A fisherman rowing his boat on a very small lake throws his anchor into the water. Does the water level of the lake rise, fall or stay the same?
Assuming that the anchor will actually sink and reach the bottom of the very small lake, the water level of the lake will
The anchor, because it sinks, is more dense than the water. While it was in the boat, because the boat was floating an amount of water equal to the weight of the boat plus the weight of the anchor was being displaced. After the anchor is thrown into the water, the weight of the boat plus the volume of the anchor is being displaced, but the volume occupied by the anchor is less than the volume occupied by an amount of water with the weight of the anchor.
More intuitive reasoning:
The boat's going to be riding higher in the water without the anchor in the boat.
Two thinking outside the box answers:
If the very small lake is shaped as a glass of water and there is water all the way up, then the water level will not rise, since any increase in water level will run over. More likely is that the throwing of the anchor (assuming it even fits the lake) will cause splashing, and the water will splash over the edge and by that decreasing the water level.
The boat is touching the bottom of the very small lake. By that, throwing it in will increase the water displacement will not be any different no matter how much you put in the boat.
The following answer is wrong, and I am just leaving it here for anyone who has the same idea.
It depends on the size and weight of the anchor in relation to the size of the boat.
When the anchor is in the boat, water will be displaced by the boat, with the weight of the anchor contributing to this. When the anchor is thrown overboard the boat will displace less water but now the anchor in the water is displacing some. If the anchor is very large and light the water level will rise, if it is small and very heavy it will go down.
The level of water will:
Remain the same
The Archimedes' principle states that "when a body is immersed in a fluid fully or partially in a fluid, the magnitude of the weight of the fluid displaced is equal to the magnitude of the weight of the body". So as the lake was barring the weight of both the anchor and the boat in both the cases, i.e., when the anchor was not yet thrown and the anchor was thrown, the amount of water displaced will remain the same, hence the water level remains the same.