Question

# Place a glass beaker, partially filled with water, in a sink. The beaker has a mass 390gm and an interior volume of 500cm3. You now start to fill the sink with water and you find, by experiment, that if the beaker is less than half full, it will float; but if it is more than half full, it remains on the bottom of the sink as the water rises to its rim. What is the density of the material of which the beaker is made?

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Solution

## It is given that when the beaker is half full, it will float, that means weight of water and beaker is supported by upthrust. Lets say V is total volume of water displaced in the sink. Mass of water in half filled beaker =250cm3×1gm/cm3=250gmSo applying the law of floatation, we have weight of water and beaker = weight of water displaced in the sink ⇒(390+2501000)×9.8=V×1000×9.8⇒V=640×10−6m3=640cm3So volume of solid mass of beaker =640cm3−500cm3=140cm3And we know the mass of the beaker =390gm⇒Density of beaker =390gm140cm3=2.7857gm/cm3≈2.79gm/cm3

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