There is no net force on the small ring.
Work Step by Step
In the large loop, the current flows counterclockwise and increases. This creates a magnetic field out of the page, increasing in strength. This increases the flux through the small ring. By Lenz’s law, the induced current in the small ring will be clockwise. Each part of the small ring feels a radial force inward, but there is no net force on the small ring. This makes sense because if the small ring were flexible, its area would decrease in size, minimizing the change in flux, as Lenz’s Law demands.