Three blocks are connected by massless ropes that move over frictionless pulleys without slipping as shown in the figure. The mass of block $A$ is $1$ kg $,$ the mass of block $B$ is $2$ kg $,$ and the mass of block C is $4$ kg $.$ Each pulley can be modeled as a uniformly dense solid cylinder with a radius of $4$ cm and a mass of $3$ kg $.$ The coefficient of kinetic friction between block B and the horizontal surface is ${}_k=0\mathrm{.}3$ and the angle is $30.$

A$.$ What is the magnitude of the acceleration of block B$?$ Show all of your work, including defining your system$($s$),$ drawing free body diagram$($s$),$ writing down Newton's $2^{nd}$ law, etc. $(3$ points$)$

B$.$ What is your answer to part A$?(1$ point$)$

C$.$ Briefly explain how you solved part A$.$ In your explanation include whether you decided to treat this as one system or as individual objects and why you made that decision. $(1$ point$)$D$.$ What is the tension in the rope between block C and the right pulley? Show all of your work, including defining your system$($s$),$ drawing free body diagram$($s$),$ writing down Newton's $2^{nd}$ law, etc. $(3$ points$)$

E$.$ What is your answer to part D$?(1$ point$)$

F$.$ Briefly explain how you solved part D$.$ In your explanation include whether you decided to treat this as one system or as individual objects and why you made that decision. $(1$ point$)$