A piece of ice is floating in a beaker, filled to the brim with water (Fig.). Will the water overflow the rim of the beaker when the ice melts? What will happen if the beaker is filled not with water, but with (1) a liquid denser than water (2) a liquid less dense than water?
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Sol. According to Archimedes' principle the weight of floating ice equals the weight of water displaced by it. Therefore the volume of water which will be formed as the ice melts will be exactly equal to the volume of displaced water and the level of water in the beaker will remain unaltered.
If the beaker contains a liquid denser than water, then as the ice melts the water so formed will have a greater volume than that of the liquid displaced by the ice, and the water will over flow. The reverse will obtain if the liquid is less dense than water and the level will fall.
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