Question

If the frequency of oscillation of a simple pendulum in simple harmonic motion is \( n \), then frequency of oscillation of simple pendulum when length is 4 times is:

• A. \( 4n \)
• B. \( 2n \)
• C. \( n \)
• D. \( \frac{n}{2} \)

Hint:

The frequency of a simple pendulum is inversely proportional to the square root of its length.

Answer 1

The Correct Option is D

Step 1: Frequency of Simple Pendulum.
The frequency of oscillation of a simple pendulum is given by: \[ f = \frac{1}{2\pi} \sqrt{\frac{g}{l}} \] where \( g \) is the acceleration due to gravity, and \( l \) is the length of the pendulum. The frequency is inversely proportional to the square root of the length. Therefore, when the length becomes 4 times, the frequency becomes: \[ f' = \frac{f}{2} \] Step 2: Final Answer.
Thus, the frequency of oscillation will be \( \frac{n}{2} \) when the length is 4 times.