Question

you have two pendulums with cords that are exactly the same length. one is on earth (with an acceleration due to gravity of 9.81 meters/second2) and the other one is on the moon (with an acceleration due to gravity of 1.63 meters/second2). which one will have a longer period?

Answer 1

From  T = 2π√(l/g).

Since the lengths are the same, so that is a constant.

T α 1/√g

So the period T is inversely proportional to the square root of gravity g.

So the one with a bigger gravity g would have a shorter period

and

the one with smaller gravity g would have a longer period.

Therefore the period on the Moon with gravity of 1.63 m/s² would be longer period than that on the Earth with gravity of 9.81 m/s²