Assertion : The time-period of pendulu, on a satellite orbiting the earth is infinity .
Reason : Time-period of a pendulum is inversely proportional to ` sqrt(g)` .

Options

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

Explanation

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

### Step 1: Understand the Assertion
The assertion states that "The time-period of a pendulum on a satellite orbiting the Earth is infinity."

- In a satellite orbiting the Earth, the effective acceleration due to gravity (g) is zero because the satellite is in free fall. This means that the pendulum does not experience any restoring force to bring it back to its equilibrium position.

### Step 2: Recall 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:
- \( T \) = time period
- \( l \) = length of the pendulum
- \( g \) = acceleration due to gravity

### Step 3: Analyze the Situation in a Satellite
In a satellite orbiting the Earth:
- The value of \( g \) approaches zero.
- Substituting \( g = 0 \) into the formula, we get:
\[ T = 2\pi \sqrt{\frac{l}{0}} \]
This expression tends to infinity, indicating that the time period of the pendulum is indeed infinite.

### Step 4: Understand the Reason
The reason states that "The time-period of a pendulum is inversely proportional to \( \sqrt{g} \)."

- This is correct because, from the formula \( T = 2\pi \sqrt{\frac{l}{g}} \), we can see that as \( g \) decreases, \( T \) increases. Specifically, if \( g \) approaches zero, \( T \) approaches infinity.

### Step 5: Conclusion
Both the assertion and the reason are correct, and the reason correctly explains the assertion. Therefore, the answer to the question is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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