Physics quiz question: ratio of sides of increased square area

Physics 205A Quiz 1, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.49

[3.0 points.] The area of a square plot of land is increased by a factor of 1.5. By what factor did the side of this plot change?
(A) 1.2.
(B) 1.3.
(C) 1.5.
(D) 2.3.

Correct answer: (A)

A_new = 1.5*A_old, where A_new = s_new*s_new, and A_old = s_old*s_old. Thus:

(s_new)/(s_old) = sqrt(A_new)/sqrt(A_old) = sqrt(1.5*A_old/A_old) = sqrt(1.5),

which is 1.224744871..., or to two significant figures, 1.2.

Student responses
Sections 70854, 70855
(A) : 25 students
(B) : 3 students
(C) : 19 students
(D) : 5 students

"Difficulty level": 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.7