STATEMENT-1: The temperature of a metallic rod is raised by a temperature At so that its length becomes double. The value of a (coefficient of linear expansion) is given `(ln2)/(Deltat)` because
STATEMENT-2: Coefficient of linear expansion is defined as `1/l (dl)/(dt)`

Options

A. Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True , Statement-2 is True , Statement-2 is NOT a 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 problem, we need to analyze both statements regarding the coefficient of linear expansion and derive the relationship between the change in length of a metallic rod and the change in temperature.

### Step-by-Step Solution

1. **Understanding the Coefficient of Linear Expansion**:
The coefficient of linear expansion (α) is defined as:
\[ \alpha = \frac{1}{L} \frac{dL}{dT} \]
where \(L\) is the original length, \(dL\) is the change in length, and \(dT\) is the change in temperature.

2. **Initial and Final Lengths**:
Let's denote the initial length of the rod as \(L\). When the temperature is raised by \(\Delta T\), the length of the rod becomes double, i.e., the final length is \(2L\).

3. **Change in Length**:
The change in length (\(dL\)) can be expressed as:
\[ dL = 2L - L = L \]

4. **Substituting into the Coefficient of Linear Expansion Formula**:
Now we can substitute \(dL\) and rearrange the equation:
\[ \alpha = \frac{1}{L} \frac{L}{\Delta T} \]
Simplifying this gives:
\[ \alpha = \frac{1}{\Delta T} \]

5. **Integrating the Coefficient of Linear Expansion**:
To find the relationship between the change in length and temperature, we can integrate:
\[ \alpha \Delta T = \int_{L}^{2L} \frac{dL}{L} \]
The integral of \(\frac{dL}{L}\) from \(L\) to \(2L\) is:
\[ \int_{L}^{2L} \frac{dL}{L} = \ln\left(\frac{2L}{L}\right) = \ln(2) \]
Therefore, we have:
\[ \alpha \Delta T = \ln(2) \]

6. **Final Expression for Coefficient of Linear Expansion**:
Rearranging gives us the expression for the coefficient of linear expansion:
\[ \alpha = \frac{\ln(2)}{\Delta T} \]

### Conclusion
Both statements are correct. Statement 1 provides a specific case of linear expansion, while Statement 2 defines the coefficient of linear expansion. Thus, Statement 2 is a correct explanation for Statement 1.