Information

The ship and the coin

The ship and the coin

We are in a boat on the high seas. We throw a coin from the deck to the sea and this, of course, sinks.

The sea level ... Does it rise, fall or remain the same?

Solution

When the coin is on top of the boat, the dislodged water has the same WEIGHT as the boat plus the coin (so they are in balance). When the coin sinks, the dislodged water equals the WEIGHT of the ship plus the VOLUME of the coin.

The difference in water dislodged between the two cases is that in the first one it is the WEIGHT of the currency and in the second one the VOLUME. As the coin sinks, the weight of the water dislodged by it is less than the weight of the coin, then evicted more water when it was on the ship.

(It can be seen “graphically” in the extreme case of a coin made of an extraterrestrial material that weighs a ton. When it rises on the boat the waterline sinks a lot but if we throw it into the sea the water dislodged is almost not noticeable).

So when you throw the coin the sea level drops (since it evicts less water) and what goes down depends on the density of the metal from which the coin is made, not from the ship.