Final answer:
The period of a pendulum becomes √2 times longer if its length is doubled, which means the period is about 1.41 times the original period. None of the provided choices exactly match this result. When the length is decreased by 5%, the period decreases by a moderate amount since it depends on the square root of the new length.
Step-by-step explanation:
The period of a pendulum is given by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. When the length of a pendulum is doubled, its period increases, but not linearly. According to the formula, T is proportional to the square root of L. So, if the length is doubled, the period becomes √2 times longer, which is approximately 1.41 times the original period, not double. Thus, for option (a), the correct answer is not listed among the provided choices, since the period increases by a factor of √2, which is about 1.41. If the length of a pendulum decreases by 5.00%, the period would decrease by a factor that is the square root of 0.95, since a 5% decrease in length means the length is 95% of its original value, or 0.95L.