The document describes an object floating first in a fluid with a density of 900 kg/m^3, then 1000 kg/m^3, and finally 1100 kg/m^3. It asks to rank the densities by: a) The magnitude of buoyant force on the object, greatest first (1100, 1000, 900 kg/m^3) b) The amount of fluid displaced by the object, greatest first (900, 1000, 1100 kg/m^3) The buoyant force is equal to the weight of the object and depends on density, while the displaced fluid volume inversely depends on density for equal buoyant forces.

1. An object floats first in fluid of density p(1)=900 kg/m^3, then in a fluid of density p(2)=1000
kg/m^3, and finally in a fluid of density p(3)=1100 kg/m^3.
a) Rank the densities according to the magnitude of the buoyant force on the object, greatest first.
b) Rank the densities according to the amount of fluid displaced by the object, greatest first.
An object floats first in fluid of density p(1)=900 kg/m^3, then in a fluid of density p(2)=1000
kg/m^3, and finally in a fluid of density p(3)=1100 kg/m^3.
a) Rank the densities according to the magnitude of the buoyant force on the object, greatest first.
b) Rank the densities according to the amount of fluid displaced by the object, greatest first.
a) Rank the densities according to the magnitude of the buoyant force on the object, greatest first.
b) Rank the densities according to the amount of fluid displaced by the object, greatest first.
Solution
a)
since the object floats on each liquid hence the amount on buoyant force on object is equal to the
wieght of the object in each case which is constant hence buoyant force in each case would be
the same,
p(1) = p(2) = p(3)
but if the same volume of object is dipped inside the liquid in each case then buoyant force
would be directly proportional to the densities , p(3)>p(2)>p(1)
b)
for equal buoyant force = the wieght of the floating object, the volume displaced would be
inversely proportional to the density,
hence, p(1)>p(2)>p(3).