Time period of a simple pendulum inside a satellite orbiting earth is

Options

A. zero
B. `oo`
C. `T`
D. `2T`

Answer

To determine the time period of a simple pendulum inside a satellite orbiting the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pendulum in a Satellite:**
- A simple pendulum consists of a mass (bob) attached to a string of length \( L \). When placed inside a satellite that is in orbit around the Earth, the pendulum experiences a unique condition due to the satellite's motion.

2. **Identifying the Forces:**
- Inside the satellite, both the pendulum and the satellite are in free fall. This means that the pendulum does not experience any gravitational force acting on it relative to the satellite. The gravitational force acting on the pendulum (mass \( m \)) is balanced by the centrifugal force due to the satellite's orbital motion.

3. **Acceleration Due to Gravity (g):**
- Normally, the time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- However, inside the satellite, the effective acceleration due to gravity \( g' \) is zero because both the pendulum and the satellite are in free fall.

4. **Calculating the Time Period:**
- Since \( g' = 0 \) inside the satellite, substituting this into the time period formula gives:
\[ T = 2\pi \sqrt{\frac{L}{0}} = \infty \]
- This indicates that the pendulum does not oscillate; it effectively has an infinite time period.

5. **Conclusion:**
- Therefore, the time period of a simple pendulum inside a satellite orbiting the Earth is infinite.

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

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