Final answer:
The length of the pendulum is calculated using the formula for the period of a simple pendulum and the measured time for 16 oscillations. After calculation, the length is found to be approximately 0.65 m, which is not an available answer choice, suggesting a potential error in the provided options or the calculation.
Step-by-step explanation:
The question asks us to calculate the length of a pendulum based on the period of its oscillations and the known acceleration due to gravity. The formula to find the period (T) of a simple pendulum (where T is the time it takes to complete one full oscillation) is given by:
T = 2π√(L/g)
where L represents the length of the pendulum and g is the acceleration due to gravity. To find the length of the pendulum, we first need to calculate the period for one oscillation. Since the student observed 16 complete cycles in 26.0 seconds, the period is 26.0 seconds divided by 16, which gives us:
T = 26.0 s / 16 = 1.625 s
We can now use this period to solve for the length L using the rearranged formula:
L = (T^2 * g) / (4π^2)
By plugging in the values for T (1.625 s) and g (9.80 m/s²), we get:
L = (1.625 s)^2 * 9.80 m/s² / (4π^2)
L ≈ 0.65 m
Since none of the given answer choices matches 0.65 m, there seems to be an error. This answer calculation assumes that the possible choices are exhaustive and correct. Therefore, please recheck the choices or the calculations.