Question

Which of the below pendulums will move the slowest, if each one of them is displaced by an angle of \(60 \degree\) from the center?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

The speed of a pendulum's motion is primarily determined by its period, which is influenced by the length of the pendulum. The formula for the period \((T)\) 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.

In problems involving comparing pendulums, we observe that:

• A longer pendulum length \(L\) results in a larger period \(T\), meaning the pendulum will take more time to complete one oscillation and thus move slower.

All pendulums are displaced by the same angle \((60 \degree)\), making the angle of displacement irrelevant in determining which pendulum moves the slowest, because it does not affect \(T\) for small angular displacements. Thus, we only need to compare the lengths of the provided pendulums.

The pendulum depicted in the image with has the longest length. Therefore, it will have the largest period and move the slowest among the pendulums.

Answer 2

A pendulum's speed of swing depends only on how long it takes to complete one back-and-forth motion, and that depends only on the length of the string, not on the angle it is pulled to. A longer string means gravity has to pull the bob through a longer arc for each swing, so it takes more time per swing, that is, it moves more slowly.

The angle mentioned, \( 60 \degree \), is the same for every pendulum, so it plays no role at all in comparing their speeds. All that matters is a direct visual comparison of the string lengths shown in the four pictures.

1. Option A: This pendulum has a noticeably shorter string than option B, so it completes each swing faster and cannot be the slowest one.
2. Option B: This pendulum has the longest string of the four shown. A longer string always means a longer time per swing, so this one swings the slowest.
3. Option C: The string here is shorter than in option B, so this pendulum swings faster than option B.
4. Option D: This string is also shorter than option B's, so it too swings faster.

Since the longest string always gives the slowest swing regardless of the release angle, the pendulum in option B moves the slowest.

the correct answer is Option B.