Floating or sinking

Seven things are dropped into a tank of water: cork, pine wood, ice, hard rubber, aluminium, iron and gold. You will make the program decide which float, how much of each floater stays under the surface, and what a spring balance would read for $1\ \text{kg}$ of each sinker held under water.

The idea. A body floats if it is less dense than water, with the fraction $\dfrac{\rho}{\rho_w}$ of its volume under. A sinker of mass $m$ held under water seems to weigh $mg\left(1 - \dfrac{\rho_w}{\rho}\right)$.

Your tasks.

1. Make floats, an array that is True for the things that float.
2. Work out under, the fraction of each one's volume under water (a sinker is all under: $1$).
3. Work out reading, what a balance shows for $1\ \text{kg}$ of each held under water (a floater reads $0$).