The time period of a simple pendulum on a freely moving artificial satellite is

Options

A. Zero
B. 2 sec
C. 3 sec
D. Infinite

Explanation

To determine the time period of a simple pendulum on a freely moving artificial satellite, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Time Period**:
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 Condition in a Satellite**:
In a freely moving artificial satellite, the condition of weightlessness exists. This means that the acceleration due to gravity \( g \) is effectively zero.

3. **Substituting \( g = 0 \) into the Formula**:
If we substitute \( g = 0 \) into the time period formula, we have:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
This expression involves division by zero.

4. **Analyzing the Result**:
Since division by zero is undefined in mathematics, we can interpret this situation. The term \( \sqrt{\frac{L}{0}} \) tends to infinity. Therefore, we conclude that:
\[ T \to \infty \]

5. **Final Conclusion**:
The time period of a simple pendulum on a freely moving artificial satellite is infinite. Thus, the correct answer is option 4.