If length of pendulum is increased by 2%. The time period will

Options

A. increases by 1%
B. decreases by 1%
C. increases by 2%
D. decreases by 2%

Answer

To solve the problem of how the time period of a pendulum changes when its length is increased by 2%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: 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 Change in Length**: The problem states that the length of the pendulum is increased by 2%. This can be expressed mathematically as:
\[ \Delta L = 0.02L \]
where \( \Delta L \) is the change in length.

3. **Calculate the Relative Change in Length**: The relative change in length \( \frac{\Delta L}{L} \) can be expressed as:
\[ \frac{\Delta L}{L} \times 100 = 2\% \]

4. **Determine the Effect on Time Period**: To find the effect on the time period, we need to calculate the relative change in time period \( \frac{\Delta T}{T} \). The formula for the error in the time period due to the change in length is given by:
\[ \frac{\Delta T}{T} \times 100 = \frac{1}{2} \left( \frac{\Delta L}{L} \times 100 \right) \]
Substituting the value we found in step 3:
\[ \frac{\Delta T}{T} \times 100 = \frac{1}{2} \times 2 = 1\% \]

5. **Conclusion**: Therefore, the time period of the pendulum increases by 1%.

### Final Answer:
The time period will increase by 1%.

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