Measuring the density of an irregularly shaped object b difficult, but useful in

Question

Measuring the density of an irregularly shaped object b difficult, but useful in helping to identify its internal composition. Suppose that a particular rock sample has a mass of 8 20 kg when weighed in air (essentially vacuum). When weighed again while completely submerged under water, its "apparent mass" is 6.18 kg. a. What is the volume of the rock sample ? b. What is the density of the rock sample ? Given that ice has a density of 0.917 and saltwater has a density of 1.025, find the fraction of the volume of any iceberg that floats above the surface

Explanation / Answer

Given

   mass of irregular rock in air m = 8.20 kg

   weighed when completely submerged under the water is ma = 6.18 kg

density of water rho = 1000 kg/m3

  

here the buoyance force = weight

       rho*v*g = mg

       rho *v*g = (m - ma) g

       v = (m-ma)/rho

           = (8.20 - 6.18)/1000 m^3

           = 0.00202 m^3
volume of the rock is V = 0.00202 m^3

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