Which has a greater buoyant force on it, a 27.0-cm3 piece of wood floating with part of its volume above water or a 27.0-cm3 piece of submerged iron?

a. the floating wood the submerged iron
b. they have the same buoyant force on them.
c. it is impossible to tell without knowing their weights.

The submerged iron.

Explanation:

Any body submerged in a liquid (it doesn't matter if it is partially or fully submerged) is acted on by an upward force, which is equal to the weight of the volume of liquid removed by the body.

If the wood and the iron have the same volume, but the wood is only in part submerged, the volume of water displaced by the body, will be only equal to the fraction of the total volume submerged.

In the case of the iron, the buoyant force can be expressed as follows:

Fbi  = ρ(H2O) * Viron * g

Now, the volume  actually submerged of the piece of wood, is just a fraction of the total volume (which is equal to the iron volume), so we can write the following equation:

Vw = k* Viron (where k < 1)

If we replace in (1), we have:

Fbw = ρ(H2O) * k*Viron * g

As k < 1, it is clear that Fbi > Fbw.