Question

You have two identical pendulums. One is on the Moon where the gravitational acceleration is 1.6 m/s^2, and the other is on Earth where the gravitational acceleration is 9.8 m/s^2. Both pendulums have the same amplitude. Which pendulum has the smallest period? The largest frequency?

Option 1: The Moon pendulum has the smallest period and the largest frequency.
Option 2: The Earth pendulum has the smallest period and the largest frequency.
Option 3: Both pendulums have the same period and frequency.
Option 4: It cannot be determined from the information given.

Answer 1

The Earth pendulum has the smallest period and the largest frequency due to the stronger gravitational acceleration compared to the Moon's. The formula T = 2π√(L/g) shows that a higher gravitational acceleration results in a smaller period and higher frequency for a pendulum.

Thus, Option 2 is correct

Step-by-step explanation:

To determine which pendulum has the smallest period and the largest frequency, we should first understand the relationship between the period T of a pendulum and the gravitational acceleration g. The period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. Since both pendulums have identical lengths and masses, and the only difference is the gravitational acceleration, we can compare their periods and frequencies directly.

Given that the gravitational acceleration on the Moon is lower (1.6 m/s²) compared to Earth (9.8 m/s²), the period of the pendulum on the Moon will be longer and its frequency will be smaller. Therefore,

• The Earth pendulum has the smallest period.
• The Earth pendulum has the largest frequency.

This is because a smaller gravitational acceleration results in a longer period and lower frequency, which makes the pendulum swing slower.

Thus, Option 2 is correct: The Earth pendulum has the smallest period and the largest frequency.