Rolling without slipping in a ring!

I did it using $IAR$ that is instantaneous axis of rotation

$\huge{\tau_{IAR}=I_{IAR} \alpha}$

$\alpha$ is angular acceleration, $I_{IAR}$ is moment of inertia about $IAR$

$mgr=(3mr^{2}+3mr^{2}+m({\sqrt{2}r})^{2})\alpha$

$\large{\boxed{\alpha=\frac{g}{8r}}}$

The shortest method i could find

where $\sigma$ is the angular acceleration of the hoop.

So Easy !!