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

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 =
`(V_T-V_F)/(V_T)`

=
`1 - (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`

`(V_F)/(V_T) = (\rho_T)/(\rho_F)`

now,

=
`1 -(\rho_T)/(\rho_F)`

a) when ice berg float in the salt water

visible fraction =
`1 -(\rho_T)/(\rho_F)`

visible fraction =
`1 -(917)/(1024)`

visible fraction = 0.10 = 10%

b) when ice berg float in the freshwater

visible fraction =
`1 -(\rho_T)/(\rho_F)`

visible fraction =
`1 -(917)/(998)`

visible fraction = 0.081 = 8.1%