Exercise I: Balancing a crate $(68$ pts$)$

In the system represented in figure $(1),$ the roller in $C$ allows the ring in point $B$ to move vertically while cord $CB$ maintains horizontal. We would like to determine the distance $y$ at which the system stabilizes.

Figure $1$: Representation of system at equilibrium.

$(14pts)$ What body $($object$)$ would you study to determine the forces in the cords? And why?

The crate has a weight of $W=2kN,$ and the cord AB has a constant length of $l_{AB}=1\mathrm{.}5m.$

$2.(12$ pts$)$ Draw the FBD of ring B$.$ Name $T_{BA}$ and $T_{BC}$ the tensions in cords $AB$ and $BC.$