Final answer:
Doubling the length of a pendulum results in an a. increase in the period of the swing because the period is proportional to the square root of the pendulum's length.
Step-by-step explanation:
When the length of a pendulum is doubled, the period of the swing increases. This is because the period of a pendulum is proportional to the square root of its length, as given by the formula T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity. Since the student's mass does not affect the period, the period will increase regardless of the mass of the student. Therefore, the answer is a) It increases.
The period of the swing will remain the same when the length from the pivot point to the center of mass is doubled. The period of a swing is determined by the length of the swing and the acceleration due to gravity, not the mass of the student. Increasing the length of the swing will increase the time it takes for one complete swing, while decreasing the length would decrease the period.
For example, if the original period of the swing was 2 seconds, it would still be 2 seconds even if the length is doubled. This is because the increased length is compensated by a decrease in the acceleration due to gravity, resulting in the same period.