Choose the correct statement :-

Options

A. Time period of a simple pendulum depends on amplitude.
B. Time shown by a spring watch varies with acceleration due to gravity g.
C. In a simple pendulum, time period varies linearly with the length of the pendulum.
D. The graph between length of the pendulum and time period is a parabola.

Answer

To solve the question, we need to analyze each of the statements provided and determine which one is correct regarding the properties of a simple pendulum and its time period.

### Step-by-Step Solution:

1. **Understanding the 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 \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Analyzing Statement 1**:
- The first statement claims that the time period of a simple pendulum depends on the amplitude.
- From the formula, we can see that \( T \) does not depend on the amplitude (as it only depends on \( L \) and \( g \)).
- **Conclusion**: This statement is **incorrect**.

3. **Analyzing Statement 2**:
- The second statement claims that the time shown by a spring watch varies with acceleration due to gravity.
- For a spring pendulum, the time period is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- This shows that the time period depends on the mass \( m \) and the spring constant \( k \), but it is independent of \( g \).
- **Conclusion**: This statement is **incorrect**.

4. **Analyzing Statement 3**:
- The third statement claims that the time period varies linearly with the length of the pendulum.
- From the formula, we see that \( T \) is proportional to the square root of \( L \) (i.e., \( T \propto \sqrt{L} \)), not linearly.
- **Conclusion**: This statement is **incorrect**.

5. **Analyzing Statement 4**:
- The fourth statement claims that the graph between the length of the pendulum and the time period is a parabola.
- Since \( T^2 \propto L \), if we plot \( T^2 \) against \( L \), we will get a straight line, but if we plot \( T \) against \( L \), the relationship is quadratic, which gives a parabolic shape.
- **Conclusion**: This statement is **correct**.

### Final Answer:
The correct statement is **Option 4**: The graph between the length of the pendulum and the time period is a parabola.