Final answer:
The period of a pendulum is determined by its length and the acceleration due to gravity, and is independent of mass. The force of gravity cancels out the effect of mass on the period of a pendulum.
Step-by-step explanation:
The period of a simple pendulum is determined by its length and the acceleration due to gravity. The mass of the ball has no effect on the motion of the pendulum. The period is completely independent of other factors such as mass or amplitude.
One way to understand why mass doesn't affect the period of a pendulum is by considering the forces involved. The only force acting on the pendulum bob is the force of gravity. This force depends on the mass of the bob, but it also depends on the acceleration due to gravity. These two factors cancel each other out, resulting in the same period for pendulums of different masses.
For example, if we have two pendulums with different masses but the same length and are subject to the same acceleration due to gravity, they will have the same period. This can be observed in simple pendulum clocks, which can be finely adjusted to remain accurate.