$2.(25$ Pts$.)$ A solid uniform sphere of mass M and radius R is thrown along a level surface so that initially $($

t $0$

$)$ it

slides with a linear speed

$0$

v

but does not rotate. The coefficient of kinetic friction between the sphere and the

horizontal surface is

$$k

$.$ Because of friction, it begins to spin, and

eventually starts to roll without slipping. What fraction of its initial energy

does the sphere lose during sliding? $($For a solid sphere

$22$

$5$

CM I MR $$

$)$