Question

The free-fall acceleration on the moon is 1.62m/s² . What is the length of a pendulum whose period on the moon matches the period of a 1.80-m-long pendulum on the earth?

Answer 1

To find the length of a pendulum on the moon that matches the period of a 1.80 m pendulum on Earth, use the equation period = 2*pi*(sqrt(length/acceleration due to gravity)). Solve for the length using the known period of the pendulum on Earth and the acceleration due to gravity on the moon.

Step-by-step explanation:

In order to find the length of a pendulum on the moon that matches the period of a 1.80 m pendulum on Earth, we can use the formula:

period = 2*pi*(sqrt(length/acceleration due to gravity))

First, we need to find the period of the 1.80 m pendulum on Earth. The formula becomes:

1.80 = 2*pi*(sqrt(1.80/9.8))

Solving for period, we find the period on Earth is approximately 2.869 seconds. Using the same formula, we can find the length of the pendulum on the moon:

2.869 = 2*pi*(sqrt(length/1.62))

Solving for length, we find the length of the pendulum on the moon is approximately 3.049 meters.