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If same mass of liquid water and a piec...

If same mass of liquid water and a piece of ice is taken, then why is the density of ice less than that of liquied water ?

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The mass per unit volume (i.e., mass/volume) is called density. Since water on freezing , therefore , volume of ice for the same mass of water is more than liquid water. In other words, density of ice is lower than liquid water and hence ice floats on water.
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