Apiece of wood is floating in a bathtub. a second piece of wood sits on top of the first piece, and does not touch the water. if the top piece is taken off and placed in the water, what happens to the water level in the tub?

the water level remains same

Explanation:

This can be explained by Archimedes's principle which says that the wood will sink if weight of wood is more than the weight of the water displaced with weight equal to the water displaced otherwise the wood will float.

Therefore, buoyancy or the buoyant force is the same as the weight of wood, the weight of the water displaced by wood is also the same as that of the weight of wood.

Thus, we can see that the weight of the wood remains same and so is the level of water.