An artisan is building a decorative wall clock that is regulated by a single rigid rod and bob behaving as a simple pendulum. The clock must complete exactly one full oscillation every 1.50s at a location where the local gravitational field strength is 9.80ms−2. Small-angle motion can be assumed.
(a) Calculate the required length of the pendulum so that the clock keeps accurate time at this location. Show all work and include proper units.
(b) After installation, the same clock is moved to a city 2200m above sea level where g is 9.77ms−2. Determine the amount (in millimeters) by which the builder must shorten or lengthen the pendulum to maintain the desired 1.50s period. State clearly whether the pendulum should be made longer or shorter.
(c) If the builder chooses not to adjust the length in part (b), estimate how many seconds the clock will gain or lose in a 24-hour day at the mountain location. Show reasoning.