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A container of large uniform cross-section area A resting on a horizontal surface holds two immiscible, non-viscous and incompressible liquids of densities d and 2d, each of height H/2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P0

A homogeneous solid cylinder of length L (L < H/2) and cross-section area A/5 is immersed such that, it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid. Determine:

(i) the density D of the solid.

(ii) the total pressure at the bottom of the container

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(i) As per Archimede’s principle, the buoyant force on a body is equal to the weight of the fluid displaced by the body.

Weight of solid cylinder = L x A/5 x D x g = F↓

F↑ = Buoyant force = weight of liquid displaced

(ii) Pressure at the bottom of the cylinder = Patmosphere + Pdense liquid + Plight liquid

Pressure due to liquid = Force/Area

Pressure due to buoyancy reaction = Buoyancy reaction force/area = (A/5) LDg/A

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