A small clamp of mass m is attached at B to a hoop of mass 3m and radius r. The system is released from rest with $\theta ={90}^0$  and rolls without sliding. The angular acceleration of the hoop is

The hoop rolls without sliding. Therefore, instantaneous axis of rotation passes through the bottommost point 

C is the centre of mass of the hoop and the clamp
Where  $AC=\frac{r}{4}$
and  $CB=\frac{3r}{4}$
$\alpha =\frac{{\tau }_p}{I_p}=\frac{mgr}{6m{r}^2+2m{r}^2}$
(or)  $\alpha =\frac{g}{8r}(I_p=I_{hoop}+I_{block})$
Hence the angular acceleration of hoop is  $\frac{g}{8r}$