(Solved): Nonuniform ball. In the figure, a ball of mass \( M \) and radius \( R \) rolls smoothly from rest ...

Nonuniform ball. In the figure, a ball of mass \( M \) and radius \( R \) rolls smoothly from rest down a ramp and onto a circular loop of radius \( 0.51 \) \( \mathrm{m} \). The initial height of the ball is \( h=0.33 \mathrm{~m} \). At the loop bottom, the magnitude of the normal force on the bail is \( 2.0 \mathrm{Mg} \). The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form \( I=\beta M R^{2} \), but \( \beta \) is not \( 0.4 \) as it is for a ball of uniform density. Determine \( \beta \). Number Units