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?

Explanation

To determine the percentage fraction of the iceberg that is visible above the water, we can use the principle of buoyancy. Here’s a step-by-step solution:

### Step 1: Understand the buoyancy principle
The buoyant force acting on the iceberg must equal the weight of the iceberg for it to float. The buoyant force is equal to the weight of the water displaced by the submerged part of the iceberg.

### Step 2: Write down the equations
Let:
- \( V \) = total volume of the iceberg
- \( V_s \) = volume of the submerged part of the iceberg
- \( \rho_{ice} \) = density of ice = 917 kg/m³
- \( \rho_{water} \) = density of water = 1024 kg/m³
- \( g \) = acceleration due to gravity (which will cancel out)

The weight of the iceberg can be expressed as:
\[ W_{ice} = V \cdot \rho_{ice} \cdot g \]

The buoyant force can be expressed as:
\[ F_b = V_s \cdot \rho_{water} \cdot g \]

### Step 3: Set the buoyant force equal to the weight of the iceberg
Since the iceberg is floating, we have:
\[ V_s \cdot \rho_{water} \cdot g = V \cdot \rho_{ice} \cdot g \]

### Step 4: Cancel out \( g \)
Since \( g \) appears on both sides, we can cancel it:
\[ V_s \cdot \rho_{water} = V \cdot \rho_{ice} \]

### Step 5: Express the volume of the submerged part
From the equation above, we can express the volume of the submerged part:
\[ V_s = V \cdot \frac{\rho_{ice}}{\rho_{water}} \]

### Step 6: Substitute the known densities
Substituting the known values:
\[ V_s = V \cdot \frac{917}{1024} \]

### Step 7: Calculate the fraction of the iceberg that is submerged
The fraction of the iceberg that is submerged is:
\[ \text{Fraction submerged} = \frac{V_s}{V} = \frac{917}{1024} \]

### Step 8: Calculate the fraction that is visible
The fraction of the iceberg that is visible above the water is:
\[ \text{Fraction visible} = 1 - \text{Fraction submerged} = 1 - \frac{917}{1024} \]

Calculating this gives:
\[ \text{Fraction visible} = \frac{1024 - 917}{1024} = \frac{107}{1024} \]

### Step 9: Convert to percentage
To find the percentage of the iceberg that is visible:
\[ \text{Percentage visible} = \left( \frac{107}{1024} \right) \times 100 \approx 10.43\% \]

### Step 10: Round to the nearest whole number
Rounding this to the nearest whole number gives approximately 10%.

### Final Answer
Thus, the percentage fraction of the iceberg that is visible is approximately **10%**.

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