Figure $4$: Problem $4$

Q$4$: A uniform spherical shell of mass $M=4\mathrm{.}5Kg$ and radius $R=8\mathrm{.}5cm$ can rotate about a vertical axis on frictionless bearings $($Figuer $4).$ A massless cord passes around the equator of the shell, over a pulley of rotational inertia $I=3\mathrm{.}0{10}^{-3}Kg.m^2$ and radius $r=5\mathrm{.}0cm,$ and is attached to a small object of mass $m=0\mathrm{.}60Kg.$ There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen $82$ cm after being released from rest? $(1.$ Use energy considerations. $2.$ The moment of inertia of a spherical shell of mass $M$ and radius $R$ is $I=\frac{2}{3}M{R}^2)$