A simple pendulum has some time period `T`. What will be the percentage change in its time period if its amplitude is decreased by `5%`

Options

A. `6 %`
B. `3 %`
C. `1.5 %`
D. `0 %`

Explanation

To solve the problem, we need to analyze how the time period of a simple pendulum is affected by changes in amplitude.

### 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,
- \( g \) is the acceleration due to gravity.

2. **Identifying the Role of Amplitude**:
In the formula for the time period, we can see that there is no term for amplitude. This indicates that the time period of a simple pendulum is independent of the amplitude of oscillation, as long as the amplitude is small.

3. **Considering the Change in Amplitude**:
The problem states that the amplitude is decreased by 5%. However, since the time period does not depend on amplitude, this change will not affect the time period.

4. **Calculating the Percentage Change in Time Period**:
Since the time period remains unchanged regardless of the change in amplitude, the percentage change in the time period can be calculated as:
\[ \text{Percentage Change} = \frac{\text{Change in Time Period}}{\text{Original Time Period}} \times 100\% \]
Since the change in time period is 0 (it remains the same), we have:
\[ \text{Percentage Change} = \frac{0}{T} \times 100\% = 0\% \]

5. **Conclusion**:
Therefore, the percentage change in the time period when the amplitude is decreased by 5% is **0%**.

### Final Answer:
The percentage change in the time period is **0%**.