Physics quiz question: Newton's form of Kepler's third law

Physics 205A Quiz 1, fall semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.37

An equation for the period T (measured in units of s) of a planet is given by the expression:

T² = (4π²·R³)/(G·M).

The orbital radius R is measured in units of m, mass of the sun M is measured in units of kg, and G is a parameter with dimensions. The units for the universal gravitational constant G are:
(A) kg·m³·s^–2.
(B) kg·m^–3·s².
(C) kg^–1·m^–3·s².
(D) kg^–1·m³·s^–2.

Correct answer (highlight to unhide): (D)

Solving for G:

G = (4π²·R³)/(T²·M),

such that its units are:

m³/(s²·kg) = m³·s^–2·kg^–1.

Student responses
Sections 70854, 70855
(A) : 4 students
(B) : 5 students
(C) : 3 students
(D) : 43 students

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.65

Student responses
Section 72177
(A) : 0 students
(B) : 4 students
(C) : 1 student
(D) : 10 students

Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.29