(Solved): 4. A uniform spherical shell of mass M=4.5kg and radius R=8.5cm can rotate about a vertical axi ...

4. A uniform spherical shell of mass $M=4.5\mathrm{kg}$ and radius $R=8.5\mathrm{cm}$ can rotate about a vertical axis on frictioness bearings (Fig. 10-47). A massless cord passes around the equator of the shell, over a pulley of rotational inertia $I=$ $3.0\times 10^{?3}\mathrm{kg}?{\mathrm{m}}^2$ and radius $r=5.0\mathrm{cm}$, and is attached to a mall object of mass $m=0.60\mathrm{kg}$. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the peed of the object when it has fallen $82\mathrm{cm}$ after being reeased from rest? Use energy considerations.