If the density of ice is `0.9gcm^(-3)`, what portion of an iceberg will remain below the surface of water in a sea? (Density of sea water `=1.1gcm^(-3)`)

Answer

To find the portion of an iceberg that remains below the surface of seawater, we can use the principle of flotation. Here's a step-by-step solution:

### Step 1: Identify the given data
- Density of ice (ρ_ice) = 0.9 g/cm³
- Density of seawater (ρ_water) = 1.1 g/cm³

### Step 2: Write the flotation principle
According to the principle of flotation, the ratio of the volume of the submerged part of the body to the total volume of the body is equal to the ratio of the density of the body to the density of the liquid:
\[ \frac{V_{submerged}}{V_{total}} = \frac{\rho_{ice}}{\rho_{water}} \]

### Step 3: Assign variables
Let:
- \( V_{submerged} \) = Volume of the submerged part of the iceberg
- \( V_{total} \) = Total volume of the iceberg

### Step 4: Substitute the known values into the equation
Substituting the densities into the flotation principle:
\[ \frac{V_{submerged}}{V_{total}} = \frac{0.9}{1.1} \]

### Step 5: Simplify the equation
To simplify the fraction:
\[ \frac{0.9}{1.1} = \frac{9}{11} \]
Thus, we have:
\[ \frac{V_{submerged}}{V_{total}} = \frac{9}{11} \]

### Step 6: Interpret the result
This means that \( \frac{9}{11} \) of the iceberg's volume is submerged in the seawater. Therefore, the portion of the iceberg that remains below the surface of the seawater is \( \frac{9}{11} \) of its total volume.

### Final Answer:
Thus, the portion of the iceberg that remains below the surface of the seawater is \( \frac{9}{11} \) or approximately 81.82%.

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