Final answer:
The rate at which a pendulum clock will run on the Moon can be determined by calculating the ratio of the periods on Earth and the Moon. Therefore, it would take approximately 23.84 hours for the clock's hour hand to make one revolution. option (B) is correct.
Step-by-step explanation:
To find the rate at which a pendulum clock will run on the Moon, we need to determine the period of the clock's hour hand on the Moon. The period is the time it takes for a complete revolution. The period of a pendulum clock is determined by the formula:
T = 2π√(l/g)
Where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. On Earth, we assume a value of g = 9.8 m/s², and for the Moon, g = 1.63 m/s². As the length of the pendulum does not change, we can calculate the ratio of the periods as follows:
TMoon/TEarth = √(gEarth/gMoon)
Substituting the given values, we have:
TMoon/TEarth = √(9.8/1.63) ≈ 2.41
Therefore, the time it takes for the clock's hour hand to make one revolution on the Moon is approximately 2.41 times longer than on Earth. Since the hour hand completes one revolution in 24 hours on Earth, on the Moon it would take approximately 2.41 * 24 = 23.84 hours. Rounding to the nearest hour, the answer is 23.84 hours.