Assertion : If a pendulum falls freely, then its time period becomes infinite.
Reason : Free falling body has acceleration, equal to 'g'.

Options

A. Both Assertion and Reason are correct, Reason is the coreect expianation of Assertion
B. Bioth Assertion and Reason are Correct but Reason is not the correct expalnation of Assertion
C. Assetion is correct and Reason is incorrect
D. Assertion is incorrect and Reason is correct

Answer

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

### Step 1: Understand the Assertion
The assertion states that if a pendulum falls freely, then its time period becomes infinite.

- A simple pendulum's time period (T) 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.

### Step 2: Analyze Free Fall Condition
When the pendulum is in free fall, it is accelerating downwards at the same rate as gravity (i.e., \(a = g\)).

- In this case, the effective acceleration due to gravity (denoted as \(g'\)) becomes:
\[ g' = g - a = g - g = 0 \]

### Step 3: Substitute into the Time Period Formula
Now, substituting \(g' = 0\) into the time period formula:
\[ T = 2\pi \sqrt{\frac{L}{g'}} \]
This leads to:
\[ T = 2\pi \sqrt{\frac{L}{0}} \]
Since division by zero is undefined, we can conclude that:
\[ T \rightarrow \infty \]
Thus, the time period of the pendulum becomes infinite when it is in free fall.

### Step 4: Understand the Reason
The reason states that a free-falling body has an acceleration equal to 'g'.

- This is indeed true, as a body in free fall experiences gravitational acceleration, which is \(g\).

### Conclusion
Both the assertion and the reason are correct. The reason correctly explains why the assertion is true.

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

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