A small vehicle of mass \(m\) travels at a constant speed \(v\) in a horizontal circular path of radius \(R\) along the frictionless inner surface of a symmetric bowl. The profile height \(y\) of the surface as a function of radial distance \(r\) from the vertical central axis is given by \(y(r) = \beta r^3\), where \(\beta\) is a positive constant. Which of the following expressions represents the speed \(v\) required for the vehicle to maintain its circular path at radius \(R\) without sliding up or down the surface?