Assertion : The time period of a freely falling pendulum is infinite.
Reason : The effective value of acceleration due to gravity becomes zero.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "The time period of a freely falling pendulum is infinite."
- A pendulum's time period is defined as the time it takes to complete one full oscillation.

2. **Understanding the Reason**:
- The reason states that "The effective value of acceleration due to gravity becomes zero."
- In a freely falling frame (like the pendulum's support), both the pendulum bob and the support are accelerating downwards at the same rate (g).

3. **Analyzing the Effective Gravity**:
- When the pendulum is in free fall, we can analyze it from a non-inertial frame (the frame falling with the pendulum).
- In this frame, the acceleration of the pendulum bob appears to be zero because it is falling with the same acceleration as its support.

4. **Calculating the Time Period**:
- The formula for the time period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g_{\text{effective}}}} \]
- Here, \( L \) is the length of the pendulum, and \( g_{\text{effective}} \) is the effective acceleration due to gravity.

5. **Substituting the Effective Gravity**:
- Since we established that \( g_{\text{effective}} = 0 \) in the case of a freely falling pendulum, substituting this into the formula gives:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
- Dividing by zero leads to \( T \) being infinite.

6. **Conclusion**:
- Since the time period \( T \) is infinite, the assertion is correct.
- The reason correctly explains why the time period is infinite, as it shows that the effective acceleration due to gravity is zero.
- Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and reason are correct, and the reason correctly explains the assertion.

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