Physics quiz question: extending length of pendulum string

Physics 205A Quiz 6, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 10.58

A 0.50 kg bob is suspended from a 1.6 m string, forming a pendulum. The period of this pendulum is measured. If the mass of the bob is decreased to 0.25 kg while the length of the string is increased to 3.2 m, the period will change by a factor of:
(A) 1.0.
(B) 1.4.
(C) 2.0.
(D) 4.0.

Correct answer: (B)

For a simple pendulum, the period T is given by:

T = 2·π·sqrt(L/g),

where g is the gravitational acceleration constant, and L is the length of the string attached to the pendulum bob, assumed to be an ideal point mass. Increasing the length by a factor of two will increase the period by a factor of sqrt(2.0) = 1.4.

Student responses
Sections 30880, 30881
(A) : 4 students
(B) : 29 students
(C) : 5 students
(D) : 2 students

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50