Final answer:
A pendulum clock's timing depends on gravity. On the Moon, the clock will run slower due to lower gravity, making the hour hand take longer than 12 hours for a full revolution. Adjusting the pendulum's length is used to calibrate the clock's timing.
Step-by-step explanation:
Understanding Pendulum Clocks on the Moon
The operation of pendulum clocks depends on the acceleration due to gravity. On Earth, standard gravity is approximately 9.81 m/s². When a pendulum clock that is accurate on Earth is taken to the Moon, its rate of keeping time will change due to the Moon's lower gravity, which is about 1.63 m/s². The period of a simple pendulum is given by the formula T = 2π√(L/g), where L is the pendulum length and g is the acceleration due to gravity. Therefore, as gravity decreases, the period of the pendulum increases.
To find the time it takes for the clock's hour hand to make one revolution on the Moon, we compare the periods of the pendulum clock on Earth and the Moon. On Earth, the period is such that it matches the time it takes for the hour hand to complete one revolution (12 hours), so the period of the pendulum on the Moon will increase in proportion to the square root of the acceleration due to gravity. Calculating this gives us a longer period on the Moon, and consequently, the hour hand will take more than 12 hours to complete one revolution.
If a pendulum clock gains or loses time, it's often because the length of the pendulum has changed or needs adjustment. If a pendulum clock gains time, it means it's running too fast, and the pendulum is too short. To correct this, the length of the pendulum needs to be increased. Conversely, if the clock runs slow and loses time, the pendulum is too long and needs to be shortened. Adjusting the pendulum's length is the traditional method of calibrating a pendulum clock to keep perfect time.