A robotic test vehicle of mass \(m\) travels at a constant speed \(v_0\) in a horizontal circle of radius \(R_0\) on a flat test track. A net horizontal force of magnitude \(F_0\) is required to maintain this circular path. In a second trial, the vehicle travels at a constant speed of \(3v_0\) in a horizontal circle of radius \(2R_0\). Which of the following expressions correctly represents the magnitude of the new net horizontal force \(F\) required to maintain the vehicle's motion during the second trial in terms of \(F_0\)?