Question

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is $\rho_i = 0.917 \,g\,cm^{-3}$ ?

• A. 0.917
• B. 1
• C. 0.458
• D. 0

Answer 1

The Correct Option is A

The correct option is(A): 0.917.

When the density of an object is less than the density of the fluid it's placed in (in this case, the iceberg's density is less than the density of water), it will float. The fraction submerged will be equal to the ratio of their densities, which is 0.917 in this case. This means 91.7% of the iceberg's volume is submerged in the water.

Let \(V\) be the total volume of the iceberg and \(V'\) of its volume be submerged into water
Floatation condition weight of iceberg = Weight of water displaced by submerged part by ice
\(V \rho_{i} g=V' \rho_{w} g\)
\(\Rightarrow V' / V=\rho_{i} / \rho_{w}\)
\(=0.917 / 1=0.917\)

Answer 2

When an iceberg floats in water, the fraction of the iceberg submerged can be found by comparing the density of the iceberg to the density of water. The fraction submerged is given by: \[ \text{Fraction submerged} = \frac{\rho_{\text{ice}}}{\rho_{\text{water}}} \] Given that the density of ice (\(\rho_{\text{ice}}\)) is 0.917 g/cm\(^3\) and the density of water (\(\rho_{\text{water}}\)) is 1.0 g/cm\(^3\), we can calculate the submerged fraction: \[ \text{Fraction submerged} = \frac{0.917}{1.0} = 0.917 \] Thus, the correct answer is (A) 0.917.