Assertion : The amplitude of an oscillation pendulum decreases gradually with time
Reason : The frequency of the pendulum decrease with time

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the assertion and reason question, we will analyze both the assertion and the reason separately.

### Step 1: Analyze the Assertion
The assertion states: "The amplitude of an oscillating pendulum decreases gradually with time."

- In a real-world scenario, a pendulum experiences damping forces such as air resistance. These forces act against the motion of the pendulum, causing the amplitude of the oscillation to decrease over time.
- Therefore, the assertion is **true**.

### Step 2: Analyze the Reason
The reason states: "The frequency of the pendulum decreases with time."

- The frequency of a simple pendulum is determined by the formula:
\[ f = \frac{1}{2\pi} \sqrt{\frac{g}{L}} \]
where \( g \) is the acceleration due to gravity and \( L \) is the length of the pendulum.
- In this formula, both \( g \) and \( L \) are constants for a given pendulum setup. Therefore, the frequency does not change over time.
- Thus, the reason is **false**.

### Step 3: Conclusion
Since the assertion is true and the reason is false, we can conclude that the correct option is that the assertion is true, but the reason is false.

### Final Answer
- **Assertion**: True
- **Reason**: False
- **Correct Option**: C

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