A solid aluminum cylinder of length *L*, radius *r* and density *p*_{al} is suspended vertically from a thin wire and slowly lowered into a still lake. Let *z* denote the depth of the bottom of the cylinder. (When *z* < 0 no portion of the cylinder is submerged in water. Note that *z* is assumed here to increase downwards.) Assume that both the mass of the wire and the density of air are negligibly small. Let *p*_{ω} denote the density of water. What is the tension *T* in the wire

a) for *z* __<__ 0?

b) for 0 < *z* < *L*?

c) for *z* __>__ L?

d) Plot *T*(*z*).