}}$
