A small solid sphere with radius $0\mathrm{.}17$ cm and mass $0\mathrm{.}71$ g rolls without slipping on the inside of a large fixed hemisphere with radius $0\mathrm{.}20$ m and a vertical axis of symmetry. The sphere starts at the top from rest. $($a$)$ What is its kinetic energy at the bottom? $($b$)$ What fraction of its kinetic energy at the bottom is associated with rotation about an axis through its center of mass? $($c$)$ What is the magnitude of the normal force on the hemisphere from the sphere when the sphere reaches the bottom?