Physics quiz question: vis viva equation

Physics 205A Quiz 1, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 1.37, 1.39

The orbital speed v of an object (measured in units of m/s) is given[*] by the so-called vis viva equation:

v² = μ·((2/r) – (1/a)).

The orbital radius r and the semi-major axis a of the object are both measured in units of m. The units for the standard gravitational parameter μ of the body being orbited are:
(A) m^–3·s².
(B) m^–1·s².
(C) m·s^–2.
(D) m³·s^–2.

[*] wki.pe/Vis-viva_equation.

Correct answer (highlight to unhide): (D)

Replacing the quantities in the equation with their m and s units, except for the standard gravitational parameter μ:

(m/s)² = μ·((2/m) – (1/m)),

m²·s^–2 = μ·m^–1,

m³·s^–2 = μ.

Sections 70854, 70855, 73320
Exam code: quiz01cH3E
(A) : 6 students
(B) : 13 students
(C) : 11 students
(D) : 46 students

Success level: 61%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.70