Which Object Reaches the Bottom First? - Solving a Rotational Dynamics Problem

[pb23me]

Homework Statement

A uniform solid cylinder and a uniform cylindrical shell are placed side by side at the top of an incline.If they sre released from rest and roll without slipping,
A)Determine their speeds when they reach the bottom
B)Which objet reaches the bottom first?

Homework Equations

I=mr² for the cylindrical shell
I=1/2(mr²)
mgyi+1/2(Iw²)+1/2(mv²)=mgyf+1/2(Iw²)+1/2(mv²)

The Attempt at a Solution

I used this conservation of energy equation for each object and got gyi=1/2(r²w²)+1/2(v²) for the hollow cyinder.
then gyi=1/4(r²w²+1/2(v²) for the solid cylinder. since gyi is the same for both i figured that the sollid mass must have a greater velocity and therefore reach the bottom first? Initially i thought they would both have the same velocity and both reach the bottom at the same time. However this result i came up with doesn't quite agree with that.

 

[Beer-monster]

You may find this helpful.

http://www.mahalo.com/answers/which...hin-hollow-sphere-a-solid-disk-or-a-thin-hoop

 

[pb23me]

Thanx, that was perfect