HSC Physics Harder Circular Motion

A sheet of harder questions on circular motion follows.

1. A railroad car is moving around a horizontal circular track of radius r with a speed v. The distance between the rails is d. If the height of the centre of mass of the car above the rails is h, show that the ratio of the normal reaction reaction force exerted by the outer rail to the inner rail is (dgr + 2hv²)/(dgr - 2hv²).
2. A thin ring of radius R and mass M rotates at an angular speed ⍵. Find the tension in the ring.