B$2.$ b$)$ The disk A shown in Figure B$2$b has a mass of $10$ kg and rotates without friction about its pivot O $.$ Block B has a mass of $3$ kg and the mass of pulley C is negligible. Determine:

i$)$ the relationship between the vertical acceleration of block B and the angular acceleration of disk A$,$

$[4$ marks$]$

ii$)$ the angular acceleration of the disk A$,$

$[4$ marks$]$

iii$)$ the tension in the cord that supports pulley C $,$

$[2$ marks$]$

iv$)$ the horizontal and vertical components of the support reaction forces at pivot O $.$

$[2$ marks$]$