A piece 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?
A) It goes up
B) it goes down
C) it does not change
D) cannot be determined from the information given
The answer is C.
The total volume of water displaced by a set of one or more objects, floating on water is has a mass equal to the mass of all the objects in the set. It does not matter if the objects are placed one over the other, or if they float separately. In the situation explained in the question, the total weight of the two pieces of wood does not change when instead of being placed on top of each other they are placed separately in the bath tub. Therefore there will be no change in the volume of water displaced, and accordingly no change in the level of water in the bathtub.
Thus option C) is correct.
By the principle of floating the first piece and the second piece together displace water equal to their mass.Since the second piece does not touch water, the first piece is floating on its own and the first piece must be less dense tha water. So when the second piece is taken off, the resulting mass of the floting piece is less than that of earlier and it floats dispelling water equal to the mass of it , the quantum of dispell has reduced. So the water level in the tub goes down.