CHAPTER-4

PRESSURE

1. Pressure (p)
Pressure is defined as the force exerted normally on unit area.
Forces
Pressure = Normal
Area
Force
Area
F
P = A
 SI unit of pressure is pascal (Pa). 1Pa =1Nm-2
 The force in the pressure formula must normal (90˚) to the
surface. Pressure is a scalar quantity.
 From the definition of pressure, pressure is inversely
proportional to the contact surface area.
If the contact area is smaller, pressure will be larger for a
definite force.
For example,

 The pointed nails penetrate the surfaces because for a definite

force, the exerted area is too small.
 Similarly sharp knives can cut easily than blunt knives because
of smaller cutting area.
If the contact area is larger, pressure will be smaller for a
definite force.
For example,
 Elephants have four large flat feet so they reduce pressure and
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less likely sink into the ground.
 Most obvious is tractors used for ploughing has large tire areas
so that they do not sink in the muddy fields.
Pressure is applied in many scientific fields and many units are
used although they have the same meaning.
 In meterology, the unit of pressure is hectopascal (hPa).
 The unit of pressure used in medicine and physiology is
millimeter of mercury (mm Hg).
 In the FPS system, pound per square inch ℓb in-2 (psi) is widely
used as pressure unit.
Standard Atmospheric Pressure is 1 atmosphere (1 atm).

The relation between different units of pressure are;

1 atm =1.013×105 Pa= 760 mm Hg

1 atm = 1013 h Pa= 1013 mb

1 h Pa= 100 Pa = 1 mb

1 Pa = 1.45 × 10-4 ℓb in-2 (psi)

1 psi =6.90 × 103 Pa

Unit of Pressure
Quantity MKS/SI CGS FPS
force newton (N) dyne sℓ
area m2 cm2 ft2
pressure pascal (Pa) dyne-cm-2 ℓb ft-2
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2. There is Myanmar riddle 'Which is heavier, a viss of cotton (or) a
viss of iron?' (leading to puzzle how small (or) large is the volume
of them.)
Density (ρ)
The density is defined as the ratio of its mass to volume of a
substance.

m=mass

V= volume

ρ=density

Unit of Density
Quantity MKS/SI CGS FPS
mass kg g sl
volume m3 cm3 ft3
density kgm-3 gcm-3 or g mL-1 sl ft-3

 In SI unit, density is expressed in kilogram per cubic metre.

 In CGS unit, it is expressed in gram per cubic centimeter or
gram per mililiter.
 Mass of an object can be measured using a balance and volume
can be measured using a measuring cylinder.
 When studying three states of matter (Solid, liquid and gas),
density is important factor.
 Mass of the object does not change, but the volume depends on
80
the temperature.
 If the volume of the object changes, the density will change.
m

V
Densities of some substances
Substance CGS MKS
(g cm-3) (kg m-3)
helium 1.64 × 10-4 0.164
air 1.3 × 10-3 1.3
Water, 4֯ C 1 1000
ice, 0֯ C 1.029 1029
aluminium 2.7 2700
copper 8.9 8900
lead 11.4 11400
mercury 13.6 13600
gold 19.3 19300
uranium 19.05 19050

(Note: Average density of a human body is a little less than water

density)

3. Relative density or specific gravity

The ratio of density of a substance to density of water at 4˚C is
called relative density or specific gravity.
 body
Re lative density 
 water

 Density, relative density and pressure are scalar quantities.

 As the relative density is the ratio of two densities, it is just a
number without unit.
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For example, density of aluminium= 2.7 g cm-3, relative density of
aluminium= 2.7
 alu min ium 2.7
Relative density of mercury = = 2.7.
 water 1

This means that aluminium is 2.7 times heavier than water.

**The value of relative density can be measured more accurately
than that of the density because it is necessary to measure only
the mass and not the volume.

4. Archimedes' Principle
When an object is partially (or) totally
immersed in a liquid, the object displaces
liquid volume that is equal to the volume
of immersed portion.
(or)
The loss in weight of the object is equal
to the weight of the liquid displaced.
(or)
The upward thrust acting on a body
which is immersed partially or totally in a liquid is equal to the
weight of the liquid displaced by the body.
According to the Archimedes' principle,
upward thrust = uplift force = buoyancy = weight of liquid
displaced
 By Archimedes' principle, weight of a body more than buoyancy
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(or) upward thrust, it will sink in the liquid.
 Substances having relative density greater than one will sink in
water.

5. HYDROMETER
When an object is placed in a liquid of a lower density, the object
sinks. If it is placed in a liquid of a greater density, it floats.
 For example, a ice cube of density 0.92 g cm-3 sinks in
turpentine of density 0.87 g cm-3 but floats in mercury of
density 13.6 g cm-3, the denser the liquid, the higher an object
will float in the liquid. The greater the specific gravity of a
liquid, the less will be submerged portion of a body floating on
it as shown in the following Fig. (ice g cm

ice
ice
ice

turpentine water mercury

ρ=0.87 g cm-3 ρ=1.00 g cm-3 ρ=13.6 g cm-3

Hydrometer
The hydrometer is an instrument for measuring the density or
relative density of liquids.
If the hydrometer floats higher, it indicates that the liquid has a
higher density.
 One form of this hydrometer is shown in following Figure.
 83

 The hydrometer sinks in the liquid until the weight of the liquid
displaced is equal to the weight of hydrometer.
 The hydrometer calibrated to measure the density of the liquid
in kg m-3.

Uses of hydrometer
Special hydrometers are used to test the specific gravity of
solutions in storage batteries in order to determine the condition of
battery.
 The relative density of the acid in a fully charged car battery is
1.25.
 Milk and wine can be tested to make sure they have not been
diluted with water.

Test tube as a hydrometer

Test tube can be used as a hydrometer to find specific gravity of
liquid. Test tube needed to float vertically in water, in methylated
spirit and milk as shown in figure.
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The mass of hydrometer = m

The weight of hydrometer = mg
The hydrometer is floating in water (Fig. b)
Weight of hydrometer = Weight of water displaced
= (volume of water displaced × density of
water)× g
mg = A h a ρ waterg
The hydrometer is floating in methylated spirit (Fig. c)
mg = A h b ρspirit g
The hydrometer is floating in milk (Fig. c)
mg = A h c ρ milkg
For specific gravity of methylated spirit,
A h a ρ waterg = A h b ρspirit g
ρ spirit ha

ρ water hb
8
  0. 8
10
For specific gravity of milk,
A h a ρ water g = A h c ρmilkg
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ρ milk h a

ρ water h c
8
  1.33
6
Formulae

F
1. Pressure p =
A
mass m
2. Density  , 
volume V
 body
3. Re lative density 
 water

Units Conversion
1 kg= 103 g , 1 m= 102 cm
For example, suppose we wish to convert 1000 kgm-3 to gcm-3.
kg 1000 g 1m3
1000 3   6 3  1gcm 3
m 1kg 10 cm

SUMMARY
1. Pressure is force acting on unit area; pressure is scalar quantity.
2. Density is the ratio of mass to volume of a substance.
3. If the volume of the object changes, the density will change.
4. Relative density is the ratio of density of substance to density of
water. It has no unit.
5. Archimedes' Principle
The upward thrust acting on a body which is immersed partially or
86
totally in a liquid is equal to the weight of the liquid displaced by
the body.
6. Hydrometer is an instrument for measuring the density (or)
relative density of liquids.
7. The amount of submerged portion is inversely proportional to the
specific gravity of the liquid.

Conceptual Questions

1. Define pressure. Is pressure a scalar or a vector? Express the unit of

pressure in SI units.
Pressure is the magnitude of normal force per unit area on a surface.
F
p =
A
It is scalar quantity. Its SI unit is pascal (Pa).
2. A Person exerts pressure on the floor when standing, sitting and lying.
Rev.
Explain why the pressure is different when the person is in each of these
Ex.
positions.
F
Since p  , the pressure is inversely proportional to the area. Therefore
A
the pressure is different when the person in each of these positions. The
smaller the area, the larger the pressure.
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The area of a person who is standing on the floor is less than that of sitting
and lying so that the pressure in this position is the greatest. The area of
sitting on the floor is less than the lying so that the pressure in this position is
greater than the lying.
3. Define density and relative density. What is the SI unit of density? Why
is relative density unit less?
Density (ρ) (odyfonf;jcif;)
The density is defined as the ratio of its mass to volume of a substance.
m=mass
V= volume
ρ=density
The SI unit of density is kilogram per cubic metre (kg m-3)
Relative density or specific
gravity(EIdif;&odyfonf;q(odkU
)
a&csdefodyfonf;q)
The ratio of the density of a body to the density of water at 4˚C is called
relative density or specific gravity.
 body
Relative density 
 water
Relative density has no unit because it is the ratio of densities (having the
same unit).
4. We say that the density of iron is 7.9 g cm-3. Write this in kg m-3.
Rev.
g 1 kg (1 cm)3 g 1 kg 1 cm3
Ex. 7.9 g cm3  7.9     7.9   
cm3 1000 g (10 2 m) 3 cm3 10 3 g 10 -6 m 3
 7.9  10 3 kg m 3
5. Which instrument should be used to measure the relative density of a
liquid?
Hydrometer
6. ‘Since gold is denser than aluminium gold is always heavier than
aluminium.’ Is this statement correct (or) not?
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The statement is not correct. The given statement is not complete as the
masses of metals depend on their volume.
 89
Conceptual Problems

Pressure Formula oHk;ykpämrsm;

1. Bicycle tire has 6 cm × 4 cm area touching the ground. The mass of the
Eg.1
bicycle is 22 kg and mass of the cyclist is 60 kg. Find the minimum
pressure needed in the tire.
2. Normal atmospheric pressure 1 atm is equal to 1.013 × 105 Pa. How much
Ex.1
force due to atmosphere acts on a man whose total area is 2 m2?
3. A man has mass 55 kg. His foot has the dimension of 24 cm × 8 cm. Find
Ex.2
the pressure on his foot.
4. A four wheels truck has each tire 20 cm × 12 cm area touching the ground.
Ex.3
The mass of the truck and the passengers are altogether 4400 kg. Find the
minimum pressure needed in a tire.
5. The pressure in the motor car tire is 40 psi. What is the equivalent MKS
Eg.3
unit and atm unit?
6. A drawing pin is pressed into the notice board. The pointed pin area is 0.25
Eg.4
mm2 and the force exerted on the pin is 10 newton. Compute the pressure.
7. Low pressure area in the bay of Bengal is 998 hPa. Finishing boat nearby
Eg.2
has sail area 4 m2 at the normal atmospheric pressure. (a) Find the pressure
difference (b) Find the force exerted on the sail. (Hints: Force exerts due to
atmospheric pressure difference)
8. A brick of mass 2 kg has length 22 cm, breadth 11 cm and height 7 cm.
Ex.4
Calculate the weight and 3 kinds of pressure when it lies on a plane for
three positions. In the missing (c), draw a sketch with base 22 cm × 7 cm.
90
Density Formula oHk;ykpämrsm;

1. The helium flying balloon has the size of 6 m radius.

Eg.5
(a) Find the volume and mass of helium.
(b) Find the mass of air displaced by the balloon.
2. Mini-submarine has the total volume of 24 m3. Its mass is 2000 kg. Can it
Ex. 6
carry a load of another 3000 kg?
3. The mass of a statue which is made of silver is 120g. If the density of
silver is 10.5 g cm3, find the volume of the statue.
4. An alloy is made by mixing 360 g of copper, of density 9 g cm-3, with 80 g
Rev.
of iron, of density 8 g cm-3. Find the density of the alloy. Assuming the
Ex.
volume of each metal used does not change during mixing.

Relative Density Formula oHk;ykpämrsm;

1. Find the relative density of helium at 0˚C ( ρHe = 0. 178kgm-3) .

2. Find the relative density of glycerine at 0˚C.
( density of glycerine =1260 kg m-3)
3. One litre of milk (density 1.2 g cm-3) is mixed with 0.5 litre of water
Ex.5
(density 1 g cm-3). What is the density of the mixture? Find the relative
density of the mixture.
4. The relative density of sulphur is 2. Find the volume of 1kg of sulphur.
Rev.
(density of water = 1000 kg m-3)
Ex.
 91
Glossary

hydrostatic wnfN
idrf submerged epfjrK
y
t&
nfynm fonf
hydrodynamic a½
G
Uvsm;ta& float aygavm
ynm ay:onf
pressure Zdtm; hydrometer dk
[dkuf'½
meteorology rdk;av0o rD
wm
aA
' stem yifpnfw
sharp knife cR
efaom" dkif
m; relative density EdIif;&
od
blunt knife wH
k;aom"m; yfonf;q
flat feet ajcz0g;tj dilute tmedoi
ym; favsmha
tractor v,fxG
efp ponf
uf partially wpdwfwydk
ploughing v,fxG
ef if;
onf totally wpfckvH
k;?
tire wm,m wpfckvH
k;
muddy field displaced z,fxkwf
½
G
Hv,fajr
U
atmosphere onf
avxk
calibrate csdefnd§
density odyfon
xm;aom
f;q
sink epfjrK
y
specific gravity a&csdef
odyfon fonf/
f;q uplift force tay:yif
displaced z,fxkwf
hwiftm;
onf
methylated aq;½
koH
H k;t&
immersed epfjrK
y
spirit uf
portion faomty
solution aysmf&
nf
dkif;
upward thrust yifhtm; alloy owåK
a&mpy
buoyancy azmh*kPf f
 77
submarine a&
ikwfoa
bFm