An iceberg is floating partly immersed in sea water, the density of sea water is `1.03 g cm^(-3)` and that of ice is `0.92 g cm^(-3)`. The fraction of the total volume of the iceberg above the level of sea water is

Options

A. `8.1 %`
B. `11%`
C. `34%`
D. `0.8%`

Explanation

To find the fraction of the total volume of the iceberg that is above the level of seawater, we can use the principle of buoyancy. Here’s a step-by-step solution:

### Step 1: Understand the problem
We have an iceberg floating in seawater. The density of seawater is given as \( \rho_{water} = 1.03 \, \text{g/cm}^3 \) and the density of ice is \( \rho_{ice} = 0.92 \, \text{g/cm}^3 \). We need to find the fraction of the iceberg's volume that is above the water level.

### Step 2: Define variables
Let:
- \( V \) = total volume of the iceberg
- \( X \) = volume of the iceberg above the water level
- \( V - X \) = volume of the iceberg submerged in water

### Step 3: Apply the principle of buoyancy
According to Archimedes' principle, the weight of the iceberg is equal to the weight of the water displaced by the submerged part of the iceberg. Therefore, we can write:

\[ \text{Weight of the iceberg} = \text{Buoyant force} \]

This can be expressed as:

\[ \rho_{ice} \cdot V \cdot g = \rho_{water} \cdot (V - X) \cdot g \]

Since \( g \) (acceleration due to gravity) is present on both sides, we can cancel it out:

\[ \rho_{ice} \cdot V = \rho_{water} \cdot (V - X) \]

### Step 4: Substitute the densities
Substituting the given densities into the equation:

\[ 0.92 \cdot V = 1.03 \cdot (V - X) \]

### Step 5: Expand and rearrange the equation
Expanding the right side gives:

\[ 0.92 \cdot V = 1.03 \cdot V - 1.03 \cdot X \]

Rearranging the equation to isolate \( X \):

\[ 1.03 \cdot X = 1.03 \cdot V - 0.92 \cdot V \]

\[ 1.03 \cdot X = (1.03 - 0.92) \cdot V \]

\[ 1.03 \cdot X = 0.11 \cdot V \]

### Step 6: Solve for \( X \)
Now, we can solve for \( X \):

\[ X = \frac{0.11}{1.03} \cdot V \]

### Step 7: Find the fraction of the volume above water
The fraction of the volume of the iceberg that is above the water level is given by:

\[ \frac{X}{V} = \frac{0.11}{1.03} \]

### Step 8: Calculate the fraction
Calculating the fraction:

\[ \frac{X}{V} = \frac{0.11}{1.03} \approx 0.1068 \]

### Step 9: Convert to percentage
To find the percentage of the volume above water:

\[ \text{Percentage} = \left(\frac{X}{V}\right) \times 100 \approx 0.1068 \times 100 \approx 10.68\% \]

### Conclusion
Thus, the fraction of the total volume of the iceberg above the level of seawater is approximately \( 10.68\% \).