Final answer:
To find the new acceleration due to gravity at the second location, we use the ratio of the two periods and calculate that the new acceleration is approximately 9.810 m/s², which suggests that the correct answer from the given options is 9.80 m/s².
Step-by-step explanation:
The period of a pendulum is related to the acceleration due to gravity (g) and the length of the pendulum (L) by the following formula: T = 2π√(L/g), where T is the period of the pendulum. Using this formula, we can compare the periods at two different locations to determine the change in gravitational acceleration.
Given that the period at the first location with g = 9.80 m/s² is T1 = 2.00000 s, we can write:
T1 = 2π√(L/9.80)
At the new location, the period is T2 = 1.99796 s. We can now set up the ratio of the two periods to find the new acceleration due to gravity (g2):
(T2/T1)² = g1/g2
(1.99796/2.00000)² = 9.80/g2
Calculating this gives us a new acceleration due to gravity at the second location. To find g2, we rearrange:
g2 = 9.80 × (T1/T2)²
g2 = 9.80 × (2.00000/1.99796)²
g2 = 9.80 × 1.00101
g2 = 9.810 m/s²
The closest answer to our calculation is 9.80 m/s² given in the multiple-choice options, as the change is very minor.