Statement-`1`: Potential energy of water at `0^(@)C` is more than ice at `0^(@)C`.
Statement-`2`: Heat given to melt ice at `0^(@)C` is used up in increasing the potential energy of water molecules formed at `0^(@)C`.

Options

A. Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`
B. Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`
C. Statement -`1` is True , Statement -`2` is False.
D. Statement -`1` is False , Statement -`2` is True.

Answer

To solve the question, we need to analyze both statements regarding the potential energy of water and ice at 0°C and the process of melting ice.

### Step-by-Step Solution:

1. **Understanding Potential Energy**:
- Potential energy is the energy stored in an object due to its position or arrangement. In the case of water and ice, we consider the arrangement of molecules.
- Water molecules are more loosely arranged compared to ice molecules, which are held in a rigid structure.

**Hint**: Think about how the arrangement of molecules affects their energy states.

2. **Analyzing Statement 1**:
- Statement 1 claims that the potential energy of water at 0°C is greater than that of ice at 0°C.
- This is true because when ice melts into water, the structure of the molecules changes from a fixed arrangement (ice) to a more mobile arrangement (water), which corresponds to an increase in potential energy.

**Hint**: Consider the molecular structure of ice versus water and how it relates to energy.

3. **Analyzing Statement 2**:
- Statement 2 states that the heat given to melt ice at 0°C is used to increase the potential energy of the water molecules formed at 0°C.
- This is also true. When ice absorbs heat (latent heat of fusion) to melt, this energy is not used to increase the temperature but rather to change the state from solid to liquid, increasing the potential energy of the water molecules.

**Hint**: Recall the concept of latent heat and how it applies to phase changes.

4. **Conclusion**:
- Both statements are true. Statement 1 is correct, and Statement 2 provides the correct explanation for Statement 1.
- Therefore, the answer is that both statements are true, and Statement 2 is the correct explanation for Statement 1.

**Final Answer**: Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation of Statement 1.