Final answer:
The pendulum with the longest period is the one with the longest length, as the period T of a simple pendulum is determined by the formula T = 2π√(l/g), illustrating that period is proportional to the square root of the pendulum's length.
Step-by-step explanation:
The student has asked, "Other things being equal, the pendulum that has the longest period will be the _______." The pendulum with the longest period will be the one with the longest length. The period T of a simple pendulum is determined by the formula T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity. This shows that the period is directly proportional to the square root of the pendulum's length. It is important to note that the period is independent of other factors such as the mass of the pendulum or its amplitude, provided the amplitude is small (less than about 15°). Therefore, to obtain a pendulum with a longer period, one would need to increase its length.