Question

If 2/3rds of a piece of wood submerges in water and 3/4ths of the same piece of wood submerges in oil. Find the density of the oil.

Answer 1

The fractional part submerged equals the ratio of the density of the material of the block to the density of the liquid.
(Density of floating body / Density of liquid) = fraction submerged.
Fraction of wooden piece submerged in water = 2/3 = 0.67.
As the liquid is water so the ratio of Density of wooden by the density of water gives a relative density of floating wooden pieces.
So, the relative density of the wooden block is 0.67.
The density of water in the SI system = 1000 Kg m^-3.
Density of wood=relative density x density of water =0.67 x 1000 Kg m^-3 =670 kgm.
Fraction of wooden piece submerged in oil = 3/4 = 0.75.
We know the density of wooden piece = 0.67
(Density of floating body / Density of liquid) = fraction submerged.
Relative Density of oil = (Relative Density of wooden block/fraction submerged)
Density of oil = 0.67/0.75 = 0.893.
The density of water in the SI system = 1000 Kg m^-3.
Density of oil =relative density x density of water =0.893 x 1000 Kg m^-3 =893 kgm^-3.