Density

• Density is the mass per unit volume of a substance.

• The SI unit of density is kg/m³or g/cm³

NB:

1000 kg/m³= 1g/cm³

Density of Regular Solid Object

• The density of regular object can be found easily.

• For example, to measure the density of rectangular block

Procedure: o Measure the mass, m

of the solid o Measure the

volume, v = l x h x b o

Calculate density, ρ

Density of irregular solid Object

 The density of irregular object can be obtained by:-

(a)

Measuring its mass using a triple beam balance or digital

balance

(b)

Determining the volume through the displacement

(immersion) method (c) Dividing the mass by the volume

obtained. That is

Example

1. A stone has a mass of 50 g. When it is totally immersed in water

of volume 60 cm³, the final volume is read 70 cm³. Calculate the

density of the stone.

Solution:

Given: m = 50 g, V_S= 70 – 60 = 10 cm³

The Table showing Densities of Different Substance

Substance Density

(g/cm³)

Substance Density

(g/cm³)

Aluminium 2.7

Silver

Steel

Cork

Ice

10.5

7.9

Copper

Gold

8.3

19.3

7.8

0.2

Iron

0.92

0.8

Lead

11.3

2.5

Alcohol

Milk

Glass

Brass

Mercury

1.03

8.5

Kerosene 1.0

13.6

Fresh

water

1.0

Sea water 1.03

Sand

2.5

Individual task – 2

1. The mass of a solid object with an irregular shape is 80 g. The

solid object is totally immersed in water of volume 60 cm³

containing in a measuring cylinder rises to 80cm³. Calculate the

density of the solid (ANS ρ = 4 g/cm³)

Density of Liquids

It can be determined by using burette or density bottle by the following

steps

• Measure the mass of an empty burette or density bottle, m₁

• Fill the liquid in the burette or density bottle and measure its

mass, m₂

• Calculate the mass of liquid by, m = m₂–m₁

• Either by graduated cylinder or overflow can Measure volume of

liquid, V

• Calculate the density of liquid, ρ

Example:

1. In an experiment to determine the density of liquid. Sophia a form

one student obtained the following results.

Mass of beaker = 500g

Mass of beaker and liquid

= 600g

Volume of liquid, v

Find the density

= 25 cm³.

Solution:

Mass of beaker, m₁= 500 g

Mass of beaker + liquid, m₂= 600 g

gcm^-3

Individual Task – 3

1. A clean dry beaker has mass of 400 g. 112 cm³kerosene is

poured into the beaker with the help of burette. If the mass of the

beaker and kerosene is 500 g, Calculate the density of the

kerosene. (ANS: 흆 = ퟎ. ퟖퟗퟑ g/cm³)

2. The following results were obtained from an experiment:

Mass of an empty dry density bottle = 18.9 g

Mass of bottle full of kerosene = 70.1 g

Volume of kerosene in the bottle = 64.0 cm³

Find the density of kerosene (ANS: 흆 = ퟎ. ퟖ gcm^-3)

Density of Granules

• It is difficult to determine the density of very small and fine

particles such as sand or lead shots. Density bottle is used to

determine the density of granules.

• Procedures:

(i) Find the mass of an empty bottle by a beam balance (m₀)

(ii)Put some sand in the bottle (see diagram (b))

(iii)

Record the mass of the bottle when partly filled with

sand (m₁)

(iv)

Pour water into the bottle until it is full

(v)Record the new mass m₂of the bottle with its contents

(vi)

Record the mass m₃when the density bottle is filled

with water only

(vii) Calculate the density of granules

Given:

Mass sand = m₁– m₀

Mass of water on top of sand = m₂– m₁

Mass of water filling the bottle = m₃– m₀

From:

The volume of sand when the density of water is 1.0 g/cm³will be

g/cm³

Example,

1. Given that

Mass of empty density bottle = 4.0 g

Mass of density bottle with sand = 94g

Mass of density bottle with sand and water = 110g

Mass of density bottle full of water = 70g

Find the density of sand from above

readings Solution:

M₀= 4.0 g

M₁= 94 g

M₂= 110

g M₃=

70 g 흆 =

?

From:

g/cm³

Relative Density of a Substance

• Relative density is the ratio of density of substance to the density

of water.

• It has no SI unit.

• This shows that how many times a substance is denser than

water

OR

Example,

1. An empty density bottle weighs 20g. When full of water it weighs

70g and when full of liquid it weighs 60g. Calculate

(a) The relative density of the liquid

(b) Its density Solution:

M₀= 20 g

M₁= 70 g

M₂= 60 g

From:

g/cm³

∴ 푰풕풔 풅풆풏풔풊풕풚 = ퟎ.ퟖ g/cm³

Individual Task

1. In an experiment to determine the relative density of liquid x, form

one physics students obtained the following results after various

measurements:

Mass of an empty relative density bottle = 15g

Mass of bottle + liquid x = 35g

Mass bottle + water = 40g

Volume of bottle = 25 cm³

Calculate

(a)Density of water in kg/m³

(ANS: 흆_풘= ퟏퟎퟎퟎ kg/m³)

(b)Density of liquid x in kg/m³

(ANS: 흆_푳= ퟖퟎퟎ 풌품/m³)

(c)Relative of liquid x

(ANS: R.D = 0.8)

Application of density and relative density in our daily Life

• It is used to design of various structures like ship, planes etc

• Used to determine density of unknown substance using known

density of another

• Used to select building materials

• Used to design equipment used in swimming and diving