MCAT Physics Question — Buoyant Force
 by
 May 21, 2018
 MCAT Question of the Day
A baseball that lands in a lake (water) experiences a buoyant force of approximately 2N while submerged. A baseball’s mass is specified as 142149g, or 55¼ oz., according to the official rules of baseball. What is the specific gravity of bromine if the same baseball experiences a buoyant force of 6.2N while submerged after landing in an open vat of liquid bromine at a nearby chemical factory?
A. 1.5
B. 3.1
C. 4
D. 40
Click for Explanation
The buoyant force exerted on an object by a fluid is given by the equation F=ρVg, where ρ is the density of fluid displaced by an object, V is the volume of fluid displaced, and g is gravitational acceleration. Specific gravity is the ratio of fluid density to density of water, and the student should know the density of water as 1 g/cm^{3} or 1000kg/m^{3}.
The buoyant force in water is F_{water}=ρ_{water}V_{baseball}g, and the buoyant force in bromine is F_{bromine}=ρ_{bromine}V_{baseball}g. Since specific gravity is ρ_{bromine}/ρ_{water}, and all other variables are constant in the two buoyant force expressions, the specific gravity of bromine for this problem is equal to F_{bromine}/F_{water}. 6.2N/2N equals SG_{bromine}= 3.1.
A. 1.5, incorrect, This is the approximate weight of the baseball in newtons.
B. 3.1, correct.
C. 4, incorrect, This is the buoyant force in bromine divided by the ball’s weight in newtons.
D. 40, incorrect, This is the buoyant force in bromine divided by the ball’s mass in grams.
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