How do we define relative density? please give some solved problems of the type - a body floats with 40% of its volume above water and 60% of its volume above oil. find the relative density of the body.

Relative density (also known as specific gravity) is a measure of the density of a material. It is dimensionless, equal to the density of the material divided by some reference density (most often the density of water, but sometimes the air when comparing to gases):

Relative Density = _object / _reference

where  denotes density.

 

Since water's density is 1.0 × 10³ kg/m³ in SI units, the relative density of a material is approximately the density of the material measured in kg/m³ divided by 1000 (the density of water). There are no units of measurement.

Water's density can also be measured as nearly one gram per cubic centimeter (at maximum density) in non-SI units. The relative density therefore has nearly the same value as density of the material expressed in grams per cubic centimeter, but without any units of measurement.

Relative density or specific gravity is often an ambiguous term. This quantity is often stated for a certain temperature. Sometimes when this is done, it is a comparison of the density of the commodity being measured at that temperature, with the density of water at the same temperature. But they are also often compared to water at a different temperature.

 

 

Now to work out for the problems based on relative density then the approach using an example is as follows:

 

Problem) A body floats with 40% of its volume above water. Find the relative density of the body.

 

Solution) Let Volume of the body = V

Density of the body = _b

Density of water = _w

Volume of the body inside the water = 0.6V

Hence, Buoyant force = 0.6V_wg

So, Buoyant force on the body due to water = Weight of the body

or  0.6V_wg = (V_b)g

or _b/_w= 0.6 which is relative density of the body.