Answer: 1.83 cm below the interface
Explanation:
There are three forces acting on the block of wood here:
- The weight of the block, downward, of magnitude
where
is the density of the block (wood)
V is the total volume of the block
is the acceleration due to gravity
- The buoyant force on the part of block immersed in the water, upward, of magnitude
where
is the water density
is the fraction of block immersed in the water
- The buoyant force on the part of block in the oil, upward, of magnitude
where
is the oil density
is the part of block immersed in the oil
Since the block is in equilibrium, we have
We also know that
Since the block is completely immersed in the two liquids; so we can re-arrange the equations and find:
This means that the fraction of volume in water is 0.974 times the fraction of volume in oil.
We also know that the volume of the block in each medium is proportional to the height of the block in each medium, so
(1)
We also know that the total height of the block is
so
And substituting into (1), we find