Physics quiz question: Houston Museum of Natural Science pendulum cable length

Physics 205A Quiz 6, fall semester 2014
Cuesta College, San Luis Obispo, CA

"Foucault Pendulum @ Houston Museum of Natural Science"
pincam23
youtu.be/WfqsfMu4VKc

A pendulum set up at the Houston Museum of Natural Science[*] has a mass of 81.6 kg and swings back-and-forth with a period of 8.71 s. Ignore friction/drag. The length of the pendulum cable is:
(A) 5.1 m.
(B) 5.9 m.
(C) 9.6 m.
(D) 19 m.

[*] youtu.be/nB2SXLYwKkM.

Correct answer (highlight to unhide): (D)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass. Since the period T = 8.71 s and gravitational constant g = 9.80 m/s² are known, the length L can then be solved for:

L = g·(T/(2·π))²,

L = (9.80 m/s²)·((8.71 s)/(2·π))² = 18.8514856 m,

or to two significant figures, the length of the pendulum cable is 19 m.

(Response (A) is g·((2·π)/T)²; response (B) is 2·π·√(T/g); response (C) is √(m·g/T).)

Sections 70854, 70855, 73320
Exam code: quiz06eAg7
(A) : 3 students
(B) : 4 students
(C) : 5 students
(D) : 52 students

Success level: 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53