Physics quiz question: partially, fully submerged submarines

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.27, 9.31

Two submarines[*] (same volumes) are either partially or fully submerged in sea water. The __________ submerged submarine experiences a greater buoyant force.
(A) partially.
(B) fully.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] Diagram adapted from "SSBN Typhoon Class (Type 941), Russian Federation," naval-technology.com/projects/ssbn-typhoon-class/ssbn-typhoon-class8.html.

Correct answer (highlight to unhide): (B)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the water density ρ and the gravitational constant g are identical for both submarines. Since the fully submerged submarine displaces more water (has a greater submerged volume) than the partially submerged submarine, the fully submerged submarine will have a greater buoyant force exerted upwards on it. (Subsequently, due to Newton's first law, the upwards buoyant force on each submarine must be balanced by their respective downwards weight forces, such that the fully submerged submarine will also have a greater weight force than the partially submerged submarine.)

Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 11 students
(B) : 34 students
(C) : 7 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42