A cork of density `0.5gcm^(-3)` floats on a calm swimming pool. The fraction of the cork's volume which is under water is

Options

A. `0%`
B. `25%`
C. `10%`
D. `50%`

Explanation

To solve the problem of finding the fraction of the cork's volume that is submerged in water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Density of the cork, \( \rho_{\text{cork}} = 0.5 \, \text{g/cm}^3 \)
- Density of water, \( \rho_{\text{water}} = 1 \, \text{g/cm}^3 \) (or \( 1000 \, \text{kg/m}^3 \))

2. **Understand the Concept of Buoyancy:**
- When an object floats, the weight of the object is equal to the buoyant force acting on it. This is described by Archimedes' principle.
- The weight of the cork can be expressed as:
\[ W_{\text{cork}} = \rho_{\text{cork}} \cdot V \cdot g \]
where \( V \) is the total volume of the cork.

3. **Express the Buoyant Force:**
- The buoyant force is equal to the weight of the water displaced by the submerged part of the cork:
\[ F_b = \rho_{\text{water}} \cdot V_{\text{submerged}} \cdot g \]
- Here, \( V_{\text{submerged}} \) is the volume of the cork that is submerged in water.

4. **Set Up the Equation:**
- According to the equilibrium condition (weight of the cork = buoyant force):
\[ \rho_{\text{cork}} \cdot V \cdot g = \rho_{\text{water}} \cdot V_{\text{submerged}} \cdot g \]
- The \( g \) cancels out from both sides:
\[ \rho_{\text{cork}} \cdot V = \rho_{\text{water}} \cdot V_{\text{submerged}} \]

5. **Express the Submerged Volume:**
- Rearranging the equation gives:
\[ V_{\text{submerged}} = \frac{\rho_{\text{cork}}}{\rho_{\text{water}}} \cdot V \]

6. **Substitute the Densities:**
- Substitute the values of the densities:
\[ V_{\text{submerged}} = \frac{0.5 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} \cdot V = 0.5 \cdot V \]

7. **Calculate the Fraction Submerged:**
- The fraction of the cork's volume that is submerged is:
\[ \text{Fraction submerged} = \frac{V_{\text{submerged}}}{V} = \frac{0.5 \cdot V}{V} = 0.5 \]

8. **Convert to Percentage:**
- To express this as a percentage:
\[ \text{Percentage submerged} = 0.5 \times 100 = 50\% \]

### Final Answer:
The fraction of the cork's volume which is under water is **50%**.