floating cubical block

Question

A cubical block of copper of side $10\ cm$ is floating containing mercury. Water is poured into the vessel so that the coper in the block just gets submerged. The height of the water column is?

Solution goes like :

Let height of water column be $h$, then $$\rho_w gh + \rho_{Hg} g(10-h)=\rho_{Cu} g 10$$

I don't understand this, why are they writing pressure using Mercury?

Comments

Mean to say, mercury will fill the space left after filling of water in the copper block?

Answer 1

I think you have misinterpreted the question.

The copper block is not hollow, it is solid copper. There is nothing inside it except copper. Mercury and water are not poured into the copper block. They are poured into a vessel in which the copper block is able to float.

Initially the copper block is floating inside a vessel (eg a beaker) which contains a layer of liquid mercury at the bottom. Some water is added on top of the mercury, surrounding the copper block, until the water is level with the top of the copper block. Now the copper block is floating in a layer of mercury and a layer of water. The question is asking for the depth of the layer of water.

The words "the copper in the block just gets submerged" in your question should read "the copper block just gets submerged".

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Mercury is a liquid. Water is a liquid. The LHS of your equation gives the pressure in the mercury level with the base of the copper block (neglecting air pressure). The RHS is the pressure due to copper block, which you can think of as another liquid.