Master of physics needed a solid uniform cylinder is rolling without slipping. what fraction of its kinetic energy is rotational? 1/2 1/3 1/4 2/3 3/4

Hey JayDilla, I get 1/3.  Here's how:
Kinetic energy due to linear motion is:

where

giving


The rotational part requires the moment of inertia of a solid cylinder

Then the rotational kinetic energy is

Adding the two types of energy and factoring out common terms gives

Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part.  Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.