Suppose a large rock is on a boat that is floating in a small pond. If the rock is dumped overboard, will the water level of the pond rise, fall, or stay the same? The answer might not be as obvious as it seems. 📸 Stephen Knowles/Getty Images // 🔗
‘Now I Am Become Death, the Destroyer of Worlds.’ The Story of Oppenheimer’s Infamous QuoteWe need this volume because this is the amount the water level in the "pond" rises when the boat is added. It’s literally the definition of displaced water.
Now, let's drop the rock into the water. The boat no longer matters and doesn't displace any water since it doesn't have a mass. Here's the force diagram for just the rock:Since this rock is much smaller than the boat, it displaces less water than when it was on the floating boat. This means that the upwards-pushing buoyancy force is also smaller—and now, it's not a large enough force to balance the downward gravitational force.
With the smaller buoyancy force, there is less displaced water. That means it’s time to reveal the answer to our question: The water level will go down! Are you surprised? People often think the answer is that the water level will rise, because the rock will displace water and force the water level upwards—but they are wrong, and that’s OK. We often base answers on our previous life experiences, and you’ve probably done something like adding marbles to a glass of water to make the level rise. It seems reasonable to imagine that the same thing will happen in this case.
But adding marbles to a glass is different than our boat scenario. Because the marbles are not floating in a boat, they’re not in the water in the first place. They’re probably in your pocket, or something like that—and taking a marble out of your pocket has no impact on the water level. When you plop that marble in the glass, the water has nowhere to go but up, and the water level rises. This is the same thing that would happen if you threw a rock into a pond while standing on the shore.
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