5. the moon's gravity is one-sixth that of the earth. what is the period of a 0.50 m long pendulum on the moon?

First, we are given that the gravity of moon is 1/6 the gravity of earth.
Knowing that the gravity of earth is 9.8, we can calculate the gravity of moon as follows:
gravity of moon = (1/6) * (9.8) = 1.63334 meter/sec^2

Now, the formula used to calculate the period is as follows:
T = 2*pi* sqrt(L/g) 
where
T is the period we need to calculate
L is the length of pendulum = 0.5 m
g is the gravity = 1.63334 m/sec^2

Substitute with the givens in the equation to get the period as follows:
T = 2*3.14* sqrt(0.5/1.63334)
T = 3.4746 seconds