Question

The density of ice is 0.92 g cm^-3 and that of sea water is 1.025 g cm^-3. Find the total volume of an iceberg which floats with its volume 800 cm³ above water. 

Answer 1

Let V be the volume of the iceberg. 

Volume of iceberg above water = 800 cm³ 

Volume of iceberg submerged in water = v 

Density of ice (ρ_ice) = 0.92 g cm^-3

Density of sea water `(ρ_"sea water")` = 1.025 gcm^-3

According to the law of floatation,

`"Volume of immersed part of body"/"Total volume of body" = "Density of body"/"Density of liquid"`

`v/"V" = ρ_"ice"/ρ_"seawater"`

⇒ `v/"V" = 0.92/1.025`

⇒ `v/"V" = 0.92/1.025`

⇒ `v/"V"` = 0.8976

⇒ `v` = 0.89756 V

Now,

∴ Floating Volume of iceberg = V - `v` 

⇒ 800 = V - 0.89756 V 

⇒ 800 = V(1 - 0.89756)

⇒ `800/0.10244` = V

⇒ V = 7809.45 cm³ ≈ 7809.5 cm³