Relative Density | Specific Gravity
Relative density(R.D.) is defined as the ratio of the density of a given substance to the density of pure water at 4°C.
R.D. = density of a given substance/density of pure water at 4°C
R.D. is a unitless and dimensionless positive scalar physical quantity.
Being a dimensionless/unitless quantity R.D. of a substance is same in SI and CGS system.
It is defined as the ratio of the specific weight of a given substance to the specific weight of pure water at 4°C.
Specific gravity = specific weight of a given substance/specific weight of pure water at 4°C
(The specific weight, also known as the unit weight, is the weight per unit volume of a material)
⇒ Specific gravity = ρs×g/ρw×g
or Specific gravity = ρs/ρw
But ρs/ρw is R.D. of a substance
Specific gravity = R.D. of a substance
Thus specific gravity of a substance is numerically equal to the relative density of that substance and for calculation purposes they are used interchangeably.
A hollow metallic sphere has inner and outer radii, respectively, as 5 cm and 10 cm. If the mass of the sphere is 2.5 kg, find (a) density of the material, (b) relative density of the material of the sphere.
The volume of the material of the sphere is
(a) Therefore, density of the material of the sphere
(b) Relative density of the material of the sphere
A body weighs 160 g in air, 130 g in water and 136 g in oil. What is the specific gravity of oil?
Weight in air, Wa = 160g
Weight in water, Ww = 130g = Wa – Bw(Buoyant force by water)
Now, Bw = Volume of the body(V) × density of water(ρw) × g
⇒ 130g = 160g – Vρw g
⇒ Vρw g = 160g – 130g
Vρw g = 30g …..(1)
Again for oil,
Weight in oil, Wo = 136g = Wa – Bo(Buoyant force by oil)
Now, Bo = Volume of the body(V) × density of oil(ρo) × g
⇒ 136g = 160g – Vρo g
⇒ Vρo g = 160g – 136g
Vρo g = 24g …..(2)
Dividing equation (2) by equation (1), we get