A grandfather clock keeps correct time at sea level. If the clock is taken to the top of a nearby mountain,
(a) Would you expect it to keep correct time, run slow, or run fast?
(b) Choose the best explanation from among the following:
I. Gravity is weaker at the top of the mountain, leading to a greater period of oscillation.
II. The length of the pendulum is unchanged, and therefore its period remains the same.
III. The extra gravity from the mountain causes the period to decrease.