Question

You have two pendulums with cords that are exactly the same length. One is on Earth (with an acceleration due to gravity of 9.81 meters/second²) and the other one is on the Moon (with an acceleration due to gravity of 1.63 meters/second²). Which one will have a longer period?

a. It is impossible to tell with the information given.
b. They will have the same period because the cords are the same length.
c. The pendulum on Earth will have a longer period.
d. The pendulum on the Moon will have a longer period.

Answer 1

The pendulum on the Moon will have a longer period because the acceleration due to gravity is less on the Moon than on Earth, leading to a slower swing rate for the pendulum given the same length of the cord.

Step-by-step explanation:

The pendulum on the Moon will have a longer period. This is because the period of a pendulum is directly related to the acceleration due to gravity. The formula for the period T of a pendulum is T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. Since both pendulums have the same length but the acceleration due to gravity is less on the Moon, the pendulum on the Moon will have a longer period than the pendulum on Earth.

For example, if we take a pendulum with a certain length and calculate its period on Earth using g = 9.81 m/s², and then do the same calculation for the Moon using g = 1.63 m/s², the result will show a longer period for the pendulum on the Moon. The decrease in the force of gravity on the Moon means that the pendulum takes more time to complete one oscillation.