Ncert Exercises & Solutions

Q. 13 An iceberg floats in water with a part of it submerged. What is the fraction of the volume of the iceberg submerged, if the density of ice is $ρ_{i} = 0.917 g {cm}^{- 3} ?$

Hint: Upthrust on the iceberg will be equal to the weight of the water displaced.

Step 1: Find the weight of the water displaced by the iceberg.

Given, the density of ice,

(ρ_{ice}) = 0.917 g / {cm}^{3}

The density of water,

(ρ_{w}) = 1 g / {cm}^{3}

Let V be the total volume of the iceberg and V’ of its volume be submerged in water. In floating condition,

Weight of the iceberg = Weight of the water displaced by the submerged part by ice

{Vρ}_{ice} g = V' ρ_{w} g

Step 2: Find the fraction of volume submerged in the water.

\frac{V'}{V} = \frac{ρ_{ice}}{ρ_{w}} = \frac{0.917}{1} = 0.917 (∵

Weight=mg=v

ρ

g).

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