Physics quiz question: Einstein's gravitational constant units

Physics 205A Quiz 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

Einstein's gravitational constant κ is given by the expression[*]:

κ = 8πG/c².

Newton's gravitational constant G is measured in units of kg^–1·m³·s^–2, and the speed of light c² is measured in units of m·s^–1. The units for Einstein's gravitational constant κ are:
(A) kg^–1·m.
(B) kg^–1·m⁴·s^–3.
(C) kg^–1·m²·s^–1.
(D) kg^–1·s^–2.

[*] wki.pe/Einstein%27s_constant.

Correct answer (highlight to unhide): (A)

Starting with the expression for Einstein's gravitational constant κ:

κ = 8πG/c²,

and replacing the quantities in the equation with their kg, m and s units (where the factor of 8π is a dimensionless constant), the units of Κ are:

κ = (kg^–1·m³·s^–2)/(m·s^–1)²,

κ = (kg^–1·m³·s^–2)/(m²·s^–2),

κ = kg^–1·m.

Sections 70854, 70855
Exam code: quiz01D4mP
(A) : 33 students
(B) : 1 student
(C) : 22 students
(D) : 2 students

Success level: 57%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49