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Pressure in a fluid-mechanical properties of fluids

A block of wood floats in a liquid with four-fifths of its volume submerged. If the relative density of wood is 0.8, what is the the density of the liquid in units of kg m-3?


Let the volume of the block be Vm3.

Volume of block under liquid =4V5m3

Volume of liquid displaced =4V5m3

Now let the density of the liquid be ρkgm3.

Mass of liquid displaced

= (volume of liquid displaced) x (density of liquid)


Weight of liquid displaced =4V5×ρ×g newton 

Relative density of wood = 0.8

Density of wood =0.8×1000


Mass of the block =800×Vkg

Weight of the block  =800×V×g newton 

From the law of flotation,

Weight of block = weight of liquid displaced


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