Final answer:
The length of a pendulum with a period of 1.00 second is approximately 0.250 meters, calculated by rearranging the pendulum period formula and plugging in the known values for period and the acceleration due to gravity.
Step-by-step explanation:
The period T of a simple pendulum is given by the formula T = 2π √(L/g), where L is the length of the pendulum and g is the acceleration due to gravity, which is approximately 9.81 m/s² near the Earth's surface. Given that the period T is 1.00 s, we can rearrange the formula to solve for L as follows:
L = (T/2π)² * g
Plugging in the values:
L = (1.00 s / 2π)² * 9.81 m/s²
L ≈ 0.250 m
Therefore, the length of a pendulum with a period of 1.00 s is approximately 0.250 meters, which corresponds to option (a).