Assertion : time period of a simple pendulum does not depend on the mass of the bob
Reason : the restoring force is independent of the mass of the bob

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

### Step 1: Analyze the Assertion
The assertion states: "The time period of a simple pendulum does not depend on the mass of the bob."

- The formula for the time period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.
- From this formula, we can see that the time period \( T \) is independent of the mass \( m \) of the bob. Therefore, the assertion is **correct**.

### Step 2: Analyze the Reason
The reason states: "The restoring force is independent of the mass of the bob."

- The restoring force \( F_R \) acting on the bob when it is displaced from its mean position is given by:
\[ F_R = -mg \sin(\theta) \]
where \( \theta \) is the angle of displacement from the vertical.
- In this expression, we can see that the restoring force \( F_R \) is directly dependent on the mass \( m \) of the bob. Therefore, the reason is **incorrect**.

### Step 3: Conclusion
Based on the analysis:
- The assertion is correct.
- The reason is incorrect.

Thus, the correct answer is that the assertion is true, but the reason is false.

### Final Answer
Assertion: True
Reason: False