An iceberg is floating in water. The density of ice in the iceberg is 917 kg `m^(-3)` and the density of water is 1024 kg `m^(-3)`. What percentage fraction of the iceberg would be visible?

Options

A. 0.05
B. 0.1
C. 0.12
D. 0.08

Explanation

To solve the problem of determining what percentage fraction of an iceberg is visible when it is floating in water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
The iceberg is floating in water, and we need to find the fraction of the iceberg that is visible above the water surface.

2. **Define Variables**:
Let:
- \( \rho_{ice} = 917 \, \text{kg/m}^3 \) (density of ice)
- \( \rho_{water} = 1024 \, \text{kg/m}^3 \) (density of water)
- \( V \) = total volume of the iceberg
- \( V_{immersed} = (1 - f) V \) (volume of the iceberg submerged in water)
- \( V_{visible} = f V \) (volume of the iceberg above the water)

3. **Apply the Principle of Buoyancy**:
According to Archimedes' principle, the weight of the water displaced by the submerged part of the iceberg equals the weight of the iceberg itself. This can be expressed as:
\[ \text{Weight of iceberg} = \text{Weight of water displaced} \]
Mathematically, this can be written as:
\[ \rho_{ice} \cdot V \cdot g = \rho_{water} \cdot V_{immersed} \cdot g \]
where \( g \) is the acceleration due to gravity (which cancels out).

4. **Substitute the Expressions**:
Substitute \( V_{immersed} \) into the equation:
\[ \rho_{ice} \cdot V = \rho_{water} \cdot (1 - f) \cdot V \]
Since \( V \) is common on both sides, we can simplify:
\[ \rho_{ice} = \rho_{water} \cdot (1 - f) \]

5. **Rearranging the Equation**:
Rearranging gives:
\[ 1 - f = \frac{\rho_{ice}}{\rho_{water}} \]
Therefore,
\[ f = 1 - \frac{\rho_{ice}}{\rho_{water}} \]

6. **Substituting the Values**:
Now substitute the known densities:
\[ f = 1 - \frac{917}{1024} \]

7. **Calculating the Fraction**:
Calculate \( \frac{917}{1024} \):
\[ \frac{917}{1024} \approx 0.8965 \]
Thus,
\[ f = 1 - 0.8965 = 0.1035 \]

8. **Convert to Percentage**:
To find the percentage of the iceberg that is visible:
\[ \text{Percentage visible} = f \times 100 = 0.1035 \times 100 \approx 10.35\% \]

### Final Answer:
Approximately **10.35%** of the iceberg is visible above the water.