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
$\rho_i = 0.917 \,g\,cm^{-3}$ ?
- 0.917
- 1
- 0.458
- 0
The Correct Option is A
Approach Solution - 1
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
\(V \rho_{i} g=V' \rho_{w} g\)
\(\Rightarrow V' / V=\rho_{i} / \rho_{w}\)
\(=0.917 / 1=0.917\)
Approach Solution -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.
Approach Solution -3
When an iceberg floats on water, it displaces a volume of water equal to the weight of the iceberg. According to Archimedes' principle, the fraction of the iceberg submerged is given by the ratio of the density of ice to the density of water. Let the density of ice be \( \rho_i \) and the density of water be \( \rho_w \). The fraction of the volume of the iceberg submerged is: \[ \text{Fraction submerged} = \frac{\rho_i}{\rho_w} \] The density of water \( \rho_w \) is approximately \( 1.00 \, \text{g/cm}^3 \), and the density of ice is given as \( \rho_i = 0.917 \, \text{g/cm}^3 \). Substituting the values: \[ \text{Fraction submerged} = \frac{0.917}{1} = 0.917 \] Thus, the fraction of the iceberg submerged is \( 0.917 \).
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Concepts Used:
Viscosity
Viscosity is a measure of a fluid’s resistance to flow. The SI unit of viscosity is poiseiulle (PI). Its other units are newton-second per square metre (N s m-2) or pascal-second (Pa s.) The dimensional formula of viscosity is [ML-1T-1].
Viscosity: Formula
Viscosity is measured in terms of a ratio of shearing stress to the velocity gradient in a fluid. If a sphere is dropped into a fluid, the viscosity can be determined using the following formula:
η = [2ga2(Δρ)] / 9v
Where ∆ρ is the density difference between fluid and sphere tested, a is the radius of the sphere, g is the acceleration due to gravity and v is the velocity of the sphere.
Viscosity: Types
- Dynamic viscosity: When the viscosity is measured directly by measuring force. It is defined as the ratio of shear stress to the shear strain of the motion. Dynamic viscosity is used to calculate the rate of flow in liquid.
- Kinematic viscosity: There is no force involved. It can be referred to as the ratio between the dynamic viscosity and density of the fluid. It can be computed by dividing the dynamic viscosity of the fluid with fluid mass density.
- Laminar flow: Laminar flow is the type of flow in which the fluid moves smoothly or in a regular path from one layer to the next. Laminar flow occurs in lower velocities.