Physics quiz question: volume lost by U.S. standard kilogram

Physics 205A Quiz 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 1.29

The U.S. standard kilogram "K4" was set to be exactly one kilogram in 1889, but by 1999 had lost 4.1×10^–5 kg when compared to the international prototype kilogram in Sèvres, France.[*] The "K4" standard is made of Pt‑10Ir, which has a density[**] of 21.5 g/cm³.

The volume lost by the "K4" standard over 110 years compared to the international prototype kilogram is:
(A) 1.9×10^–9 cm³.
(B) 8.9×10^–7 cm³.
(C) 1.9×10^–3 cm³.
(D) 0.89 cm³.

[*] wki.pe/Kilogram.
[**] smt.sandvik.com/en/materials-center/material-datasheets/wire/sandvik-bioline-ptir-alloys/ .

Correct answer (highlight to unhide): (C)

The only relevant conversion factor is 1 kg = 1,000 g. To find volume would require that unwanted units cancel (kg and g) while the desired unit remains (cm³), the only unique way to combine the two given factors (4.1×10^–5 kg, 21.5 g/cm³) to do this would then be:

(4.1×10^–5 kg)/(21.5 g/cm³) = 1.90697674419×10^–6 cm³·(kg/g),

which results in units of cm³ in the numerator, and to eliminate the (kg/g) term:

1.90697674419×10^–6 cm³·(kg/g)·(1,000 g/1 kg) = 1.90697674419×10^–3 cm³,

or to two significant figures is 1.9×10^–3 cm³.

Sections 70854, 70855, 73320
Exam code: quiz01w34K
(A) : 9 students
(B) : 17 students
(C) : 32 students
(D) : 16 students

Success level: 43%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53