Physics quiz question: speed of light

Physics 205A Quiz 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.25

Light travels at a speed of 3.26 parsecs per year. One year is defined to be 365.242 days. The speed of light in parsecs per second is:
(A) 1.03×10^–7 pc/s.
(B) 6.20×10^–6 pc/s.
(C) 1.49×10^–4 pc/s.
(D) 8.93×10^–3 pc/s.

Correct answer (highlight to unhide): (A)

Relevant conversion factors are:

1 yr = 365.242 d,
1 d = 24 h,
1 h =60 min,
1 min = 60 s.

Then setting up conversion factors such that unwanted units cancel (yr, d, h, min) while desired units remain (pc, s):

3.26 pc/yr = (3.26 pc/yr)·(1 yr/365.242 d)·(1 d/24 h)·(1 h/60 min)·(1 min/60 s) = 1.03305429×10^–7 pc/s,

and since these conversion factors are all definitions (which effectively have an infinite number of significant figures), the number of significant figures in the final result must have the same number (three) of significant figures in the given 3.26 pc/yr quantity, which is then 1.03×10^–7 pc/s.

Sections 70854, 70855, 73320
Exam code: quiz01w34K
(A) : 59 students
(B) : 11 students
(C) : 2 students
(D) : 2 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.44