The graph between L and `T^(2)` is

Options

A.
B.
C.
D.

Explanation

To determine the relationship between the length of a pendulum (L) and the square of its time period (T²), we can follow these steps:

### Step-by-Step Solution:

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

2. **Square the Time Period Formula**:
To find the relationship between \(L\) and \(T^2\), we square both sides of the equation:
\[ T^2 = (2\pi)^2 \cdot \frac{L}{g} \]
This simplifies to:
\[ T^2 = \frac{4\pi^2}{g} \cdot L \]

3. **Identify the Relationship**:
From the equation \(T^2 = \frac{4\pi^2}{g} \cdot L\), we can see that \(T^2\) is directly proportional to \(L\). This means that as the length \(L\) increases, \(T^2\) also increases.

4. **Graphical Representation**:
When plotting \(T^2\) on the y-axis and \(L\) on the x-axis, the graph will be a straight line. This is because of the direct proportionality established in the previous step.

5. **Conclusion**:
The graph between \(L\) and \(T^2\) will be a straight line, indicating a linear relationship.

### Final Answer:
The graph between \(L\) and \(T^2\) is a straight line.

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