Archimedes Principle

To determine the density of the liquid in which the block of wood just floats, we use the principle of flotation. According to this principle, the weight of the fluid displaced by the submerged part of the block is equal to the weight of the block.

Given that the block floats in water with of its volume submerged, the density of water is , and the following relationship holds:

where

• is the density of the block.
• is the volume of the block.
• is the submerged volume of the block, given by .

Thus, the weight balance in water is:

In this case,

Now, when the block floats in a different liquid, such that it just floats, the density of the liquid ( ) equals the density of the block, which is:

Thus, the density of the liquid is 800 kg/m³.