Physics quiz question: finding acceleration due to gravity from pendulum

Physics 205A Quiz 6, fall semester 2019
Cuesta College, San Luis Obispo, CA

The California Academy of Sciences in San Francisco has a pendulum with a period of 6.406 s, consisting of a 106.6 kg ball attached to a 10.20 m long wire hanging from the ceiling. Assume that the ball can be considered a simple point mass. Neglect friction and drag. The magnitude of the acceleration due to gravity g at that location is:
(A) 9.432 m/s².
(B) 9.620 m/s².
(C) 9.808 m/s².
(D) 9.813 m/s².

[*] kathleensf.files.wordpress.com/2008/07/the-foucault-pendulum-at-the-california-academy-of-sciences-december-14-2010.pdf.

Correct answer (highlight to unhide): (D)

The period of a pendulum is given by:

T = 2·π·√(L/g),

Since the period T = 6.406 s and string length L = 10.20 m are known, the acceleration due to gravity g can then be solved for:

T/(2·π) = √(L/g),

(T/(2·π))² = L/g,

g = L·((2·π)/T)²,

g = (10.20 m)·((2·π)/(6.406 s))² = 9.8126439271 m/s²,

or to four significant figures, the acceleration due to gravity is 9.813 m/s².

(Response (A) is (1/L)·((2·π)/T)²; response (B) is 10·((2·π)/T)²); response (C) is 10·((2·π)/T).)

Sections 70854, 70855
Exam code: quiz06co6O
(A) : 1 student
(B) : 5 students
(C) : 9 students
(D) : 37 students

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.44