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

Step 1: Recall the formula for time period of a simple pendulum.
The time period 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.
Step 2: Analyze Statement–I.
From the formula, mass of the bob does not appear. Hence, changing the mass of the bob does not affect the time period.
Therefore, Statement–I is false.
Step 3: Analyze Statement–II.
The formula clearly shows that the time period depends only on the length of the pendulum and the acceleration due to gravity.
Therefore, Statement–II is true.
Step 4: Final conclusion.
Statement–I is false and Statement–II is true.