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The pressure is measured at the bottom of a cylindrical container with cross-sectional area A that is filled to a height H by a liquid with density rhoL . A cube of volume Vc and density rhoc is placed in the liquid and floats partially submerged, causing a change Δh in the height of the liquid. As a result, the pressure at the bottom of the container increases.

In a coherent, paragraph-length response, describe the relevant forces acting on the cube and the liquid, and explain how they result in the increase in pressure at the bottom of the container.
Write an expression for the pressure at the bottom of the container in terms of H , Δh , and physical constants, as appropriate.
Determine Δh in terms of Vc and other given quantities and physical constants, as appropriate.

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Answer:

Explanation:

As the cube is added in the liquid the weight of the beaker increases hence the pressure at the bottom of the beaker inside the liquid increases

The liquid pressures is P=H\rho _{L} g

When the cube is placed in the liquid it floats in liquid. The cube experiences a Buoyancy, which is equal to the weight of the floating body. The buoyancy is B=A\Delta h\rho _{L} g .

But buoyancy weight of the body B= on equating above two equations

we have \Delta h = Vc\rho _{c}g/A\rho _{L}g = Vc\rho _{c}/A\rho _{L}

The increase in pressure at the bottom is AP Vopcg A A

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