The relative density (ρr) is the relationship between the density of a substance (ρs), with another density which is taken as reference. For liquids and solids, it is taken as reference the density of water (ρH2O).
ρr = ρ(s)/ρ(H2O)
Another thing is that the weight (W) of a body in a liquid, is the difference between its weight in air and the buoyancy force exerted by the liquid on the body.
W = W(air) – ρgV
ρgV → Buoyant force of the liquid.
ρ → Density of the liquid.
g → Acceleration of gravity.
V → Volume of the body.
So, according to the data, we can write:
W(liq) = W(air) – ρ(liq) gV → ρ(liq) gV = W(air) – W(liq) = 40 – 36.4 = 3.6 N
ρ(liq) = 3.6/gV
W(H2O) = W(air) – ρ(H2O) gV → ρ(H2O) gV = W(air) – W(H2O) = 40 – 36 = 4 N
ρ(H2O) = 4/gV
Applying equation (1), we have:
ρr = ρ(liq)/ρ(H2O) = (3.6/gV)/(4/gV) = 3.6/4
ρr = 0.9
The relative density of the liquid is ρr = 0.9
Relative density of the liquid is its density relative to the water and it can be calculated as a ratio of weight loss of body in liquid to weight loss of body in water.
This can also be written as,
relative density of liquid = `(m_1-m_2)/(m_1-m_3)`
where, m1: weight of body in air
m2: weight of body in liquid and m3 is weight of body in water
hence, relative density of liquid = (40-36.4)/(40-36) = 3.6/4 = 0.9