Final answer:
To keep correct time when moving to a location with a greater acceleration due to gravity, the pendulum of a clock must be shortened due to the inverse relationship between the length of the pendulum and the period of oscillation.
Step-by-step explanation:
When you move from one city to another where the acceleration due to gravity is slightly greater, and you bring your pendulum clock with you, you will need to shorten the pendulum to keep the correct time. This is because the period of a pendulum, which is the time it takes for one complete oscillation, is determined by the formula T = 2π √(l/g), where T is the period, l is the pendulum length, and g is the acceleration due to gravity. An increased acceleration due to gravity (g) would result in a shorter period if the length (l) remained constant. Therefore, to maintain the correct period, and consequently the correct time-keeping of the clock, the pendulum's length must be reduced.
Pendulum clocks rely on this principle of simple harmonic motion to keep accurate time. The length of the pendulum directly affects its oscillation rate; longer pendulums swing with a longer period, while shorter pendulums swing more quickly. This is also why pendulum clocks can experience changes in timekeeping due to thermal expansion or contraction of the pendulum rod, affecting its length, during different seasons.