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62. Problem 15.6E (HRW) A fish maintains its depth in fresh water by adjusting the air content of the porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed fish has a density of 108 g/cm3. We have to find the fraction of the expanded volume that the fish must inflate its air sacs to reduce its density to that of water. |
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Solution: Click For PDF Version Fish change their density by inflating their air sacs and for
floating reduce their density to that of water. Let the volume of a fish with
collapsed air sacs be V. Its density in this condition is
Fractional change in volume that a fish attains for reducing its density to that of water is 8%. |
. Let the
volume of the fish after it has inflated itself be
.
After inflating its volume fish adjusts its density such that it becomes equal
to that of water, which is
. As the
mass of the fish remains unchanged during inflation of volume, we have