The graph between L and Tis correctly shown by (Fig. 7.2)

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the graph between the length (L) of a simple pendulum and its time period (T), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Identify the Proportionality**: From the formula, we can deduce that:
\[ T \propto \sqrt{L} \]
This means that the time period \( T \) is directly proportional to the square root of the length \( L \).

3. **Square the Relationship**: To express this relationship in a more graph-friendly format, we can square both sides:
\[ T^2 \propto L \]
This indicates that if we plot \( T^2 \) against \( L \), we should get a straight line.

4. **Graphical Representation**: Since \( T^2 \) is proportional to \( L \), the graph of \( T^2 \) (on the y-axis) versus \( L \) (on the x-axis) will be a straight line passing through the origin.

5. **Identifying the Correct Option**: Based on the options provided in the question, we need to look for a graph that shows a parabolic curve when plotting \( T \) against \( L \). Since \( T \) is proportional to \( \sqrt{L} \), the graph of \( T \) versus \( L \) will be a curve that rises as \( L \) increases, but it will not be a straight line.

6. **Conclusion**: The correct graph will show that as the length \( L \) increases, the time period \( T \) also increases, and the relationship is not linear but rather follows a parabolic shape.

### Final Answer:
The correct graph between \( L \) and \( T \) is the one that shows a curve indicating that \( T \) increases with increasing \( L \), specifically a parabolic curve.