Chapter 11, Problem 13P

GO Nonuniform ball. In Fig. 11-36, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.48 m. The initial height of the ball is h = 0.36 m. At the loop bottom, the magnitude of the normal force on the ball is 2.00Mg. 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 = βMR², but β is not 0.4 as it is for a ball of uniform density. Determine β.

Figure 11-36 Problem 13.