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

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