A boat, a lake, a handful of steel marbles. The question seems like a physics one, but the answer depends on something more subtle than simple weight. It is worth thinking about it slowly.
The boat and the marbles in the lake
Riddle statement
You are in a boat in the middle of a lake. Inside the boat is a box full of very heavy steel marbles.
If you throw all the marbles into the water, does the level of the lake rise, fall, or stay the same?
Show solution
Solution
Answer: The water level lowers.
Explanation:
While the marbles are in the boat, their weight causes the boat to displace water. And a floating object displaces exactly the volume of water whose weight equals its own.
That means that, while in the boat, each marble “displaces” an amount of water equivalent to its weight.
When you throw it into the lake, however, the marble no longer floats: it sinks. From that moment on, it only displaces the water corresponding to its own volume.
As steel is much denser than water, the volume of water whose weight is equivalent to that of the marble is greater than the volume of the marble itself. Therefore, a marble in the boat displaces more water than that same marble sunk in the lake.
By throwing them all into the water, the total displacement decreases, and the level of the lake lowers.