Tension of String in Yo-Yo Motion

[jasony]

Homework Statement

A yo-yo consists of two uniform heavy discs, each of mass M and radius R, connected
by a light axle of radius a around which one end of a string is wound. One end of the string is attached to the axle and the other to a fixed point P. The yo-yo is held with its centre of mass vertically below P and then released.

Homework Equations

Assuming that the unwound part of the string is approximately vertical, use the principle of conservation of energy to find the equation of motion of the centre of mass of yo-yo. What is the tension of the string when the centre of mass has fallen a distance y?

The Attempt at a Solution

I just want to check if my answer is correct.
My answers are x''=(2a^2g)/(2a^2+R^2) for the equation of motion
and T=2MgR^2/(2a^2+R^2)

Thanks

 

[jsmith12]

That's what I get.
But why does the question ask for the tension at a distance y? Surely the tension is the same everywhere? Or have I gone wrong somewhere?