Density of ice is `900 kg//m^(3)`. A piece of ice is floating in water of density `1000kg//m^(3)`. Find the fraction of volume of the picec of ice outside the water.

Explanation

To solve the problem of finding the fraction of the volume of a piece of ice that is floating outside of water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data**:
- Density of ice, \( \rho_{\text{ice}} = 900 \, \text{kg/m}^3 \)
- Density of water, \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \)

2. **Understand the Concept of Buoyancy**:
- When an object is floating, the weight of the object is balanced by the buoyant force acting on it. This is known as Archimedes' principle.

3. **Set Up the Equilibrium Condition**:
- Let the total volume of the ice be \( V \).
- Let the volume of the ice submerged in water be \( V_i \).
- The weight of the ice can be expressed as:
\[ \text{Weight of ice} = \text{mass} \times g = \rho_{\text{ice}} \times V \times g \]
- The buoyant force acting on the ice is equal to the weight of the water displaced by the submerged volume:
\[ \text{Buoyant force} = \rho_{\text{water}} \times V_i \times g \]

4. **Equate the Weight and Buoyant Force**:
- Setting the weight of the ice equal to the buoyant force gives us:
\[ \rho_{\text{ice}} \times V \times g = \rho_{\text{water}} \times V_i \times g \]
- The \( g \) cancels out from both sides:
\[ \rho_{\text{ice}} \times V = \rho_{\text{water}} \times V_i \]

5. **Express the Submerged Volume**:
- Rearranging the equation, we find:
\[ V_i = \frac{\rho_{\text{ice}}}{\rho_{\text{water}}} \times V \]

6. **Substitute the Densities**:
- Plugging in the values:
\[ V_i = \frac{900}{1000} \times V = 0.9 V \]

7. **Calculate the Volume Outside the Water**:
- The volume of ice that is outside the water, \( V_o \), can be expressed as:
\[ V_o = V - V_i = V - 0.9 V = 0.1 V \]

8. **Find the Fraction of Volume Outside**:
- The fraction of the volume of ice that is outside the water is given by:
\[ \text{Fraction outside} = \frac{V_o}{V} = \frac{0.1 V}{V} = 0.1 \]

### Final Answer:
The fraction of the volume of the piece of ice that is outside the water is \( 0.1 \) or \( 10\% \).

---