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UNIT -1 PHYSICAL WORLD
1. What is science?
Systematic and organized knowledge about the various natural phenomena which is obtained by
careful experiments, keen observation and accurate readings.
Science (from Latin scientia 'knowledge')
In Sanskrit it is called sastra (vijyan) and in Urdu it is called elm.
Science may be divided into two types
A. Biological science
The science which deals with the living organism is called biological sciences. The main parts of
biological science are botany, zoology, forensic science etc.
B. Physical science
The science which deals with the non living organism is called physical sciences. The main
parts of physical science are
i. Chemistry
The branch of science which deals with the study of every substance, there structure, composition
and change in which the reaction takes parts.
ii. Physics
The branch of science which deals with the study of nature and the natural phenomenon is called
physics.
2. What is the attitude of science?
In science a solution is suggested for a problem. This solution is tried, if it works properly than it
is adopted otherwise it is replaced by a better solution to the same problem.
Thus scientific attitude requires a flexible, open minded approach toward solving a problem in
which other important points are not neglected without any reason.
3. Scientific methods
The step by step approaches used by the scientist in study of nature and natural phenomenon and
establishing the law which govern this phenomenon is called the scientific methods.
Generally it involves the following steps:-
1. By taking a large number of the systematic observations.
2. Studying these observations and making qualitative reasoning.
3. Suggesting a mathematical method to the observations.
4. Predicting new phenomenon on the suggested model.
5. Modifying the new theory if necessary in the light of new evidences.
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4. Scientific theory
A set of the laws according to which the behavior of a physical system can be explained is called
the scientific theory. In science, no any theory is final.
5. Principal of physics
In physics there are two basic principal works.
i. Unification
In physics many problems can be explained by a few concepts and the theory, this
phenomenon is called unification.
ii. Reductionism
Sometime a problem is studded under a certain condition; at the same time that problem may
be studied in some other conditions. E.g.
The macroscopic properties of matter may be studied under thermodynamics while the
microscopic property may be studied under quantum mechanics.
6. Scope of the physics
The physics have very wide scopes; every event which occurs around us is governed by the one
or more branches of the physics.
There are mainly two branches of the physics
1. Classical physics
The branch of the physics which deals with the macroscopic property of the matter is called
classical mechanics or classical physics.
2. Quantum physics
The branch of the physics which deals with the microscopic property of the matter is called
quantum mechanics or quantum physics.
7. Some other branches of the physics
A. Mechanics
The branch of the physics which deals with the study of the equilibrium of the objects or the
motion of the objects is called mechanics.
B. Optics
The branch of physics which deals with the nature of light is called optics.
C. Thermodynamics
The word thermodynamics is made up of two word thermo and dynamics. Thermo means heat
and dynamics means motion, hence thermodynamics may be defined as the branch of physics
which deals with motion of heat is called thermodynamics.
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D. Electrodynamics
It deals with the electric and magnetic property of the charges and the magnetic bodies is called
electrodynamics.
E. Relativity
It is the theory of invariance in nature. It deals with the motion of the particles having speeds
comparable to the speed of light.
F. Meso-scopics physics
These days a new physics is developing which is intermediate between the macroscopic and
microscopic physics; it deals with the study of a few or hundreds of the atoms.
8. Physics in relation to the other branches of the sciences:
a. Physics in relation to mathematics
Mathematics provides the necessary formulas to obtain a mathematical relation to a given
physical problems, mathematics is also called the language of physics.
b. Physics in relation to chemistry
In chemistry the structure of matter, their constituents, bonding between the atoms and
complex chemical reactions are studied with the techniques provided by the physics such as
radioactivity, x ray diffraction, etc
c. Physics in relation to biological sciences
The instruments or the technique such as x ray, ultrasound, M.R.I, sonography, endoscopy to
investigate a patient in biological science is provided by the physics. Thus physics is greatly
related to biological sciences.
d. Physics in relation to astronomy
The motion of the planets and the stars, and to discover the stars, we need the instrument
telescope which is provided by the physics.
Doppler Effect predicted the big bang theory of the universe
e. Physics in relation to geology
Diffraction techniques help to study the crystal structure of the various rocks. Radioactivity is
used to estimate the age of the rocks and fossils.
f. Physics in relation to seismology
The movement of the earth crust and types of the waves so generated helps a lot in the study of
earthquake and its effect.
g. Physics in relation to meteorology
By studying variation of the pressure with temperature, we can forecast weather.
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h. Physics in relation to society
The discovery in physics greatly affects society. E.g.
The development of the telephone, helped us to communicate
The discovery of the radio and TV helps us to communicate and to entertainment.
The launches of satellites help to detect weather etc.
The computer, laser, superconductivity, nuclear energy, changed the status of the society.
i. Physics in relation to technology
Physics and technology are two sides of a coin. If a physical law is in books than it is physics
but when it is implemented then it becomes technology.
S.NO.
PHYSICS
TECHNOLOGY
1
Electromagnetic waves
Radio, television, radar, and wireless communication etc.
2
Newton’s laws of gravitation
satellite
3
X ray
radiotherapy
4
Silicon chip
computer electronics
9. Fundamental forces in nature
There are basically four fundamental forces in nature
a. Gravitational force
The force of attraction between two bodies due to their mutual interaction is called
gravitational force. It is directly proportional to product of the masses and inversely
proportional to square of distance between them. I.e.
Important properties of the gravitational force
It is a universal attractive force.
It obeys inverse square law.
It is long range force, and does not need any material medium for their propagation.
It is weakest force in nature
Gravitational force between two bodies does not depend upon the presence of the other bodies.
It is central force.
It is conservative force.
The field particle or the origin of this force is graviton.
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b. Electromagnetic Force
The force between two charges due to their mutual interaction is called Electromagnetic force. It is
directly proportional to product of the charges and inversely proportional to square of distance
between them. I.e.
Important properties of the Electromagnetic force
It may be attractive or repulsive.
It obeys inverse square law.
It is long range force, and does not need any material medium for their propagation.
Electromagnetic force between two bodies does not depend upon the presence of the other bodies.
It is central force.
It is conservative force.
The field particle or the origin of this force is exchange of photon between two charges.
It is 1036 time stronger then the gravitational force.
c. Strong nuclear force
The force of which bounds the nucleons (neutron and proton) inside a nucleus are called strong
nuclear force.
Important property of strong nuclear force
It is strongest force in the nature, 1038 times stronger than gravitational force.
It is short range force.
It is non central force and non conservative force.
It have charge independence character i.e. the force between n-n, p-n, p-p is equal.
It occurs due to exchange of the particle called π meson.
d. Weak nuclear force
The force which occurs between the elementary particles involving in a nuclear process is called the
weak nuclear force.
Important properties of the weak nuclear force
The messenger particles that transmit the weak nuclear force between the elementary particles
are massive vector bosons.
Any process which uses neutrino and antineutrino has weak nuclear force.
Weak nuclear force is 1025 time stronger than gravitational force.
It is short range force and operates up to a range equal to the size of nucleus (10-15m)
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Some important points of the fundamental forces:
Fundamental Force
Relative
Strength
Range
Particles on which force
acts
Messenger
Particles
Gravitational force
1
Infinite
All particles
Graviton
Weak nuclear force
1025
Very short with in
nucleus
Elementary particles
Vector
Bosons
Electromagnetic force
1036
Infinite
Charged particles
Photons
Strong nuclear force
1038
Very short with in
nuclear size
π meson
10. Conservation laws
In physics we usually deal with the following four conservative laws.
1. Law of conservation of the energy
According to law of conservation of the energy, energy can neither be created nor be destroyed it
can be converted from one form to another form.
The potential energy of the water converts into kinetic energy when water falls from a dam
and then converts into electric energy by the help of a turbine.
2. Law of conservation of the linear momentum
It states that if no any external force act on the system than the total momentum of the system
remains constant.
3. law of conservation of angular momentum
It states that if there is no any external torque is acting on the system then the angular momentum of
the system remains conserved.
4. Law of conservation of the charge
It states that the total charge on an isolated system remains constant or charge can neither be created
nor be destroyed.
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11. Some great physicists and their discoveries
S. No.
Name of the scientist
Country
Discovery
1.
Homi Jahangir Bhabha
India
Cosmic ray showers
2.
J. C. Boss
India
Ultra short radio waves
3.
S.N. Boss
India
Boss Einstein statistics
4.
C.V. Raman
India
Inelastic scattering of the light(Raman effect)
5.
M.N. Saha
India
Thermal ionization
6.
G.N. Ramachandran
India
Triple helical structure of protein molecules.
7.
S. Chandershekhar
America(Ib)
Evaluation of the stars, Chandershekhar limit
8.
Abdus Salam
Pakistan
Unification of weak and electromagnetic interaction
9.
Alfred Noble
Sweden
Dynamite
10.
Ampere
France
Magnetism due to current
11.
Niels Bohr
Denmark
Quantum model of H- atom
12.
James Chadwick
England
Neutron
13.
Albert Einstein
Germany
Theory of relativity, mass energy equivalence, photoelectric effect
14.
Galileo
Italy
Law of inertia
15.
C. Huygens
Holland
Wave theory of light
16.
Wernes Heisenberg
Germany
Uncertainty Principle, Quantum Mechanics
17.
Kelvin
England
Thermodynamic scale of temperature
18.
Marconi
Italy
Wireless telegraphy
19.
R.A Millikan
America
Charge on electron
20.
Isaac Newton
England
Law of motion, law of gravitation, reflecting telescope
21.
Oersted
France
Magnetic effect of current
22.
Max. Planck
Germany
Quantum theory of radiations
23.
Robert Boyles
England
Boyles law
24.
Ernest Rutherford
England
Nuclear modal of atom
25.
W.K. Roentgen
Germany
x-ray
26.
E. Schrödinger
Germany
Wave mechanics
27.
J.J. Thomson
England
Electron
28.
J.D. Van Der Walls
Dutch
Expansion of gas and liquid
29.
Volta
Italy
Discovered first battery
30.
James Watt
England
Steam engine
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1(b) Units and Measurement
12 PHYSICAL QUANTITIES:-
The quantities which obey law of physics are called physical quantity. Everything in this nature that
we see or measure is physical quantity. To study physical quantity we need number and units.
Physical quantity =number + unit
Number: -
How many times a physical quantity is taken is called number.
Unit:-
The standard by which we measure physical quantity is called unit.
13 MEASUREMENTS
Hence measurement of a physical quantity =numerical value of the physical quantity× size of the
unit or
For example, let length of a rod = 5m=500cm.
Here smaller the size of the unit larger is the numerical value, thus numerical value(n) is inversely
proportional to size(u) of the unit.
So
Or
Also we may write
A good unit will have the following characteristics.
It should be (a) well defined (b) easily accessible (c) invariable (d) easily reproducible
Question:1 The SI unit of force is Newton such that 1N = 1kg
2
ms
. In C.G.S. system, force is expressed in
Dyne. How many dyne of force is equivalent to a force of 5 N?
Solution: Let 1 N = n dynes
22 s
cm
s
mkg1g
n
Or
22 s
cmg
s
cm(100)1000g n
5
10n
5 N = 5 ×
5
10
dyne.
Units can be divided into two parts
(a) Fundamental units. (b) Derived units
(a) Fundamental units:-
The units which can neither be derived from another unit, nor can they be further resolved.
E.g. Length, mass, time is the fundamental units.
(b) Derive Units:-
The units which can be expressed in the form of fundamental units are called derived units.
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Distance covered
time taken
speed
Therefore, units of speed =
1
unit of distance i.e. length
unit of time second
metre ms
Rules for writing units
The symbol of a unit, which is not a name of a person, is written in small letter.
E.g.: metre (m) kilogram (kg)
The symbol of a unit, which is given on the name of a person, is written with a capital initial
letter.
E.g.: Newton (N), Kelvin (K)
Full name of a unit, even if it is named after a person is written with a lower initial letter.
E.g.: Newton, Kelvin.
A compound unit formed by multiplication of two or more units is written after putting a dot
or leaving a space between the two symbols.
E.g.: Newton metre – N.m or N m.
A unit in its short form is never written in plural.
i.e.5 Newton may be written as 5N not 5Ns
14 SYSTEMS OF UNITS
(a) The F.p.s. system
In this system of unit’s fps represents foot, pound, second for the measurement of length
mass time respectively. It was the British system of measurement.
(b) The c.g.s system
In this system of unit’s c.g.s represent centimeter, gram, second for the measurement of
length mass time respectively.
(c) The m.k.s system
In this system of unit’s m.k.s represents metre, kilogram, second for the measurement of
length mass time respectively.
Now a day’s only c.g.s. and m.k.s. system of units are used. The cgs system is used for
small quantities.
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(d) International system of units (SI)
The S.I system of units was developed by General Conference of Weight and Measurement in 1971.
It consists of 7 fundamental units and 2 supplementary units.
Aberration in power of ten
S.No.
Basic physical quantity
Fundamental units
Symbol
1.
Mass
kilogram
kg
2.
Length
metre
m
3.
Time
second
s
4.
Temperature
Kelvin
K
5.
Electric current
Ampere
A
6.
Luminous intensity
Candela
cd
7.
Quantity of matter
mole
mol
S.No.
supplementary quantity
supplementary unit
Symbol
1.
Plane angle
radian
rad
2.
Solid angle
steradian
sr
S.No
POWER
PREFIX
SYMBOL
S.No
POWER
PREFIX
SYMBOL
1
10-1
deci
d
10
101
deca
da
2
10-2
centi
c
11
102
hecto
h
3
10-3
milli
m
12
103
Kilo
k
4
10-6
micro
μ
13
106
mega
M
5
10-9
nano
n
14
109
giga
G
6
10-10
Angstrom
A0
15
1012
tera
T
7
10-12
pico
p
16
1015
peta
P
8
10-15
fermi or femto
f
17
1018
exa
E
9
18-18
atto
a
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15. Characteristics of a system of unit/properties of SI units:-
1. It is well defined.
2. It is of suitable size i.e. neither too large nor too small in comparison to the quantity to be
measured.
3. It is easily reproducible at all places.
4. It does not change with time and from place to place.
5. It does not change with change in its physical condition, such as temperature, pressure, etc.
6. It is accessible easily.
7. It is internationally accepted.
16 Advantages of the SI system of the unit over other system of unit
1. Si is coherent system of the unit:- all derived unit can be obtained by simple multiplication or
division of the units and the numbers
2. Si is rational:-it uses only one unit for one physical quantity e,g all form of energy are
measured in joule.
3. It is metric system :- multiple and submultiples of SI unit can be expressed in power of 10
4. It is absolute system: - it does not use gravitational units. The use of g is not required.
5. It is internationally accepted.
17 INTRODUCTIONS TO PHYSICAL QUANTITIES AND THEIR S.I. UNITS
(a) MASS
The quantity of matter contained in a body is called mass. It can never be zero for a body.
The SI unit of mass is kilogram
One kilogram is defined as the mass of one cubic decimeter of water at 40C (the temperatures of
water at which its density is maximum or
One kilogram is defined as the mass of a platinum-iridium cylinder placed at international
Bureau of weight and measurement near Paris, France.
Measurement of Mass
There are two types of mass of a body.
I Inertial mass
The mass under the effect of an external force rather than gravity is called inertial mass. It is
measured by spring balance
ii. Gravitational mass
When the body is under the effect of gravity, than the measured mass is called gravitational
mass, it is measured by a physical balance.
Both inertial mass and gravitational mass are equal.
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Difference between mass and weight
Mass
Weight
The quantity of matter contained in a body is
called mass.
The force with which a body is pulled toward centre of
earth is called weight.
Mass is a measure of inertia
Weight is a measure of gravity.
It is scalar quantity
it is a vector quantity
It cannot be zero
it is zero at centre of earth
It is essential property of a material body
It is not essential property of a material body
Not affected by presence of other body
affected by presence of the other body
Its unit are g, kg,
Its unit are dyne, Newton etc.
SOME IMPORTANT PARACTICAL UNITS OF MASS
1 atomic mass unit =1.66×10-27kg 1 tone or 1 metric ton 1000kg
1 quintal =100kg 1 slug = 14.57kg 1 pound =1lb=0.4536kg
1 Chandra Shekher limit= 1CSL=1.4 time the mass of the sun.(largest unit of mass)
(b) LENGTH
Length is defined as the separation between two points in free space.
It is measure in metre.
One metre is defined as the path followed by light in vacuum in 1/299,792,458 of a second
Measurement of length
Now a day we can measure length from 10-16 m (diameter of electron) to 1026(size of universe)
Measurement of length is done by two methods
1 Direct method 2 indirect method
i. Direct method
In this method length is measured by instruments i.e. by metre scale, a vernier caliper, a
screw gauge, or a speedometer. The minimum distance measured by these instruments is
called least count of the instrument.
ii. Indirect method used in length measurement:-
It is used to measure height of a tower, poles, mountains, distance of moons and other
celestial objects from earth.
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(a) Measurement of the large distance
Parallax method:-
This method is used for measuring distance of planet and stars distance less than 100 light year.
Parallax means the change in position of an object w.r.t. background when we shift our eyes
sidewise.
Let a star which is fixed at O is seen from earth from two different points A and B having equal
distance R from the star. Let the distance between A and B is L which may be
taken as the arc because L << R. Then the parelactic angle θ can be given as
θ
(1)
The angle θ can only be measured if the position of O is measured at the same
time, which is not possible. Than another star F is considered whose distance
does not change with time such that.
θ = θ1+ θ2
Than from (1)
θθ
Hence distance from stars can be measured.
(b) Triangular method for the measurement of an accessible object
Suppose is the height of a tower or a tree which is to be measured. Then this method is used. Let
A is the point of observation having distance from the base of the tree B. now
place a sextant at c and measure the angle of elevation θ.
Now from right angle triangle ABC, we have
Or height =
By knowing the distance, the height can be determined.
(c) Triangular method for the height of an inaccessible object
Let AB is the height of the object which is to be measured. By using a sextant we measure first
angle C then angle D As shown in fig.
Now from right angle triangle ABC θ
And in triangle ABD θ
θθ
θθ
Knowing d, the height h can be determined.
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Example2: A man wishes to estimate the distance of a nearby tower from him. He
stands at a point A in front of the tower C and spots a very distant object O in line with
AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O
and C again. Since O is very distant, the direction BO is practically the same as AO;
but he finds the line of sight of C shifted from the original line of sight by an angle θ =
400 (θ is known as parallax) estimate the distance of the tower C from his original
position A.
Answer We have, parallax angle
From Fig., and
(d) Determination of the distance of a far away star by intensity method
This method based on the inverse square law of intensity. I.e the intensity of the illumination at a
point is inversely proportional to the square of distance from the source of light.
Suppose I1 is the intensity of the far away star and I2 is the intensity of the nearby star taken on a
photographic plate. Let r1 and r2 is the respective distances of stars.
Than from inverse square law of intensity
Or
Knowing the distance r2 of the nearby star, the distance of the far away star can be calculated.
This method is used to measure the distance of the stars more than 100 light years.
Q. what do you mean by inferior and superior planet?
Inferior planet
The planets which are closer to the sun then earth are called inferior planet (mercury and Venus)
Superior planet:
The planets which are closer to the earth then sun are called superior planet (Jupiter, Saturn, Uranus,
Neptune, and Pluto)
(e) Measurement of the diameter of the moon
Suppose AB=D is the diameter of the moon which is to be measured
by an observer O on the earth. As shown in the fig.
Now from triangle OAB
Hence
Knowing the value of S and θ the diameter D can be measured.
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Example: 3 the moon is observed from two diametrically opposite points A and B on Earth. The angle θ subtended at the
moon by the two directions of observation is. Given the diameter of the Earth to be about, compute
the distance of the moon from the Earth.
Answer We have
Since Also
We have the earth-moon distance,
Example: 4 The Sun is angular diameter is measured to be 1920′′. The distance D of the Sun from the Earth is
m. What is the diameter of the Sun?
Answer Sun is angular diameter
Sun is diameter
(f) Reflection or echo method
This method is based on the speed of the sound. To find the distance of a hill a gun is fired toward
the hill, the time interval between the instant of the firing and instant of the hearing is noted. During
this time interval the sound travels 2S distance with v velocity.
So the distance traveled by the light may be given as 2S=v × t
Or S =
(g) Laser method
The word laser means light amplification by the stimulated emission of the radiations.
A laser beam is sent toward moon and its reflected pulse is received. If t is time elapsed between the
instants of light sent and light received back, then the distance of the moon from the earth is given
by
S =
Where c=3 108 m/s is the velocity of the light traveled.
(h) RADAR method
The word RADAR means radio detection and ranging. Radar is used to measure the distance of a
nearby planet. A radio wave is sent from a transmitter and after reflection from the planet received
by a detector. Then the distance travelled by the radio waves can be given as
S =
This method is also used to measure the height and the distance of an aeroplane.
(i) SONAR method
The word sonar means sound navigation and ranging. On sonar, ultrasonic wave of frequency
greater than 20,000Hz are transmitted through the ocean. They are reflected by the rock or the
submerged rocks and received by the receiver. Then the distance travelled by the sound waves
toward rock can be given as
S =
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(ii) Measurement of the small distance
Small distances such as size of atom, molecules are measured by electron microscope, Avogadro
method, Rutherford α particle scattering method etc.
Measurement of the small distance (Size of molecule of oleic acid)
Oleic acid is a soapy liquid with large molecular size. Dissolve 1 cm3 of oleic acid in 20 cm3 of
alcohol and then re-dissolve 1cm3 of this solution in 20 cm3 of alcohol. Then the concentration of
oleic acid is 1/400 cm3 of alcohols. We than determine approximate volume of each drop (V cm3).
Now pour n drops of this solution on surface of water. We stretch the film carefully, as alcohol is
evaporate, a very thin film of left on water surface. We measure the area A of film using graph
paper.
Volume of the n drops of the solution = cm3.
Amount of oleic acid in the solution =
cm3.
Thickness of oil film t =
cm.
The value of t is found to be of order of 10-9 m.
SOME IMPORTANT PARACTICAL UNITS OF DISTANCE
(a)For large distance
1. Astronomical Unit (AU):-
The average distance from center of earth to center of moon
1 AU=1.496×1011 m1.5×1011m
2. Light year (ly):-
The distance travelled by light in vacuum in one year
1 ly=3×108×365×24×60×60=9.46×1015 m
3 parsec:-
It is the distance at which an arc of length equal to one astronomical unit subtends an angle of one
second.
11 16
1 1.496 10
1 parsac 3.1 10
1'' (1/ 3600) ( /180)
AU m m
rad
Relation between AU, ly, Parsec
(c) Practical unit for measuring area
1 barn =10-28m2 1 acre= 4047m2 1 hectare =104m2
1 ly=6.3×104 AU
1 Parsec =3.28 ly
1 Parsec=2.07×105 AU
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(c) TIME
Time is defined as the duration between two events. The SI unit of time is second.
One second is defined as the duration of 9,192,631,770 vibrations between two hyperfine levels
of cesium-133 atom in ground states.
Measurement of Time:-
Time is measured by solar clock, quartz crystal clock, atomic clock, decay of elementary particle,
age of rocks, earth etc
Some practical units for the measurement of the time
Solar day
The time taken by the earth to compete one rotation about its own axis w.r.t the sun is called a solar
day. 1 solar day =24hour= 86400 s
Sedrial day
The time taken by the earth to compete one rotation about its own axis w.r.t a distant star is called a
Sedrial day.
Solar year
The time taken by the earth to compete one revolution around the sun in its orbit is called a solar
year. 1 solar year=365.25 average solar day
Tropical year:
The year in which there is total eclipse is called one tropical year.
Leap year
The year which is total divisible by number 4 is called leap year, in this year the month of February
have 29 days.
Lunar month
The time taken by the moon to complete one revolution around the earth is called one lunar month.
1lunar month =27.3 days
The smallest unit of time is shake 1 shake=10-8s
Now a days we can measure time from 10-24 to 1017second (from life time of unstable particles
in nucleus to age of universe)
(e) CURRENT:
Rate of flow of charge in a conductor is called current. It is measured in Ampere.
One Ampere current is defined as the current between two parallel straight conductors of infinite
length, negligible area of cross-section and placed one metre distance apart in vacuum would
produce a repulsive force equal to 2×10-7. N.
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(f) TEMPRATURE:
Temperature is defined as the degree of hotness or coldness of a body. It is measured in Kelvin
One Kelvin is defined as the 1/273.16 the fraction of temperature at the triple point (the point at
which ice water and water vapor coexist) of the water
(g) LUMIONUS INTENSITY:
Luminous intensity is defined as the amount of light emitted per second by a source. It is measure in
candela.
One candela is defined as the light emitted perpendicularly by 1/60,000 sq. m area of a black
body at freezing point of platinum at 2042k temperature and 101,325N/m2 pressure.
(g) QUANTITY OF MATTER
Amount of a substance contain in a body. It is measure in mole
One mole is defined as amount of substance which contains same number of atoms as there are
atoms in 0.012kg of carbon C-12.
SUPPLYMEANTRY UNIT
1 PLANE ANGLE
Plane angle is defined as the angle between two planes. It is
measured in radian.
One radian is defined as the angle subtended at the centre of the
circle by an arc of length equal to radius of the circle.
1 radian=57.70
2 SOLID ANGLE
Solid angle is defined as the angle at the centre of sphere
It is measure in steradian.
One steradian is defined as the angle subtended at the centre
of sphere by its surface whose area is equal to the square of
radius of the sphere.
Ω
Example:5 Calculate the angle of (a) (b) 1′ and (c) 1″ in radians.
Use rad, and 1′ = 60 ″
Answer (a) we have So
(b)
(c)
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(c) DIMENSIONAL ANALYSIS
18 DIMENSIONS
Dimensions of a physical quantity may be defined as the powers to which the fundamental units be
raised in order to represent that quantity.
For example: we know, Area = length x breadth.
Thus unit of area = L L = L2. Since unit of mass M and time T are not being used for the
measurement of area, the unit of area can be represented by M0L2T0. Powers 0, 2, 0 of fundamental
units are called the dimensions of area in mass, length and time respectively.
** Dimensional equation
The equation, which indicates the units of a physical quantity in terms of the fundamental units,
is called dimensional equation.
Eg: Dimensional equation of velocity is [V] = M0LT–1.
1) Area = length x breadth = L x L = L2 = M0L2T0
2) Volume = L3 = M0L3T0
19 DIMENTIONAL FORMULAS AND SI UNIT OF SOME PHYSICAL QUANTITY
S.No
PHYSICAL QUANTITY
Formula
Dimensional formula
SI unit
1
Length
Length
m
2
Mass
Mass
kg
3
Time
Time
sec
4
Area
Length × breadth
m2
5
Volume
Length × breadth× height
m3
6
Density
kgm3
7
Speed OR Velocity
ms-1
8
Acceleration
ms-2
9
Linear Momentum
Mass × velocity
kgms-1
10
Force
Mass × acceleration
Newton(N)
11
Work
Force × displacement
Joule (J)
12
Energy
Amount of work
Joule (J)
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S.No
PHYSICAL QUANTITY
Formula
Dimensional formula
SI unit
13
Power
Watt (W)
14
Pressure
Pa or Nm-2
15
Torque
Force × distance
Nm
16
Gravitational constant
Nm2kg-2
17
Impulse
Force × time
Ns
18
Stress
Nm-2
19
Strain
-
20
Coefficient of elasticity
Nm-2
21
Surface tension
Nm-1
22
Surface energy
Jm-2
23
Coefficient of viscosity
Nm-2s or Pas
24
Angle
No unit
25
Angular velocity
Rads-1
26
Angular acceleration
Rads-2
27
Moment of inertia
Mass ×
Kgm2
28
Radius of gyration
Distance
M
29
Angular momentum
mass × velocity × radius
Kgm2s-1
30
T-ratio (sin. Cos.tan)
No unit
31
Frequency
s-1
32
Relative density
No unit
33
Velocity gradient
s-1
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S.No
PHYSICAL QUANTITY
Formula
Dimensional formula
SI unit
34
Force constant
Nm-1
35
Heat or enthalpy
Energy
J
36
Specific heat
Jkg-1k-1
37
Latent heat
Jkg-1
38
Thermal conductivity
Js-1m-1k-1
39
Entropy
Jk-1
40
Universal gas constant
Jmol-1k-1
41
Electric charge
Time × current
C (coulomb)
42
Electric potential
V (volt)
43
Resistance
Ohm
44
Capacitance
Farad
45
Inductance
Henry
46
Electric field intensity
Nc-1 or vm-1
47
Conductance
Mho
48
Resistivity
Ohm meter
49
Conductivity
50
Electric dipole moment
charge× 2l
Cm
51
Magnetic field
Tesla (T)
52
Magnetic flux
Magnetic field× area
Wb (Weber)
53
Magnetic moment
Current ×area
Am2
54
Pole strength
Am
55
Logarithm, A number
No formula
No unit
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20 Different types of variables and constants:
I. Dimensional variable
The physical quantity having dimensional formula and variable value is called dimensional
variable. E.g. area, volume, velocity, force
II. Dimensional constant
The physical quantity having dimensional formula and constant value is called dimensional
constant. Gravitational constant, Planck’s constant
III. Dimensionless variable
The physical quantity having no dimensional formula but have variable value is called
Dimensionless variable. E.g. angle, strain
IV. Dimensionless constant
The physical quantity having no dimensional formula and have constant value is called
Dimensionless constant. Π, e, etc.
21 Principle of homogeneity
An equation representing a physical quantity will be correct if the dimensions of each term on
both sides of the equation are the same. This is called the principle of homogeneity of
dimensions.
22 Uses of dimensional analysis
1. To check the correctness of an equation.
2. To convert one system of unit into another system
3. To derive the correct relationship between physical quantities.
(1) To check the correctness of an equation.
An equation is correct only if the dimensions of each term on either side of the equation are
equal.
Example:6 Check the accuracy of the equation S=ut+
at2
Ans given formula is S=ut+
at2
Taking dimensions on both sides, L = L + L
i.e. L = L + L
According to principle of homogeneity, the equation is dimensionally correct.
Example:7 Let us consider an equation
. Check whether this equation is dimensionally
correct.
Answer the dimensions of LHS are
The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct
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Question: 8 The equation of state of some gases can be expressed as
RTb)(V
V
a
P2
.Here, P is the
pressure, V the volume, T the absolute temperature, and a, b, R are constants. Find the dimensions of a.
Solution: Dimensions of
2
v
a
will be same as dimensions of pressure
23 ][L
a
= ML–1T–2 so [a] = ML5T–2
(2) To convert one system of unit into another system
This is based on the principal that the magnitude of the physical quantity remains same, whatever
is its unit.
Suppose a physical quantity Q having u1 and u2 units with corresponding numbers n1 and n2.
Then Q= n1u1=n2u2
Again suppose that M1L1T1 are the fundamental units in one system and M2L2T2 are the
fundamental units of mass length and time in second system.
If the dimension formula of the physical quantity is
Then
And
So
=
Or
This equation may be used to find the numerical value of the second system of unit.
Q.9 convert one joule of energy into erg?
Here joule is the SI unit of the energy and erg is the cgs unit of the energy. The dimensional formula of energy is ML-
2T-2. So
So
o r
=1×103×104=107
Si
CGS
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(3) To derive the correct relationship between physical quantities.
Dimensions can be used to derive the relation between physical quantities.
Question To derive an expression for period of oscillation of a simple pendulum.
The period of oscillation (T) of a simple pendulum may depend on (1) Length of the pendulum (L); (2) Mass of bob
(m) and (3) the acceleration due to gravity (g).
Then T =
Taking dimensions on both sides =
Equating dimensions of M, L and T,
x + z = 0
y = 0
–2z = 1
Hence z=-
and x=
By putting the values we get T=
Or T=
The value of constant k cannot be found by dimensional method. The value of k is found to be 2π using some other
methods.
π
Question:10 In a new system of units, unit of mass is taken as 50 kg, unit of length is taken as 100 m and unit of
time is 1 minute. What will be the weight of a body in this system, if in SI system, its weight is 10 N.
Solution: Let the weight of the body in new system is X units 10 N = X units
Let
111 ,, TLM
and
222 ,, TLM
be the symbols for mass, length and time in the two system respectively,
then
][][10 2
222
2
111 TLMXTLM
s60,s1,m100,m1,kg50,kg1212121 TTLLMM
units2.7
5000
36000
60
1
100
1
50
10 2
X
10 N = 7.2 units
23 Limitations of dimensional analysis.
This method gives us no information about dimensionless constants.
We cannot use this method if the physical quantity depends on more than three other
physical quantities.
This method cannot be used if the left hand side of the equation contains more than one term.
Often it is difficult to guess the parameters on which the physical quantity depends.
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1(d) Significant figures AND error
24 Significant figures:
Significant figures give the number of meaningful digits in a number.
The significant figures are the number of digits used to express the measurement of the physical
quantity such that the last digit in it is doubtful and the rest all digits are accurate.
The number of significant figures depends on the accuracy of the instrument. More the number of
significant figures in a measurement, more accurate the measurement is.
25 Rules to determine the significant figures:
(1) All zeros in between the numerals 1 to 9 are counted.
(2) In a measurement involving decimal, the position of decimal is disregarded.
(3) All zeros after the last numeral are counted.
(4) The zeros preceding the first numeral are not counted.
(5) All the zeros to the right of the last non-zero digit (trailing zeros) in a number without a
decimal point are not significant, unless they come from experiment.
Thus 123 m = 12300 cm = 123000 mm has three significant figures. The trailing zeros are
not significant. But if these are obtained from a measurement, they are significant.
26 Rules for rounding off to the required number of significant figures:
(1) If the digit to be dropped is less than 5, the digit immediately preceding it remains
unchanged.
(2) If the digit to be dropped is more than 5, the digit immediately preceding it is increased by 1.
(3) If the digit to be dropped is 5, then the preceding digit is made even by
(a) Increasing it by 1 if it is odd,
(b) Keeping it unchanged if it is even.
27 Significant figures in calculations
(1) Significant figures in multiplication and division.
The result of multiplying or diving two or more numbers can have no more significant figures than
those present in the number having the least significant figures.
Eg: (1) [sig fig 4] [sig fig 5]
Than
(2) [sig fig 4]
Then
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(2) Significant figures in addition and subtraction.
In adding or subtracting, the least significant digit of the sum or difference occupies the same
relative position as the least significant digit of the quantities being added or subtracted. Here
number of significant figures is not important; position is important.
Eg: (1) 204.9 [9 is least sig.digit. Position – 1st decimal place]
2.10 [0 is least digit. Position 2nd decimal place]
+ 0.319 [9 is least sig. Digit. Position 3rd decimal place.]
= 207.319 = 207.3
In sum, the least sig. Fig should come in the first decimal place.
Eg: (2) If a = 10.43 and b=2.8612
Then a – b= 10.43 – 2.8612
= 7.5688 = 7.57.
Example11. 5.74 g of a substance occupies 1.2 cm3. Express its density by keeping the significant figures in view.
Answers There are 3 significant figures in the measured mass whereas there are only 2 significant figures in the
measured volume. Hence the density should be expressed to only 2 significant figures.
Example12. Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume of
the cube to appropriate significant figures?
Answer The number of significant figures in the measured length is 4. The calculated area and the volume should
therefore be rounded off to 4 significant figures.
Surface area of the cube =
Volume of the cube =
ACCURACY AND PRECISION OF INSTRUMENTS
Accuracy of an instrument represents the closeness of the measured value of actual value. Precision
of an instrument represents the resolution of the instrument. It depends on least count.
Least count of an instrument is the
least measurement, which can be made
accurately with that instrument.
Least count of an ordinary metre scale
is 0.1 cm, 0.01 cm is the least count of
vernier calipers and 0.001 cm is that
for screw gauge.
For example a physical quantity is measured
from two instruments A and B. The reading of
A is 2.54 cm (say) and that of B is 2.516 cm.
The actual value is 2.53 cm. The first reading
is closed to actual value, it has more accuracy. The second reading is less accurate, but the
instrument B has greater resolution as it can measure up to 3 decimal places.
Internal Jaws
0 1 2 3 4 5 6 7
0 10
Main scale
Vernier scale
External Jaws
Strip for depth
measurement
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28 Errors in Measurements
Difference between the value obtained in a measurement and the true value of the quantity is
called error in that measurement.
The following are the commonly occurring errors:
(1) Constant error:
If the error in a series of readings taken with an instrument is same, the error is said to be
constant error.
(2) Systematic errors:
Errors, which are due to known causes and act according to a definite law are called systematic
errors.
(a) Instrumental errors:
These errors are due to the defect of the instrument.
Eg: 1. Zero error in screw gauge and vernier.
2. Faulty calibration of thermometer, metre scale etc.
(b) Personal error:
This is due to the mode of observation of the person taking the reading. E.g.: Parallax error.
(b) Error due to imperfection:
This is due to imperfection of the experimental setup.
Eg: Whatever precautions are taken, heat is always lost from a calorimeter due to radiation.
(c) Error due to external causes:
These are errors caused due to change in external conditions like temp, pressure, humidity etc.
Eg: With increase in temperature, a metal tape will expand. Any length measured using this tape
will not give corrects reading.
(3) Random Error:
The errors, which occur irregularly and at random in magnitude and direction, are called
random errors. These errors are not due to any definite cause and so they are also called
accidental errors.
Random errors can be minimized by taking several measurements and then finding the arithmetic
mean. The mean is taken as the true value of the measured quantity.
Let a quantity measured n times give values , then the possible value a of the
quantity is
The arithmetic mean
is taken as the true value of the quantity.
(4) Gross Errors:
The errors caused by the carelessness of the person are called gross errors. It may be due to
(1) Improper adjustment of apparatus
(2) Mistakes while taking and recording readings etc.
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(5) Absolute Errors:
The magnitude of the difference between the true value of the quantity measured and the individual
measured value is called the absolute error.
If a1, a2,…..,an are the measured values and
is the true value,
Then absolute error,
Δ
Δ
and so on.
(5) Mean absolute error:
The arithmetic mean of the absolute error of the different measurements taken is called mean
absolute error.
If Δ
, Δ
,……. Δ
are the absolute errors in the measurements a1, a2, a3,…an, then
7) Relative and percentage errors.
The ratio of the mean absolute error to the true value of the measured quantity is called relative
error.
And percentage
Example13. We measure the period of oscillation of a simple pendulum. In successive measurements, the
readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s. calculate the absolute errors, relative error or
percentage error.
Answer The mean period of oscillation of the pendulum
The errors in the measurements are
The arithmetic mean of all the absolute errors (for arithmetic mean, we take only the magnitudes) is
That means, the period of oscillation of the simple pendulum is (2.62 ± 0.11) s i.e. it lies between (2.62 + 0.11) s and
(2.62 - 0.11) s or between 2.73 s and 2.51 s. As the arithmetic Mean of all the absolute errors is 0.11 s, there is already
an error in the tenth of a second. Hence there is no point in giving the period to a hundredth. A more correct way will
be to write T = 2.6 ± 0.1 s
The relative error or the percentage error is
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30 Combination of errors
(1) Error in a sum or difference: —
Let two quantities A and B have errors Δ A and Δ B respectively in their measured values. We have
to calculate the error Δ Z in their sum Z = A + B.
We will get the same result even if we take the difference.
When two quantities are added or subtracted, the absolute error in the final result is the sum
of the absolute errors in the quantities.
Example14 The temperatures of two bodies measured by a thermometer are
Calculate the temperature difference and the error there in.
Answer
(2) Error in a product or quotient
Let A and B be two quantities and Z be their product. ie Z = AB. If A andB are the
measured values of A and B, then
Z = A)( B)=ABABABAB
Dividing LHS by Z and RHS by AB, Z
=AB
AB AB
AB AB
AB AB
AB
=1Z
=1B
BA
A
ie,AandB being small. So neglecting AB
AB
Hence the maximum possible relative error or fractional error in Z is Z
=B
BA
A
The result is true for division also.
Therefore, when two quantities are multiplied or divided, the relative error of the result is equal to
the sum of relative errors of the quantities.
Example15. the resistance
where V = (100 ± 5) V and I = (10 ± 2) A. Find the percentage error in R.
Answer The percentage error in V is 5% and in I it is 2%. The total error in R would therefore be 5% + 2% = 7%.
Example16. Two resistors of resistances = 100 ±3 ohm and = 200 ± 4 ohm are connected in series. Find
the equivalent resistance of the series combination. Use the relation ,
Answer the equivalent resistance of series combination
SANDEEP SONI’S PHYSICS COMPETITION CLASSES
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(3) Error when a quantity is raised to a power.
Consider a quantity
Taking logarithm on both sides, log X = log xn = n log x.
Differentiating, we get X
=x
x
Thus if a quantity has to be raised to a power n, then the relative error of the result is n times the
relative error of that quantity.
Example17. The period of oscillation of a simple pendulum is
Measured value of L is 20.0 cm
known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch
of 1 s resolution. What is the accuracy in the determination of g?
Answer
Here,
Example18. A physical quantity P is related to four observables a, b, c and d as follows:
. The percentage
errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively, What is the percentage error in
the quantity P ?
Ans
Some important questions
1.
How is SI is a coherent system of units
2.
Why parallex method is not useful for measuring distances of star more than 100 light year.
3.
Do all physical quantity has same dimensions? If no, name three physical quantity which are
dimensionless.
4.
Velocity of a particle depends on time t as v=+bt+c where v is in m/s and t in s. what are unit of
a,b,c,
5.
Justify L+L=L and L-L=L
6.
Which of given measurement more accurate and why? (a) 5.0g (b) 5.00g(c) 5g
SANDEEP SONI’S PHYSICS COMPETITION CLASSES
(10+1, 10+2, IIT-JEE (Main & Advance), NEET, B.Sc. Agriculture, NDA)
OPP: JHUNTHARA DHARAMSHALA NEAR SURKHAB CHOWK, HISSAR ROAD SIRSA
UNIT -1 PHYSICAL WORLD PH- 94676-12340, 8708535733
31
31 Selected objectives (for competitive entrance exam)
1.
Light year is a unit of
a. time b. mass c. distance. d. energy
2
Which unit is not for length
a. Parsec b. light year c. Angstrom d. nano.
3
Wavelength of ray of light is 0.00006m. it is equal to
a. 6micron b. 60micron. c. 600micron d. 0.6micron
4
Which is the correct unit for measuring the nuclear radii
a. micron b. millimeters c. Angstrom d. Fermi.
5.
Kilowatt hour is the unit of
a. electric charge b. energy. c. power d. force
6.
Dimensional formula for impulse is same as the dimensional formula of
a. momentum. b. force c. torque d. rate of change of momentum
7.
Which physical quantity have same dimension
a. force, power b. torque , energy. c. torque, power d. force , power
8.
Planks constant has dimension has dimension of
a. energy b. linear momentum c. work d. angular momentum.
9.
The physical quantity that has no dimension is
a. angular velocity b. linear momentum c. angular momentum d. strain.
10.
The resistance R =V/I where V=100±5volts and I=10±0.2Amperes.What is the total error in R
a. 5% b. 7%. c. 5.2% d. 5/2%
11.
If L=2.331 cm, B=2.1cm than L+B is
a. 4.431cm b. 4.43cm c. 4.4cm. d. 4cm
12.
Number of significant fig in all given number 25.12, 2009,4.156 and 1.217×107
a. 1 b. 2 c. 3 d. 4.
13.
A physical quantity A is related to four observations a,b,c and d are as A=
. The % error of
the measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. what is the % error in A
a. 12% b. 7% c. 5% d. 14%.
14.
An Indian scientist who won noble prize for physics is
a. J.C. Bose b. H.J. Bhabha c. M.N. saha d. C.V.Raman.
15.
If error in radius is 3% .what is the error in volume of the sphere
a . 3% b.27% c.9 %. d. 6%
16.
Albert Einstein got noble prize in physics for his work on
a. special theory of relativity b. general theory of relativity
c. photoelectric effect. d. theory of specific heat.
