Eureka

There is a story that Archimedes, the Greek mathematician, was asked to find out if the new golden crown of the king was made of pure gold, while keeping the crown intact. Sitting in a public bath and thinking about it, Archimedes noticed the displacement of the water caused by sinking his body lower into the water. He suddenly realized that he had found the solution: if the crown was made of pure gold, it should displace the same volume of water as a bar of pure gold with an equal weight. Excited, he jumped out of the bath and ran home shouting "Eureka!" ("I've found it!"), forgetting that he was still naked...

We do not know if the story is true. But we do know that Archimedes discovered the first law of hydrostatics: when a body is immersed in a fluid, it experiences an upward buoyant force which is equal to the weight of the fluid displaced by the immersed part of the body.

Can you solve the following questions, and have your "Eureka!" moments, using this famous law?

In an aquarium filled with water, a block of ice floats. We mark the current water level.

When the ice has molten completely, will the water level be higher, lower, or still the same?




 

Answer:

The upward force, needed to keep a block of ice floating, is equal to the weight of the ice. According to Archimedes, the weight of the ice therefore equals the weight of the displaced water. But when the ice has melted, the weight of the resulting water still equals the original weight of the ice. So the amount of water from the melted ice equals the amount of displaced water.

Conclusion: the water level stays the same.