Density

Density of a substance is the ratio of mass to a volume of a substance.

OR

Density is mass per unit volume of a substance.

Density = \( \frac {mass}{volume}\)

= \( \frac {kilogramme}{m^3}\) = Kgm^-3

Its unit is kgm^-3.

Different materials have different densities as shown;

Determination of Density of a Solid:

(i) Regular Shaped Object: The mass of a regular object is measured with a chemical balance or beam balance and its volume measured by metre rule, Vernier Calliper or micrometre screw gauge, depending on the shape of the body. Applying the formula,

Density = \( \frac {mass}{volume}\)

(ii) Irregular Shaped Object: The volume of the object is determined by displacement method using Eureka can.

The volume of water displaced by suspending the object in the water is equal to the volume of the object.

The Formula for density \( \frac {mass}{volume}\) is used to determine the density of the body.

Relative Density:

Relative density of a substance is the ratio of mass of a given volume of a substance to the mass of an equal volume of water.

Relative density = \( \frac {mass\: of \: substance}{mass \: of \:equal \:volume}\)

Relative density = \( \frac {weight\: of \: substance}{weight \: of \:equal \:volume \: of \: water}\)

(Because mass is directly proportional to the weight of a body)

Relative density = \( \frac {density\: of \: a\:substance}{density \: of \:equal \:volume \: of \: water}\)

Relative density has no unit.

Example 1:

A solid weighs 1.80N in air and 0.90N in a liquid of density 900kgm^-3.

Calculate;
(i) the upthrust of liquid in solid
(ii) the volume of the liquid.

Solution:

(i) Upthrust = Weight in air – weight in liquid

                   = 1.80 – 0.90

                   = 0.90N

(ii) mass = 0.09kg (1kg = 10N) = \( \frac {W}{g} = \frac {0.9}{10}\)

= 0.09kg

  = 90g

Volume of liquid = \( \frac {mass}{density} \\ = \frac {m}{\rho} \\ = \frac{0.09}{900} \)

= 0.0001m³ = 10^-4m³ 

 = 10cm³

Example 2:

A solid material of volume 2 x 10^-5m³ and density 2.5 x 10³kgm³ is suspended from a spring balance with half of the volume of the solid immersed in water. What is the reading on the spring balance? (g = 10ms^-2).

Solution:

Relative density = \( \frac {weight\: of \: substance}{weight \: of \:equal \:volume \: of \: water}\)

Weight = Vρg

            = 2.5 x 10³ x 2.0 x 10^-5 x 10

            = 0.5N

Upthrust in water = weight of water displaced

= Vρg = \( \frac {V}{2} \scriptsize \rho g \)

density f water = 1 x 10³ kgm^-3

 = \(\normalsize \frac {2 \:\times \: 10^{-2}}{2} \scriptsize \: \times \: 1.0 \times 10^3 \: \times \: 10 \)

= 0.1N

Spring balance reading = Weight in air – Upthrust

        = 0.5 – 0.1

        = 0.4N