Physics quiz question: radial acceleration

Physics 5A Quiz 1, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 1.51

[3.0 points.] An object of mass m moving at constant speed v around a circle of radius r has a radial acceleration a = mv^2/r. If the speed is increased 12.0%, by what percentage does the radial acceleration increase?
(A) 1.44%.
(B) 13.6%.
(C) 25.4%.
(D) 29.1%.

Correct answer: (C)
a_1 = m*(v_1)^2/r, and a_2 = m*(v_2)^2/r. With v_2 = 1.120*v_1, then:

a_2/a_1 = (m*(v_2)^2/r)/(m*(v_1)^2/r) = (v_2/v_1)^2 = (1.120*v_1/v_1)^2 = (1.120)^2 = 1.2544,

or an increase of 25.4%, to three significant figures (expressed in percent form).

The incorrect response (A) is 100*(0.12)^2.

Student responses
Sections 0906, 0907
(A) : 16 students
(B) : 4 students
(C) : 23 students
(D) : 0 students