Physics quiz question: maximum shear stress

Physics 205A Quiz 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

The maximum shear stress τ (measured in units of kg·m^–1·s^–2) in a round solid bar subject to impact is given by the expression[*]:

τ = 2√(E·S/V).

The change in energy E is measured in units of kg·m²·s^–2, and the volume V of the rod is measured in units of m³. The units for the shear modulus S are:
(A) kg³·m^–3·s^–6.
(B) kg^–3·m^–3·s^–6.
(C) kg·m^–1·s^–2.
(D) (No units, as it is a dimensionless quantity.)

[*] wki.pe/Shear_stress.

Correct answer (highlight to unhide): (C)

The shear modulus S can be expressed as:

S = τ²·V/E,

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

S = (kg·m^–1·s^–2)²·m³/(kg·m²·s^–2),

S = kg²·m^–2·s^–4·m³/(kg·m²·s^–2),

S = kg·m^–1·s^–2.

Sections 70854, 70855, 73320
Exam code: quiz01rdBL
(A) : 13 students
(B) : 4 students
(C) : 55 students
(D) : 8 students

Success level: 69%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45