Question

Statement: The amplitude of an oscillating pendulum decreases gradually with time. Reason: The frequency of the pendulum decreases with time.

• A. Both statement and reason are true and the reason is the correct explanation of the statement
• B. Both statement and reason are true but the reason is not the correct explanation of the statement
• C. Statement is true, but the reason is false
• D. Statement and reason are false

Hint:

In simple harmonic motion, the frequency of oscillation is typically constant unless the damping is large enough to significantly alter the period. The amplitude decreases due to energy loss, not because of a decrease in frequency.

Answer 1

The Correct Option is C

Step 1: Understanding the Statement
The statement is true because, in a damped oscillating pendulum, the amplitude decreases over time due to energy loss (typically due to friction or air resistance).
This results in the pendulum coming to rest eventually.
Step 2: Understanding the Reason
The reason provided is incorrect.
The frequency of an oscillating pendulum remains constant during the damped motion (for small damping), even though the amplitude decreases.
In fact, the frequency of a damped pendulum changes only when damping is significant enough to alter the time period.
Step 3: Conclusion Thus, the statement is true, but the reason is false.