Question

What happens if you take a clock from Kentfield up to the top of Mt. Tamalpais? Does it
gain or lose time, or is it unaffected
(a) if your clock is a pendulum clock? Explain.
(b) if your clock keeps time based on the period of up and down oscillations of a mass
on a spring? Explain.
(NOTE TO ANY ASTROPHYSICISTS IN THE CLASS: Ignore gravitational time
dilation, as predicted by Einstein’s general theory of relativity.)


The hint to this question is: In Kentfield, g = 9.80 N/kg. It is just slightly less on top of Mt. Tamalpais where you are
farther from the Earth’s center. To answer this problem, you need to think about how an
object’s period depends on g.

Answer 1

a)

time period of a simple pendulum is given as

is the length of string or the length of pendulum,

so as g on Mt. Tamalpais is less than thatt on kentfield hence Time period on Mountain would be greater than that at the kentfield , hence clock would gain some time.

b) in case of mass + spring system time period of oscillations is given by,

here m is the mass of oscillating object and k is the stiffness constant of spring.

since this expression is independeant of g hence there would be no change in time measured by clock.