A soild sphere with radius 0.25 centimeter and mass 0.56 gram rolls without slipping on the inside of a large fixed hemisphere with radius 15 centimeter and a vertical axis of symmetry. The solid sphere starts at the top from rest.

Moment of inetia for a solid sphere I=25MR2

(4 points) a detail sketch of the problem

Part a) (8 points) At the bottom of the hemisphere, what is the kinetic energy of the solid sphere?

Detail calculation to arrive at the result with all the units in detail calculation

up to 4 points only without all the units

Part b) (8 points) What fraction of the total kinetic energy at the bottom of the hemisphere is associated with rotation about an axis through its center of mass?