This document contains an appeal to contribute to the Prime Minister's or Chief Minister's fund to help fight COVID-19. It discusses density and relative density, providing definitions and examples. It also contains slides on experiments and calculations related to determining density and relative density using Archimedes' principle and other methods. Key terms like density, specific gravity, pyknometer are discussed in detail with examples.

1. Appeal: Please Contribute to Prime Minister’s or Chief
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Density and Relative Density
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara

2. Density
Mass density or density (ρ)of a material is
defined as its mass per unit volume.
Density is an intensive property.
Reciprocal of the density ( volume per unit
mass)of a substance is called its specific
volume
Osmium is the densest known metal
element at standard conditions for
temperature and pressure but not the
densest material.
Dr. Pius Augustine, S H College, Kochi

3. Dr. Pius Augustine, S H College, Kochi

4. Density tells how tightly
matter is crammed together.
The principle of density was
discovered by the Greek
scientist Archimedes.

5. Unit of Density
SI system – Kg m-3.
CGS system – gcm-3.
1kgm-3. = 1000 g
1000000cm3
= 1/1000 g/cm3.
1 gcm-3 = 1000 kgm-3.
Dr. Pius Augustine, S H College, Kochi

6. Read kilogram per
cubic meter, gram per
cubic centimeter etc

7. The density of iron is 7800 kg/m3.
What do you understand by this
statement?
1 m3 of iron will have mass 7800 kg.
Dr. Pius Augustine, S H College, Kochi

8. Variation of density with pressure.
The variance is small for solids
and liquids and much greater
for gasses.
Increasing the pressure on an
object decreases the volume of
the object and therefore
increase its density.
Dr. Pius Augustine, S H College, Kochi

9. Variation of density with temperature
Increasing the temperature of a
substance (with some exceptions)
decreases its density by
increasing the volume (mass
constant) of that substance.
Dr. Pius Augustine, S H College, Kochi

10. • Water contracts from 0oC to 4oC
due to anomalous expansion .
This range of temperature density
increases with temp.
• Max density of water is at 4oC =
1g/cc
Dr. Pius Augustine, S H College, Kochi

11. How can you make oil
sink in water?
Dr. Pius Augustine, S H College, Kochi

12. How is (i) mass, (ii) volume, and (iii)
density of a metallic piece affected,
if at all, with increase in
temperature.
Check the answers by applying your brain.
Ans: (i)unchanged
(ii) increases
(iii) decreases.
Dr. Pius Augustine, S H College, Kochi

13. How does density of water change with temperature?

14. Why don’t we
use water to
contain fire due
to oil?
Dr. Pius Augustine, S H College, Kochi

15. Relative Density or Specific Gravity
Is the ratio of the density (mass of a unit
volume) of a substance to the density of a
given reference material.
Specific gravity usually means relative
density with respect to water. The term
"relative density" is often preferred in
modern scientific usage.
Dr. Pius Augustine, S H College, Kochi

16. • If a substance's relative density is less
than one then it is less dense than the
reference; if greater than 1 then it is
denser than the reference. If the relative
density is exactly 1 then the densities are
equal; that is, equal volumes of the two
substances have the same mass.
Dr. Pius Augustine, S H College, Kochi

17. Relative density (RD) or
specific gravity (SG) is a
dimensionless quantity
it is the ratio of either
densities or weights
Dr. Pius Augustine, S H College, Kochi

18. • Since density of water is 1 g/cc,
Density of a substance in cgs
units and R.D are numerically
equal.
Or
• Density in Kg/m3 = R.D x 1000
Dr. Pius Augustine, S H College, Kochi

19. R.D
= dsubstance / dwater at 4oC .
= mass per unit volume of substance
mass per unit volume of water at 4oC
= mass of certain vol of substance
mass of equal vol of water at 4oC
Dr. Pius Augustine, S H College, Kochi

20. Few Relative densities
• Petrol : 0.8 Ice : 0.92
• Sea water : 1.02 Glycerine : 1.26
• Glass : 2.5 Aluminium : 2.7
• Iron : 7.86 Copper : 8.92
• Silver : 10.5 Mercury : 13.6
• Gold : 19.3 Platinum : 21.5
• Osmium (highest on earth ) : 22.5
Dr. Pius Augustine, S H College, Kochi

21. Name two substances, which
are denser in their liquid states
than their solid state?
Iron and iodine
Dr. Pius Augustine, S H College, Kochi

22. What is the unit of relative
density? Comment.
Dr. Pius Augustine, S H College, Kochi

23. Calculate the mass of a body
whose volume is 2 m3 and
relative density is 0.52. ?
Dr. Pius Augustine, S H College, Kochi

24. Density vs Relaive desity
Defn
Unit
Dr. Pius Augustine, S H College, Kochi

25. Expt 1. RD of insoluble solid heavier than
water . – using Archimedes principle.
Dr. Pius Augustine, S H College, Kochi

26. Find using spring balance and trough of water
Wt of body in air = ( Wair )
= mg = Vbody Dbody g
Wt. of body in water = ( Wwater)
Upthrust = loss of wt in water = wt of water
displaced ( Archimedes’ principle)
= Wair – Wwater = Vbody dwater g
Wair / upthrust = Vbody Dbody g = R.D solid
Vbody dwater g
Dr. Pius Augustine, S H College, Kochi

27. Expt 2. RD of solid soluble in water – using
Archimedes principle.
Liquid not
water
Dr. Pius Augustine, S H College, Kochi

28. Find using spring balance and trough of liquid of known RD.
Wt of body in air = ( Wair )
= mg = Vbody Dbody g
Wt. of body in liquid = ( Wwater)
Upthrust = loss of wt in liquid = wt of liquid
displaced ( Archimedes’ principle)
= Wair – Wliquid = Vbody dliquid g
Wair / upthrust = Vbody Dbody g = Dbody / Dliq
Vbody dliquid g
R.D of body = Dbody x R.D of liquid
Dliquid
Dr. Pius Augustine, S H College, Kochi

29. Dr. Pius Augustine, S H College, Kochi

30. Using physical balance note the following
Wt. of sinker (heavier than water)
in water = WSW
Wt. of (sinker in water + cork in air) = WSWCA
Wt. of sinker and cork in water = WSWCW
Dr. Pius Augustine, S H College, Kochi

31. Wt. of light body in air
= WSWCA – WSW = WCA.
Wt. of body in water
= WSWCW – WSW = WCW.
Loss of wt of body in water
= WCA - WCW.
= WSWCA -WSWCW
Dr. Pius Augustine, S H College, Kochi

32. Describe an experiment, using
Archimedes’ principle, to find
the relative density of a solid
(say, cork) which floats on
water.
Dr. Pius Augustine, S H College, Kochi

33. Will the weight of an iron sinker
plus cork combination in water
be more or less than that of
the iron sinker alone in water?
Give reason.
Dr. Pius Augustine, S H College, Kochi

34. A dead body floats in water with its
head immersed in water. Why?
Volume increases as the dead
body decays.
Become lighter than water and
floats up.
Head being heavy cannot
displace water more than its
own weight. Dr. Pius Augustine, S H College, Kochi

35. Density of mixture of liquids - 1
• Two liquids of densities ρ1 and ρ2, masses m1 and m2
mixed .
• Density of mixture ρ =
(m1 + m2 ) / (V1 + V2)
= (m1 + m2 )
[ (m1 / ρ1) + (m2 / ρ2) ]
If m1 = m2, ρ = 2 ρ1 ρ2 / (ρ1 + ρ2 )

36. Density of mixture of liquids - 2
• Two liquids of densities ρ1 and ρ2, having
volumes V1 and V2 mixed
Density of mixture ρ
= (m1 + m2 ) / (V1 + V2)
= (ρ1 V1 + ρ2 V2 )
(V1 + V2)
If V1 = V2, ρ = (ρ1 + ρ2) / 2

37. A solid body weight 2.10 Nin air.
Its relative density is 8.4. How
much will the body weigh if
palced (i) in water (ii) in a
liquid of relative density 1.2 ?
Dr. Pius Augustine, S H College, Kochi

38. Check your answer
(i)
R.D = W/(W-W1) W1 – wt. in water.
8.4 = 2.1/(2.1-W1)
W1 = 1.85 N
(ii) Upthrust due to water = 2.10-1.85 = 0.25N
Upthrust due to liquid = 0.25 x 1.2 = 0.30 N
Wt. in liquid = 2.10 – 0.30 = 1.8 N
Dr. Pius Augustine, S H College, Kochi

39. Variation in density with expansion
Density is inversely proportional to volume
ρ α 1/V
ρ‘/ρ = V/V’ = V/(V+dV)
= V/(V+Vγ∆T)
= 1 / (1+γ∆T)
ρ‘ = ρ/ (1+γ∆T)
γ – coefficient of volume expansion
Dr. Pius Augustine, S H College, Kochi

40. Dr. Pius Augustine, S H College, Kochi

41. A body of volume 100 cm3
weighs 1 kgf in air. Find (i)
weight in water and (ii) its
relative density.
Dr. Pius Augustine, S H College, Kochi

42. Check your answer
Upthrust = Volume x density of liquid x g
= 100 x 1
= 100 gf = W – W1 = loss of wt. in water
(i) W1 = 1000 – 100 = 900 gf
(ii) R.D = Wt. in air/ loss of wt. in water
= 1000/100 = 0.9
Dr. Pius Augustine, S H College, Kochi

43. A body of mass 70 kg, when completely
immersed in water, displaces 20,000 cm3 of
water. Find the relative density of material of
the body.
Mass = 70 kg = 70000 g
Wt. = 70000 gf.
R.D. = 70000 gf/(vol in cm3 x density in cgs) gf
= 70000 gf/(20000x1) gf
= 3.5
Dr. Pius Augustine, S H College, Kochi

44. A solid weighs 32 gf in air and
28.8 gf in water. Find the
volume and R.D of the solid.
Find how much it will weigh in
a liquid of density 0.9 g/cc.
Dr. Pius Augustine, S H College, Kochi

45. Check your answer
Upthrust in gf = (volume in cm3 x density in cgs)
in gf = 32 - 28.8 = 3.2 gf.
Since the liquid used is water , density = 1 in cgs
So, volume = 3.2 cm3.
R.D = 32/32-28.8 = 32/3.2 = 10
Upthrust in gf = (volume in cm3 x density in cgs)
So in new liquid,
Upthrust = 3.2 x 0.9 = 2.88 gf
So Wt. in new liquid = 32-2.88 =29.12 gf

46. A jeweller claims that he makes ornament of pure
gold that has a relative density of 19.3. He sells a
bangle weighing 25.25 gf to a person. The clever
customer weighs the bangle when immersed in
water and finds that it weights 23.075 gf in
water. With the help of suitable calculations find
out if the ornament is made of pure gold or not.
Hint: If you calculate R.D, from the data, it is 11.61
and not 19.3. So it is not pure gold. Cheat!!
Dr. Pius Augustine, S H College, Kochi

47. A spring balance reads 200 gf when
carrying a lump of lead in air. If the
lead is now immersed with half of its
volume in brine, what will be the
new reading of the spring balance?
R.D of lead is 11.4 and R.D of brine is
1.1.
Dr. Pius Augustine, S H College, Kochi

48. Check your answer
Volume of lump of lead = 200/11.4 = 17.5
Volume submerged = 17.5/2 = 8.75 cm3.
Wt. of brine displaced = (8.75 x 1.1) gf
= 9.6 gf
This is equal to loss of wt in brine, when
half submerged.
Apparent wt= 200-9.6 = 190.4 gf

49. Instrument used to measure the
density and coefficient of
expansion of liquids
Pyknometer
Dr. Pius Augustine, S H College, Kochi

50. Try following questions
Dr. Pius Augustine, S H College, Kochi

51. 1. Define the term density.
2. State CGS and SI unit of density.
3. Express the relation between the CGS and
SI unit of density
4. Give the value of density of water at 4 oC
(in SI and CGS)
5. Relative density of copper is 8.83. Express
it in SI system
Dr. Pius Augustine, S H College, Kochi

52. What volume of water would
have the same mass as 1 m3
of platinum. If this water is
occupied in a cube, what
would be the length of each
side of the cube?
Dr. Pius Augustine, S H College, Kochi

53. Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
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Dr. Pius Augustine, S H College, Kochi