Question

How fast should the sphere pass the Galley loop at the highest point, with radius R = 2 m, so that it does not compress the loop.

Answer 1

To not compress the loop, the force that the sphere exerts on the loop must be 0. It means that the centripetal acceleration must be equal to the acceleration due to gravity:

$$a_c=g,\\\space\\ g=\frac{v^2}{R},\\\space\\ v=\sqrt{gR}=4.43\text{ m/s}.$$