A cube of density 3ρ/4 floats in a liquid of density ρ. A downward force equal to one-fourth of the cube's weight is applied. If the submerged fraction becomes p/16, find p.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

A cube of density 3ρ/4 floats in a liquid of density ρ. A downward force equal to one-fourth of the cube's weight is applied. If the submerged fraction becomes p/16, find p.

G1 Physics · Accepted Answer

Let cube volume be V. Weight=(3/4)ρVg; added force=(1/4)W=(3/16)ρVg. Required buoyancy=(12/16+3/16)ρVg=15ρVg/16. Thus submerged fraction=15/16 and p=15.