Question

Statement–I: Time period of a simple pendulum increases if the mass of the bob is increased.
Statement–II: Time period of a simple pendulum depends only on its length and acceleration due to gravity.

• A. Both statements are true
• B. Statement I is true; Statement II is false
• C. Statement I is false; Statement II is true
• D. Both statements are false

Hint:

For a simple pendulum, the time period is independent of the mass and depends only on length and gravitational acceleration.

Answer 1

The Correct Option is C

To solve this problem, we need to evaluate both statements given about the time period of a simple pendulum.

1. Understanding the Concept of a Simple Pendulum:

The time period \(T\) of a simple pendulum 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.

1. Evaluating Statement I:

Statement I claims that the time period increases with an increase in the mass of the bob. This contradicts our established formula which shows the time period does not depend on mass. Hence, Statement I is false.

1. Evaluating Statement II:

Statement II asserts that the time period depends only on its length and acceleration due to gravity. This is precisely what our formula indicates. Therefore, Statement II is true.

Concluding from the evaluation:

• Statement I is false: The time period does not increase with the mass of the bob.
• Statement II is true: The time period depends only on the pendulum's length and the acceleration due to gravity.

Therefore, the correct answer is: Statement I is false; Statement II is true.