Physics quiz question: finding acceleration due to gravity from pendulum

Physics 205A Quiz 6, fall semester 2017
Cuesta College, San Luis Obispo, CA

A "seconds pendulum" is defined to be a pendulum with a period of exactly two seconds[*]. The length of string used to construct this pendulum at the equator was measured to be 0.99065 m during an expedition in 1735[**]. Based on this result, the magnitude of the acceleration due to gravity g at the equator in 1735 was:
(A) 9.6859 m/s².
(B) 9.7773 m/s².
(C) 9.8696 m/s².
(D) 9.9628 m/s².

[*] wki.pe/Seconds_pendulum.
[**] Michael R. Matthews, Time for Science Education: How Teaching the History and Philosophy of Pendulum Motion Can Contribute to Science Literacy, Springer Science & Business Media (2000), p. 147.

Correct answer (highlight to unhide): (B)

The period of a pendulum is given by:

T = 2·π·√(L/g),

Since the period T = 2 s and string length L = 0.99065 m are known, the acceleration due to gravity g can then be solved for:

g = L·((2·π)/T)²,

g = (0.99065 m)·((2·π)/(2 s)/)² = 9.7773235999 m/s²,

or to five significant figures, the acceleration due to gravity is 9.7773 m/s².

(Response (A) is (π·L)²; response (C) is π²); response (D) is π²/L.)

Sections 70854, 70855
Exam code: quiz06Ho0k
(A) : 1 student
(B) : 34 students
(C) : 7 students
(D) : 3 students

Success level: 76%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.82