#$6)$ Dr$.$ Sachiko McBride created a glass submarine for her squirrel, named Jackie. Now Jackie could go in the ocean with Dr$.$ McBride when she went scuba diving. The squirrel submarine is spherical in shape with a radius of $18$ cm $($the wall thickness is negligible$).$ A cable is attached to the bottom of submarine so that Dr$.$ McBride can pull the submarine down with her. The density of the seawater is $1\mathrm{.}03$ x ${10}^{3}k\frac{g}{m^3}.$

$($A$)$ Initially this cable is not taught, and there is no net force on the submarine. How large is the buoyant force on the submarine when it floats $($and the cable is not taught$)$ with one third of the original volume submerged?

$($B$)$ Now Dr$.$ McBride pulls the cable and the submarine goes completely under water. Now using the full volume of the submarine, what's the minimum downward pulling force applied by Dr$.$ McBride to the submarine $($Draw FBD$)?$ Consider the submarine doesn't have any acceleration.