Question

The frequency of a simple pendulum is f. If its length is increased by four times, its frequency will become

• A. f/2
• B. 2f
• C. 4f
• D. f/4
• E. f

Hint:

Remember that a longer pendulum swings more slowly. Since frequency is how many times it swings per second, a slower swing means a lower frequency. Specifically, frequency is inversely proportional to the square root of the length.

Answer 1

The Correct Option is A

Concept:
Physics - Simple Pendulum Dynamics.
The time period $T$ is given by $T = 2\pi\sqrt{\frac{L}{g}}$. Since frequency $f = \frac{1}{T}$, the relationship is $f \propto \frac{1}{\sqrt{L}}$.
Step 1: Establish the ratio between frequency and length.
Based on the formula $f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$, we can write the ratio for two different lengths: $$ \frac{f_2}{f_1} = \sqrt{\frac{L_1}{L_2}} $$
Step 2: Substitute the given changes.
The length is increased by four times, so $L_2 = 4L_1$. The initial frequency $f_1 = f$. $$ \frac{f_2}{f} = \sqrt{\frac{L_1}{4L_1}} $$
Step 3: Solve for the new frequency.
$$ \frac{f_2}{f} = \sqrt{\frac{1}{4}} = \frac{1}{2} $$ $$ f_2 = \frac{f}{2} $$