Question

Find the ratio of the new/old periods of a pendulum if the pendulum were transported from Earth to the Moon, where the acceleration due to gravity is 1.63 m/s².

a) 0.83
b) 1.00
c) 1.22
d) 1.63

Answer 1

The period of a pendulum changes with the acceleration due to gravity. On the Moon, the gravity is less, leading to a lengthened period. Computing the square root of the ratio of gravities on Earth and the Moon (~2.46) yields the new period, indicating the pendulum swings more slowly.

Step-by-step explanation:

To find the ratio of the new to old periods of a pendulum when transferred from Earth to the Moon, we must consider the formula for the period T of a simple pendulum, which is T = 2π√(L/g), where L is the length of the pendulum, and g is the acceleration due to gravity. On Earth, g is approximately 9.81 m/s², whereas on the Moon, it is given as 1.63 m/s².

To compute the ratio Tmoon/Tearth, we can set up the ratio of the two formulas: Tmoon/Tearth = √(gearth/gmoon), which equates to √(9.81/1.63). When calculated, this yields approximately 2.46, indicating that the pendulum will swing more slowly on the Moon.

The correct answer for the ratio of the periods is not provided in the options given. The ratio is approximately 2.46, but for educational purposes, it is important to understand the principles and calculation process involved.