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In a sporting goods store you see what appears to be two
identical life preservers of the same size. One is filled with
Styrofoam and the other one is filled with lead pellets.
If you submerge these life preservers in the water, upon
which is the buoyant force greater? Upon which is the
buoyant force ineffective? Why are your answers different?

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Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
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Buoyant force acting on a submerged body = weight of the water displaced by it.  Since both life preservers are identical in shape will displace same amount of water when completely submerged and will be subjected to same buoyant force.
However buoyant force on life preserver filled with lead pallets will not be enough to keep it float because density of lead pallets is more than water and its weight will be more than buoyant force. It will be not be an affective life preserver.
Buoyant force = weight of the water displaced = mass of the water displaced x g = Volume of the water displaced X density of the water displaced x g
Weight of the submersed body = mass of body x g = volume of body x density of body x g
Since bodies are completely submersed volume of body = volume of water displaced
Therefore buoyant force acting on body will be proportional to density of water and its weight will be proportional to its density. Since density of lead pallet is more than density of water, buoyant force will be less than its weight and will sink in water.