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What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the iceberg floats in (a) the ocean (salt water, density 1024 kg/m3) and (b) in a river (fresh water, density 998 kg/m3)

Respuesta :

Answer

let Vt be the  total volume of ice berg

V_f be the volume displaced by the ice berg

fraction of visible ice berg

   visible fraction = [tex]\dfrac{V_T-V_F}{V_T}[/tex]

                            = [tex]1 - \dfrac{V_F}{V_T}[/tex]

we know mass of iceberg is equal to the mass of fluid displaced

    [tex]\rho_T V_T = \rho_f V_f[/tex]

    [tex] \dfrac{V_F}{V_T} = \dfrac{\rho_T}{\rho_F}[/tex]

now,

                            = [tex]1 -\dfrac{\rho_T}{\rho_F}[/tex]

a) when ice berg float in the salt water

   visible fraction = [tex]1 -\dfrac{\rho_T}{\rho_F}[/tex]

   visible fraction = [tex]1 -\dfrac{917}{1024}[/tex]

   visible fraction = 0.10 = 10%

b) when ice berg float in the freshwater

   visible fraction = [tex]1 -\dfrac{\rho_T}{\rho_F}[/tex]

   visible fraction = [tex]1 -\dfrac{917}{998}[/tex]

   visible fraction = 0.081 = 8.1%

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