A small cart of mass \(m\) is released from rest at a variable height \(h\) above the lowest point of a track that forms a vertical circular loop of radius \(R\), as shown. Friction and air resistance are negligible, and the track is designed such that it can only exert an inward normal force on the cart (\(F_N \ge 0\)). In the limiting case as the release height approaches the theoretical minimum value \(h_{\min}\) required for the cart to navigate the loop without losing contact at the apex, which of the following correctly identifies \(h_{\min}\) and the kinetic energy \(K_{\text{apex}}\) of the cart at the apex, along with the correct physical justification?