MCAT quiz of the day 13/6/2017
Sphere A of radius R and sphere B of radius 2R both sink in a bathtub. Assuming the density of both spheres is identical, which of the following is the ratio of the buoyant force on sphere A to the buoyant force on sphere B.
A 1:1
B 1:2
C 1:4
D 1:8
Buoyant force is equivalent to the weight of the displaced water, which can be calculated by the density of fluid multiplied by the volume of the fluid displaced multiplied by the acceleration due to gravity (pVg). The buoyant force on sphere A will be p(4/3 * pi * R3)g. The buoyant force on sphere B will be p(4/3 * pi * (2R)3)g = 8p(4/3 * pi * R3)g.
Thus the ratio will be 1:8
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