Question

When a block of wood is partially submerged in water how is it that Vsubmerged/Vblock =Pblock/Pwater (P stands for density )

Because i read that in my text book and it was not convincing

Answer 1

This is true if the block of wood is just floating in the water, and not being pushed downward by an outside force (other than gravity).

For something to float, it must displace an amount of a liquid equal to it's mass.
\[M_{Displaced} = M_{Object}\]
We also know that an objects mass equals it's density times it's volume. As the object submerges in the water, the volume of liquid that has been displaced is exactly the volume of the submerged portion of the object. And, of course, the liquid is what's being displaced, so we use the density of the liquid.
\[\rho_{Liquid}V_{Submerged}=\rho_{Object}V_{Object}\]
And then we just rearrange the equation.
\[\frac{V_{Submerged}}{V_{Object}} = \frac{\rho_{Object}}{\rho_{Liquid}}\]