Thought Experiment: Now imagine that you were to dump the iron off the side of the boat, would more water be displaced be when the iron was on the boat or when the iron was dumped overboard and now sits in the bottom of the ocean?

- the iron + boat system displaces more volume than the iron alone

- the system is the iron alone, it displaces the same volume in the boat and the water

Explanation:

The Archimedes principle states that the thrust is equal to the weight of the dislodged liquid.

B = ρ g V

Let us analyze this case the weight of the iron is the same either in the boat or at the bottom of the sea, but the volume that moves from water is greater when it is in the boat, it is already the area of the boat that moves the water, whereby the iron and the boat does not sink.

When the iron is on the surface of the water in displaced volume it is in the iron (V_Iron << V_boat), so in the relation

B - W = m a

The weight of the iron is greater than the thrust and it sinks

two posibilities

Therefore, the iron + boat system displaces more volume than the iron alone

If the system is the iron alone, it displaces the same volume in the boat and the water