Physics quiz question: buoyant force

Physics 5A Quiz 5, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 9.37, Comprehensive Problem 9.74

[3.0 points.] An aluminum cylinder (of density 2.70 x 10^3 kg/m^3) weighs 8.0 N, and has a volume of 3.0 x 10^(-4) m^3. If the cylinder is suspended from a scale while completely submerged in a fluid, the scale reading is 5.5 N. What is the density of the fluid?
(A) 8.5 x 10^2 kg/m^3.
(B) 1.9 x 10^3 kg/m^3.
(C) 2.7 x 10^3 kg/m^3.
(D) 4.6 x 10^3 kg/m^3.

Correct answer: (A)

From Newton's first law, the upwards bouyant force and tension force must be equal in magnitude to the downwards weight force:

F_B + T = w.

From the definition of the bouyant force, since the object is completely submerged, F_B = rho_fluid*g*Vol, thus:

rho_fluid = (w - T)/(g*Vol).

Choice (B) is T/(g*Vol); choice (B) is w/(g*Vol), which is the density of aluminum; while choice (D) is (w + T)/(g*Vol), which would make the fluid denser than aluminum.

Student responses
Sections 0906, 0907
(A) : 8 students
(B) : 17 students
(C) : 7 students
(D) : 7 students