Physics quiz question: weights of comparable floaters

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

Two solid objects of different sizes both float with 75% of their volumes below water. It is 
not known whether these objects are made of the same material. The __________ object has a greater weight.
(A) smaller.
(B) larger.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (water) and the gravitational constant g = 9.80 m/s². Since the volume of water displaced by the smaller object is less than the volume of water displaced by the larger object, then the smaller object has a smaller magnitude buoyant force exerted on it.

Newton's first law applies to both objects, as they are stationary, and thus the forces acting on either object must sum to zero.
Since the smaller object has a small upwards buoyant force acting on it, then it must have a correspondingly small downwards weight force acting on it. Similarly, the larger object has a larger buoyant force and a larger weight force acting on it. Thus the larger object has a greater weight than the smaller object.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 1 student
(B) : 32 students
(C) : 4 students
(D) : 12 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.17