As the temperature is increased, the period of a pendulum

Options

A. increases as its effective length increases even though its centre of mass still remains at the centre of the bob
B. decreases as its effective length increases even though its centre of mass still remains at the centre of the bob
C. increases as its effective increases due to shifting to centre of mass below the centre of the bob
D. decreases as its effective length remains same but the centre of mass shifts above the centre of the bob

Explanation

To solve the question regarding the effect of temperature on the period of a pendulum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Period of a 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. **Identify the Effect of Temperature on Length**:
As the temperature increases, the materials of the pendulum (like the string or rod) expand. This expansion leads to an increase in the effective length \( L \) of the pendulum.

3. **Analyze the Relationship Between Length and Period**:
Since \( T \) is directly proportional to the square root of the length \( L \), if \( L \) increases, \( T \) will also increase. This is because:
\[ T \propto \sqrt{L} \]
Therefore, as \( L \) increases with temperature, \( T \) will also increase.

4. **Conclusion**:
Based on the analysis, we conclude that the period of the pendulum increases as the temperature increases due to the increase in its effective length.

5. **Select the Correct Option**:
From the options provided, the correct choice is:
- **Option A**: Increases as its effective length increases even though its center of mass still remains at the center of the bob.