A block of wood is floating on water at `0^@C`, with a certain volume V above water level. The temperature of water is slowly raised from `0^@C`. How will the volume V change with the rise of temperature?

Options

A. V will be unchanged
B. V will decrease from `0^@`C
C. V will decrease till `4^@C` and then increase
D. V will increase till `4^@`C and then decrease

Answer

To solve the problem of how the volume \( V \) of a block of wood floating on water changes as the temperature of the water is raised from \( 0^\circ C \), we can follow these steps:

### Step 1: Understand the Initial Conditions
At \( 0^\circ C \), the block of wood is floating, meaning it displaces a certain volume of water. The volume of water displaced is equal to the weight of the wood block.

**Hint:** Remember that the principle of buoyancy states that the weight of the fluid displaced by the object is equal to the weight of the object itself.

### Step 2: Analyze the Density of Water
As the temperature of water increases from \( 0^\circ C \) to \( 4^\circ C \), the density of water increases. This is an important characteristic of water; it reaches its maximum density at \( 4^\circ C \).

**Hint:** Look at the density-temperature relationship of water, which shows that density increases until \( 4^\circ C \).

### Step 3: Effect of Increasing Density on Volume Displacement
Since the density of water increases as the temperature rises from \( 0^\circ C \) to \( 4^\circ C \), the volume of water displaced by the wood block must also increase to maintain equilibrium (the weight of the displaced water must equal the weight of the wood).

**Hint:** Consider how buoyancy works: as the density of the water increases, the volume of water displaced must also increase to balance the weight of the wood.

### Step 4: Analyze the Situation Beyond \( 4^\circ C \)
Once the temperature exceeds \( 4^\circ C \), the density of water begins to decrease. As the density of water decreases, the volume of water displaced by the wood block will also decrease to maintain equilibrium.

**Hint:** Remember that after \( 4^\circ C \), the relationship between temperature and density of water reverses, leading to a decrease in density.

### Step 5: Conclusion
- From \( 0^\circ C \) to \( 4^\circ C \): The volume \( V \) of the wood block above the water level will **decrease** as more water is displaced due to the increase in water density.
- Beyond \( 4^\circ C \): The volume \( V \) of the wood block above the water level will **increase** as the density of water decreases, leading to less water being displaced.

### Final Answer
The volume \( V \) of the block of wood above the water level will first decrease as the temperature rises from \( 0^\circ C \) to \( 4^\circ C \) and then increase as the temperature rises beyond \( 4^\circ C \).

---