A block of wood is floating in water at `0^@ C`. The temperature of water is slowly raised from `0^@ C` to `10^@ C`. How will the precentage of volume of block above water level change with rise in temperature?

Explanation

To solve the problem of how the percentage of the volume of a wooden block floating in water changes as the temperature of the water is raised from 0°C to 10°C, we can follow these steps:

### Step 1: Understand the Principle of Buoyancy
According to Archimedes' principle, a floating object displaces a volume of fluid equal to the weight of the object. Therefore, the weight of the wood block must equal the weight of the water displaced.

### Step 2: Define Variables
Let:
- \( V \) = total volume of the wooden block
- \( V_{displaced} \) = volume of water displaced by the block
- \( \rho_s \) = density of the wood block
- \( \rho_l \) = density of water

### Step 3: Establish the Relationship
When the block is floating, the weight of the block is equal to the weight of the displaced water:
\[ \rho_s \cdot V \cdot g = \rho_l \cdot V_{displaced} \cdot g \]
Here, \( g \) cancels out, leading to:
\[ \rho_s \cdot V = \rho_l \cdot V_{displaced} \]

### Step 4: Determine the Volume of Water Displaced
The volume of water displaced can be expressed as:
\[ V_{displaced} = V \cdot \frac{\rho_s}{\rho_l} \]

### Step 5: Analyze the Effect of Temperature on Water Density
As the temperature of water increases from 0°C to 10°C:
- At 0°C, the density of water is approximately \( 0.999 \, \text{g/cm}^3 \).
- As the temperature increases to 4°C, the density of water reaches its maximum (around \( 1.000 \, \text{g/cm}^3 \)).
- Beyond 4°C, the density of water decreases. By 10°C, the density is approximately \( 0.998 \, \text{g/cm}^3 \).

### Step 6: Calculate the Change in Volume Above Water
1. **From 0°C to 4°C**: The density of water increases, leading to an increase in the volume of water displaced, which means the block will float lower in the water. Thus, the percentage of the block above water decreases.

2. **From 4°C to 10°C**: The density of water decreases, leading to a decrease in the volume of water displaced. Consequently, the block will float higher, and the percentage of the block above water increases.

### Step 7: Conclusion
- From 0°C to 4°C: The percentage of the volume of the block above the water level decreases.
- From 4°C to 10°C: The percentage of the volume of the block above the water level increases.

### Final Answer
The percentage of the volume of the block above the water level decreases from 0°C to 4°C and then increases from 4°C to 10°C.

---