Final answer:
Placing a pencil midway up the string of a pendulum shortens its effective length, resulting in a shorter period and a lower maximum height on the swing's other side. The pendulum's mass doesn't affect its period, only the length and gravity do. To adjust a pendulum clock's rate in a place with higher gravity, the string should be lengthened.
Step-by-step explanation:
When a pendulum's string is partially blocked by placing a pencil midway, the effective length of the pendulum is shortened. The period of the pendulum, which determines the frequency of its swings, is proportional to the square root of its length. When the effective length of the pendulum is shortened by the obstruction (the pencil), the pendulum will swing with a higher frequency, which means it will complete its swings more quickly. This results in a lower maximum height reached on the other side, assuming there is no additional energy input into the system.
The reason the mass of the bob (a metal ball in this case) does not affect the motion of the pendulum in terms of its period can be explained by the fact that in the formula for the period T = 2π√(L/g), the mass is not a variable—only the length L and acceleration due to gravity g are involved. When you move to a location with a higher acceleration due to gravity, to keep the clock time correct, you would have to lengthen the pendulum, as the period decreases with an increase in gravity, and a longer pendulum would counteract this effect.