Time period of pendulum, on a satellite orbiting the earth, is

Options

A. Zero
B. T
C. Infinite
D. `T/sqrt(6)`

Answer

To find the time period of a pendulum on a satellite orbiting the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pendulum's Time Period 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. **Acceleration Due to Gravity in Orbit**:
In a satellite orbiting the Earth, the satellite is in free fall, which means it experiences weightlessness. The effective acceleration due to gravity \( g \) at the altitude of the satellite is essentially zero.

3. **Substituting \( g = 0 \) into the Formula**:
If we substitute \( g = 0 \) into the time period formula:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
This results in an undefined situation because division by zero is not possible.

4. **Understanding the Implication**:
Mathematically, as \( g \) approaches zero, the term \( \sqrt{\frac{L}{g}} \) approaches infinity. Therefore, the time period \( T \) becomes theoretically infinite.

5. **Conclusion**:
Thus, the time period of a pendulum on a satellite orbiting the Earth is:
\[ T = \infty \]

### Final Answer:
The time period of a pendulum on a satellite orbiting the Earth is infinite.