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 the relationship between the time period of a simple pendulum and its 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 Independence from Amplitude**:
From the formula, we can see that the time period \( T \) depends only on the length \( L \) and the gravitational acceleration \( g \). It does not depend on the amplitude of the pendulum's swing.

3. **Effect of Decreasing Amplitude**:
The problem states that the amplitude of the pendulum is decreased by \( 5\% \). However, since the time period is independent of amplitude, this change in amplitude will not affect the time period.

4. **Calculating the Change in Time Period**:
Since the time period remains constant regardless of the amplitude change, the change in time period \( \Delta T \) is:
\[ \Delta T = 0 \]

5. **Finding the Percentage Change**:
The percentage change in the time period can be calculated using the formula:
\[ \text{Percentage Change} = \left(\frac{\Delta T}{T}\right) \times 100\% \]
Substituting \( \Delta T = 0 \):
\[ \text{Percentage Change} = \left(\frac{0}{T}\right) \times 100\% = 0\% \]

### Final Answer:
The percentage change in the time period of the pendulum when its amplitude is decreased by \( 5\% \) is \( 0\% \).

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