Final answer:
The period of a pendulum will increase when moved from Earth to the Moon due to the Moon's lower acceleration due to gravity (1.63 m/s² compared to Earth's 9.81 m/s²). To find the new to old period ratio, use the square root of the ratio of gravitational accelerations.
Step-by-step explanation:
The period of a pendulum is influenced by the acceleration due to gravity (g). On Earth, this acceleration is approximately 9.81 m/s². If you were to move the pendulum to the Moon, where g is just 1.63 m/s², the period would change. The formula for the period of a simple pendulum is T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. Since g is lower on the Moon, the period would increase.
Now, to find the ratio of the new period on the Moon to the old period on Earth, we must compare the periods with their respective g values. Keeping the length (l) constant and using the formula T = 2π√(l/g), we can obtain the new period by substituting the Moon's g value. As g is smaller on the Moon, the value of √(g) in the denominator of the formula is also smaller, resulting in a larger overall period.
Therefore, if a pendulum has a certain period T on Earth, when moved to the Moon, its new period T' would be longer because the Moon's acceleration due to gravity is significantly less than Earth's. To get the ratio of the periods, one would calculate T'/T = √(g_earth/g_moon).