Question

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)

Answer 1

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 = $\dfrac{V_T-V_F}{V_T}$

                            = $1 - \dfrac{V_F}{V_T}$

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

    $\rho_T V_T = \rho_f V_f$

    $\dfrac{V_F}{V_T} = \dfrac{\rho_T}{\rho_F}$

now,

                            = $1 -\dfrac{\rho_T}{\rho_F}$

a) when ice berg float in the salt water

   visible fraction = $1 -\dfrac{\rho_T}{\rho_F}$

   visible fraction = $1 -\dfrac{917}{1024}$

   visible fraction = 0.10 = 10%

b) when ice berg float in the freshwater

   visible fraction = $1 -\dfrac{\rho_T}{\rho_F}$

   visible fraction = $1 -\dfrac{917}{998}$

   visible fraction = 0.081 = 8.1%