Assertion : A simple pendulum inside a satellite orbiting the earth has an infinite time period .
Reason : Time period of simple pendulum varies inversely with `sqrtg`

Options

A. If the 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 both assertion and reason are incorrect

Explanation

To analyze the given assertion and reason, let's break down the problem step by step.

### Step 1: Understand the Assertion
The assertion states that "A simple pendulum inside a satellite orbiting the Earth has an infinite time period."

**Explanation**: In a satellite orbiting the Earth, the satellite and everything inside it, including the pendulum, are in a state of free fall. This means that the effective acceleration due to gravity (g) inside the satellite is zero.

### Step 2: Understand the Reason
The reason states that "The time period of a simple pendulum varies inversely with √g."

**Explanation**: The formula for the time period (T) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \(T\) is the time period,
- \(L\) is the length of the pendulum,
- \(g\) is the acceleration due to gravity.

From this formula, we can see that as \(g\) approaches zero, the time period \(T\) approaches infinity.

### Step 3: Analyze Both Statements
- Since \(g = 0\) inside the satellite, substituting this into the time period formula gives:
\[ T = 2\pi \sqrt{\frac{L}{0}} \rightarrow T = \infty \]
Thus, the assertion is correct.

- The reason correctly states that the time period of a simple pendulum varies inversely with the square root of \(g\), which is also true.

### Step 4: Conclusion
Both the assertion and the reason are correct, and the reason provides a correct explanation for the assertion.

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

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