A frictionless pulley which has a uniform solid disc shape has a mass of $5kg$ and

a radius of $0\mathrm{.}20m.$ A $10kg$ block is attached to a weightless wire wrapped around the

rim of the pulley. The system is released from rest. $(I_{CM,\text{d}\text{u}\text{c}}=\frac{1}{2}M{R}^2,g=9\mathrm{.}8\frac{m}{s^2})$

a$)$ What is the linear speed of the block if the pulley has $10J$ of kinetic energy? $(10$p$)$

b$)$ How far must the stone fall so that the pulley has $10J$ of kinetic energy? $(10$p$)$