Physics quiz question: escape velocity constant

Physics 205A Quiz 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

The escape velocity v_e (measured in units of m·s^–1) from the surface of a spherical object of uniform density is given by[*]:

v_e = K·r√ρ.

The radius r is measured in units of m, and the density ρ is measured in units of kg·m^–3. The units for the constant K are:
(A) kg·m^3/2·s².
(B) kg^–1·m^–5/2·s.
(C) kg^–1/2·m^3/2·s^–1.
(D) kg^–1/2·m^–1/2·s^–2.

[*] wki.pe/Escape_velocity#From_the_surface_of_a_body.

Correct answer (highlight to unhide): (C)

Starting with the expression for the escape velocity v_e:

v_e = K·r√ρ,

the constant K can be expressed as:

K = v_e/(r√ρ).

Then replacing the quantities in the equation with their kg, m and s units, the units of K are:

K = m·s^–1/(m·√(kg·m^–3)),

K = m·s^–1/(m·kg^1/2·m^–3/2),

K = kg^–1/2·m^3/2s^–1.

Sections 70854, 70855
Exam code: quiz01CrR4
(A) : 6 students
(B) : 4 students
(C) : 46 students
(D) : 5 students

Success level: 74%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.60