How many Earth minutes have elapsed when the clock face reads 12:31 on the moon?

What is the relationship between the pendulum's period and the moon's gravity in determining the elapsed Earth minutes when the clock face reads 12:31 on the moon?

To determine the number of Earth minutes that have elapsed when the clock face reads 12:31 on the moon, we need to consider the relationship between the pendulum's period and the moon's gravity.

Pendulum Period and Moon's Gravity Relationship

The period (T) of a pendulum is given by the equation:

T = 2π√(L / g)

Where L is the length of the pendulum and g is the acceleration due to gravity.

Given that the pendulum length is 1.0 m and the moon's gravity is 1.62 m/s^2, we can calculate the period of the pendulum on the moon:

T = 2π√(1.0 m / 1.62 m/s^2)

Using this value, we can calculate the number of periods that have elapsed between 12:00 and 12:31:

Number of periods = (31 minutes) / (T)

Finally, to find the number of Earth minutes that have elapsed, we can multiply the number of periods by the period of the pendulum on the moon:

Elapsed time (in Earth minutes) = Number of periods * T

Performing the calculations will give you the number of Earth minutes that have elapsed when the clock face reads 12:31 on the moon.