Which would be faster: A ball rolling down a ramp with no groove

1. The problem statement, all variables and given/known data
Which would be faster: A ball rolling down a ramp with no groove, or a ball rolling down a ramp with a groove?
What effect does the radius have, if any? Disregarding resistance and whether or not the ball rolls in a straight line.
2. Relevant equations

3. The attempt at a solution

I thought that a decrease in rolling radius due to being in the groove might have an effect but apparently not. Any input appreciated.

http://ift.tt/1rAPXOH

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