The period t of a pendulum on the moon would be longer than the period of the same pendulum on Earth.
This difference is primarily due to the force of gravity. The acceleration due to gravity on Earth is approximately 9.81 m/s², whereas on the moon, it is only about 1.62 m/s². The period of a simple pendulum 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.
Since the gravitational pull (g) on the moon is significantly weaker, the value of g in the equation is smaller. As a result, when you plug in the values for the moon, the formula yields a larger period T compared to when using the Earth’s gravity. Thus, a pendulum would swing back and forth more slowly on the moon, resulting in a longer period.