Answer:
Part 1. Pendulum clock is slower.
Part 2. Spring-loaded clock remains the same.
Explanation:
The period of a simple pendulum is given by
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
where [tex]l[/tex] = length of pendulum and [tex]g[/tex] = acceleration due to gravity.
It is seen that the period is inversely proportional to the square root of the gravitational acceleration. So if gravity increases, period decreases and vice versa.
[tex]g[/tex] on the moon is about one-fifth that of the Earth. Hence, the pendulum will have a larger period, about twice ([tex]\sqrt{5}
= 2.24[/tex]). A larger period means it takes longer to finish an oscillation, so the pendulum clock is slower.
The period of a loaded spring is given by
[tex]T=2\pi\sqrt{\dfrac{k}{m}}[/tex]
where [tex]k[/tex] = the spring constant and [tex]m[/tex] = mass of load on the spring.
It is seen that this relation does not depend on gravity nor does it have any parameter that depends on gravity: k is a constant of the spring that does not change while mass is independent of location.
Hence, the spring-loaded clock will remain the same.
As a note, one might assume that gravity affects the loaded spring because the load is 'pushed' down by gravity. In fact, only the equilibrium position is affected by gravity; it only determines where the oscillation starts from, not how long it takes.
