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Physics
chapter-1
Introduction to physical world and
measurement
The word physics is come from Greek word which means nature
 Physics is branch of science which deals with study if nature and natural
phenomena
 Its divided into
 1-mechanics
 2-heat(thermal physics)
 3-light(optics)
 4-sound(acoustics)
 5-magnetism
 6-electrostatics
 7-modern physics(atomic and nuclear)
 8-Electronics and communications
Scientific method:This method which the scientists used
in pursuit of science. It involves in 6 steps
 Systematic observation
 Reasoning
 Making model
 Theoretical predictions of phenomena
 Modification of theory if any
Physics in relation to other sciences
Physics in relation to chemistry : The study of x ray diffraction ,
radioactivity , structure of atom etc. Different chemical bonding and
complex chemical structure is based on physics
Physics in relation to biological sciences: Used in optical
microscope , electron microscope . Radio therapy by radio-isotopes is
used to cure diseases like cancer and other diseases
Physics in relation mathematics : Mathematics is the backbone
of physics
Physics relation in astronomy: Used for observing planets and
other heavenly bodies in the sky
Needs of measurement : From the very
antient time , man started measuring different physical
quantities by using conventional method
Units of measurements:
Physical quantity : Any characteristic that can be given to matter
Unit: Standard measure used for the measurement of physical quantity.
Two requirement for physical quantity:
• The unit in which the quantity measured ‘u’
• The no. of times the units involved in the quantity
Q= n * u
Characteristics of a standard unit:
• Well defined
• Imperishable
• Easily reproducible
• Not change with place,time and physical conditions
• Easily comparable with other similar units
Fundamental and derived units:
Fundamental quantities: Quantities which do not
depend on any other quantities.
eg: Length , mass
Derived units:Quantities which are derived from
fundamental quantities
eg:Work , velocity
Systems of units
 C.G.S system(cm,g,sec): it is a French system . Deals with 3 fundamental
quantities length,mass,time
 F.P.S system (foot,bound,second): It is British system . Deals with 3
fundamental quantities length,mass,time
 M.K. system(m,kg,sec):It is a French system.deals with quantities
length,mass,time
S.I. units
It is a French system there are seven fundamental and two supplementary units
Advantages of S.I Units:
 It is a rational system of units
 It is a coherent system of units
 Base units satisfy all the charactiristics that unit should have
 It is a metric system
 It is closely related to C.G.S.system
 International accepted
Definitions of S.I. unit:
 Length – meter(m) -The metre is length equal to 165076373 wavelengths of orange red light
emitted by krypton-86 atom in electric discharge
 Mass – kilogram(kg) - It is the mass of a cylinder of nearly the same height and diameter and
made of an alloy 90% platinum and 10% iridium (platinum-iridium-cylinder) kept at
International Bureau of Standard inSevres, France
 Time – second(s) - It is the time required for 9192631770 cycles of radiations that cause
transition of cesium (133) atom between two specified lower energy levels.
 Electric current – ampere(a) - is that constant current which whenflowing in two parallel
conductors of infinite length and of negligible area ofcross-section and placed one metre
apart in vacuum, would produce be tween the conductors a force equal to 2 x 10"newton per
metre of length.
 Temperature – kelvin(k) - It is equal to 6 of the thermodynamic temperature of
triple point of water.
 Luminous intensity – candela(cd) -is the luminous intensity, in a direction at right
angles to a surface of 0,000 square metre area of a black body kept at a
temperature of freezing platinumunder a pressure of 101,325
 Amount of substance – mole(mol) - is the amount of substance of a sys tem which
contains as many elemen tary entities (atoms, molecules, or other particles) as
there are carbon atoms in 0.012 kg of carbon-12.
Some practical units of
length,mass,time:
 Length:
• Parallactic second (par sec)
1para sec =3.08*10power16 m=3.26 light yr
• Light yr (ly):
1ly = 9.46*10power 15 m
• Astronomical unit(AU):
1 AU =1.496*10power 11 m
 Mass:
• Solar mass
1mo =2*10power 30 kg
• Metric ton:
1metric ton = 1 tonne = 1000 kg
 Time:
• Millennium
1 millennium=1000 yrs
• Century
1 century=100 yrs
• Solar day
• Solar yr or yr
• Lunar month
1 lunar month=27.3 days
• Shake
1 shake=10 power -8 s
Introduction of dimensions and
dimensional analysis
We can use symbols instead of the names of the base quantities. L,M,T
etc are used to represent length ,mass, time etc.
• Dimensions:power of fundamental quantities,through which they are
to be raised to represent unit derived quantity
area= length *length=L×L=𝐿2=
[A]=[𝑀0 𝐿2 𝑇0]
Acceleration = velocity/time
=distance/time/time=L/T/T=
𝐿
𝑇2 = 𝐿𝑇−2
𝑎 = 𝑀0
𝐿1
𝑇−2
V=DISTANCE/TIME
V=𝑉 =
𝐿
𝑇
= 𝐿𝑇−1
 Momentum=mass *velocity
 𝑝 = 𝑀′
] ∗ [𝐿1
𝑇−1
 force=mass *acceleration(f=ma)

[F]=?
 F= 𝑀 × [𝐿𝑇−2
]
 [F]=[𝑀0
𝐿1
𝑇−2
]
 PRESSURE=FORCE/AREA
 [P]=?
 WORK=FORCE× 𝐿𝐸𝑁𝐺𝑇𝐻
[W]=[𝑀0
𝐿1
𝑇−2
] × [𝐿] = [𝑀0
𝐿2
𝑇−2
]
Types Of Quantities
 Dimensional variables:
physical quantities which have dimensions and do not have a constant value
eg:velocity,work,power
 Dimensional constants:
physical quantities that have constant value but still have dimensions
eg:plancks(h),universal gravitational constant (G)
 Dimensionless constant:
pure number like1,2,3,𝜋 etc
 Dimensionless variables:
physical quantities which have no dimension but are variables
eg:strain,plane angle
Applications of dimensional analysis
 Covert the value of physical quantity
 Check the correctness of given relation
 Derive a relation btw various physical
quantities
Accuracy and errors in measurement
 Error : the difference between true value and
measured value is called error
 Accuracy: Accuracy of a measured value refers to how
close a measurement is to the correct value.
 Precision :Precision of measured values refers to how close
the agreement is between repeated measurements.
Types of errors
 Constant error:Constant errors are those which affect the result by the same
amount
 Systemic error: Systematic error is due to some known causes according to a
definite law.
• Instrumental error:These errors are of apparatus and measuring instruments
used.
• Personal error or observation error: The errors committed due to personal
peculiarities of the experiment are known as personal error.
• Error due to external causes:These emotions due to change
of external conditions like temperature, pressure, electric or magnetic
field etc..
• Error due to imperfection:Some errors occur due to
imperfection in experimental arrangement.
 Random error:Random error is the error caused by the individual
who measures the quantity
 Gross errors:The errors due to the carelessness of the person are
called gross errors.
 Absolute error:The arithmetic mean of the absolute error of
different measurements taken is called mean absolute error
Δ𝑎1 = 𝑎 − 𝑎𝑖
 Mean absolute error:The arithmetic mean of the
absolute error of different measurements taken is
called mean absolute error
 Relative error: The ratio of the mean absolute error to
the true value of the measured quantity is called the
relative error
 Percentage error:It is the relative error expressed in
percentage
Percentage error X100
Δ 𝑎
𝑎
× 100
Δ 𝑎
𝑎
Error in sum of quantities
 𝑋 ∓ ∆𝑥 = 𝑎 ∓ ∆𝑎 + 𝑏 ∓ ∆𝑏
 Let ∆𝑎 =absolute error in a
 ∆b= absolute error in b
 ∆x=absolute error in 𝑥
 X=a+b
 ∆x= ∆a+ ∆b
Error in difference of quantities
 𝑋 ∓ ∆𝑥 = 𝑎 ∓ ∆𝑎 − 𝑏 ∓ ∆𝑏
 Let ∆𝑎 =absolute error in a
 ∆b= absolute error in b
 ∆x=absolute error in 𝑥
 X=a-b
 ∆x= ∆a+ ∆b
Error in product
 X=A/B
 X= x∓∆𝑥 A= 𝑎 ∓ ∆𝑎 B=𝑏 ∓ ∆𝑏
 x=a/b

∆𝑥
x
=
∆𝑎
𝑎
+
∆𝑏
𝑏
Error in quotient
 X=A*B
 X= x∓∆𝑥 A= 𝑎 ∓ ∆𝑎 B=𝑏 ∓ ∆𝑏
 x=a*b

∆𝑥
x
=
∆𝑎
𝑎
+
∆𝑏
𝑏
Error when a quantity raised to a power
 X=𝐴 𝑚/𝐵 𝑛
 X= x∓∆𝑥 A= (a ∓ ∆𝑎)
𝑚
B=(𝑏 ∓ ∆𝑏)
𝑛
 X= a 𝑚
/ 𝑏 𝑛
 Error
Δ𝑥
𝑥
= 𝑚 ×
Δ𝑎
𝑎
+ 𝑛 ×
Δ𝑏
𝑏
 Let x=𝑎2
 Here error
Δ𝑥
𝑥
=
2Δ𝑎
𝑎
Significant figures
significant figures are the number of digits required to report the
result of an experiment or calculation accurately
 All non zero digits are significant
 123.56 has 5 significant figure
 All zeros in between nan zero are significant
 120.56 has 5 sig fig
 All the non zero after decimal but before a non zero digit are significant
 0.00855 has 3 sig fig
 All zero right side to decimal and right side of a non-zeo digit are significant
 0.8200 has 4 sig fig
 All zeros,right of anon zero digit in a whole non are not significant
 11500 has 3 sig fig
 If there are a decimal at end in the above case then all no are significant
 11500. has 5 sig fig
 If a number has integral part and decimal part then all zeros in the number are
significant
 30.10 has 4 significant fig
 7447—
 4
 23.07----
 4
 0.083----
 2
 5500----
 2
 0.04350------
 4
 10.30-----
 4
Rounding off

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Physical world and units and measurment

  • 2. The word physics is come from Greek word which means nature  Physics is branch of science which deals with study if nature and natural phenomena  Its divided into  1-mechanics  2-heat(thermal physics)  3-light(optics)  4-sound(acoustics)  5-magnetism  6-electrostatics  7-modern physics(atomic and nuclear)  8-Electronics and communications
  • 3. Scientific method:This method which the scientists used in pursuit of science. It involves in 6 steps  Systematic observation  Reasoning  Making model  Theoretical predictions of phenomena  Modification of theory if any
  • 4. Physics in relation to other sciences Physics in relation to chemistry : The study of x ray diffraction , radioactivity , structure of atom etc. Different chemical bonding and complex chemical structure is based on physics Physics in relation to biological sciences: Used in optical microscope , electron microscope . Radio therapy by radio-isotopes is used to cure diseases like cancer and other diseases Physics in relation mathematics : Mathematics is the backbone of physics Physics relation in astronomy: Used for observing planets and other heavenly bodies in the sky
  • 5. Needs of measurement : From the very antient time , man started measuring different physical quantities by using conventional method Units of measurements: Physical quantity : Any characteristic that can be given to matter Unit: Standard measure used for the measurement of physical quantity. Two requirement for physical quantity: • The unit in which the quantity measured ‘u’ • The no. of times the units involved in the quantity Q= n * u
  • 6. Characteristics of a standard unit: • Well defined • Imperishable • Easily reproducible • Not change with place,time and physical conditions • Easily comparable with other similar units
  • 7. Fundamental and derived units: Fundamental quantities: Quantities which do not depend on any other quantities. eg: Length , mass Derived units:Quantities which are derived from fundamental quantities eg:Work , velocity
  • 8. Systems of units  C.G.S system(cm,g,sec): it is a French system . Deals with 3 fundamental quantities length,mass,time  F.P.S system (foot,bound,second): It is British system . Deals with 3 fundamental quantities length,mass,time  M.K. system(m,kg,sec):It is a French system.deals with quantities length,mass,time
  • 9. S.I. units It is a French system there are seven fundamental and two supplementary units
  • 10. Advantages of S.I Units:  It is a rational system of units  It is a coherent system of units  Base units satisfy all the charactiristics that unit should have  It is a metric system  It is closely related to C.G.S.system  International accepted
  • 11. Definitions of S.I. unit:  Length – meter(m) -The metre is length equal to 165076373 wavelengths of orange red light emitted by krypton-86 atom in electric discharge  Mass – kilogram(kg) - It is the mass of a cylinder of nearly the same height and diameter and made of an alloy 90% platinum and 10% iridium (platinum-iridium-cylinder) kept at International Bureau of Standard inSevres, France  Time – second(s) - It is the time required for 9192631770 cycles of radiations that cause transition of cesium (133) atom between two specified lower energy levels.  Electric current – ampere(a) - is that constant current which whenflowing in two parallel conductors of infinite length and of negligible area ofcross-section and placed one metre apart in vacuum, would produce be tween the conductors a force equal to 2 x 10"newton per metre of length.
  • 12.  Temperature – kelvin(k) - It is equal to 6 of the thermodynamic temperature of triple point of water.  Luminous intensity – candela(cd) -is the luminous intensity, in a direction at right angles to a surface of 0,000 square metre area of a black body kept at a temperature of freezing platinumunder a pressure of 101,325  Amount of substance – mole(mol) - is the amount of substance of a sys tem which contains as many elemen tary entities (atoms, molecules, or other particles) as there are carbon atoms in 0.012 kg of carbon-12.
  • 13. Some practical units of length,mass,time:  Length: • Parallactic second (par sec) 1para sec =3.08*10power16 m=3.26 light yr • Light yr (ly): 1ly = 9.46*10power 15 m • Astronomical unit(AU): 1 AU =1.496*10power 11 m
  • 14.  Mass: • Solar mass 1mo =2*10power 30 kg • Metric ton: 1metric ton = 1 tonne = 1000 kg  Time: • Millennium 1 millennium=1000 yrs • Century 1 century=100 yrs • Solar day • Solar yr or yr • Lunar month 1 lunar month=27.3 days • Shake 1 shake=10 power -8 s
  • 15. Introduction of dimensions and dimensional analysis We can use symbols instead of the names of the base quantities. L,M,T etc are used to represent length ,mass, time etc. • Dimensions:power of fundamental quantities,through which they are to be raised to represent unit derived quantity area= length *length=L×L=𝐿2= [A]=[𝑀0 𝐿2 𝑇0] Acceleration = velocity/time =distance/time/time=L/T/T= 𝐿 𝑇2 = 𝐿𝑇−2 𝑎 = 𝑀0 𝐿1 𝑇−2 V=DISTANCE/TIME V=𝑉 = 𝐿 𝑇 = 𝐿𝑇−1
  • 16.  Momentum=mass *velocity  𝑝 = 𝑀′ ] ∗ [𝐿1 𝑇−1  force=mass *acceleration(f=ma)  [F]=?  F= 𝑀 × [𝐿𝑇−2 ]  [F]=[𝑀0 𝐿1 𝑇−2 ]  PRESSURE=FORCE/AREA  [P]=?  WORK=FORCE× 𝐿𝐸𝑁𝐺𝑇𝐻 [W]=[𝑀0 𝐿1 𝑇−2 ] × [𝐿] = [𝑀0 𝐿2 𝑇−2 ]
  • 17. Types Of Quantities  Dimensional variables: physical quantities which have dimensions and do not have a constant value eg:velocity,work,power  Dimensional constants: physical quantities that have constant value but still have dimensions eg:plancks(h),universal gravitational constant (G)  Dimensionless constant: pure number like1,2,3,𝜋 etc  Dimensionless variables: physical quantities which have no dimension but are variables eg:strain,plane angle
  • 18. Applications of dimensional analysis  Covert the value of physical quantity  Check the correctness of given relation  Derive a relation btw various physical quantities
  • 19. Accuracy and errors in measurement  Error : the difference between true value and measured value is called error  Accuracy: Accuracy of a measured value refers to how close a measurement is to the correct value.  Precision :Precision of measured values refers to how close the agreement is between repeated measurements.
  • 20. Types of errors  Constant error:Constant errors are those which affect the result by the same amount  Systemic error: Systematic error is due to some known causes according to a definite law. • Instrumental error:These errors are of apparatus and measuring instruments used. • Personal error or observation error: The errors committed due to personal peculiarities of the experiment are known as personal error.
  • 21. • Error due to external causes:These emotions due to change of external conditions like temperature, pressure, electric or magnetic field etc.. • Error due to imperfection:Some errors occur due to imperfection in experimental arrangement.  Random error:Random error is the error caused by the individual who measures the quantity  Gross errors:The errors due to the carelessness of the person are called gross errors.  Absolute error:The arithmetic mean of the absolute error of different measurements taken is called mean absolute error Δ𝑎1 = 𝑎 − 𝑎𝑖
  • 22.  Mean absolute error:The arithmetic mean of the absolute error of different measurements taken is called mean absolute error  Relative error: The ratio of the mean absolute error to the true value of the measured quantity is called the relative error  Percentage error:It is the relative error expressed in percentage Percentage error X100 Δ 𝑎 𝑎 × 100 Δ 𝑎 𝑎
  • 23. Error in sum of quantities  𝑋 ∓ ∆𝑥 = 𝑎 ∓ ∆𝑎 + 𝑏 ∓ ∆𝑏  Let ∆𝑎 =absolute error in a  ∆b= absolute error in b  ∆x=absolute error in 𝑥  X=a+b  ∆x= ∆a+ ∆b
  • 24. Error in difference of quantities  𝑋 ∓ ∆𝑥 = 𝑎 ∓ ∆𝑎 − 𝑏 ∓ ∆𝑏  Let ∆𝑎 =absolute error in a  ∆b= absolute error in b  ∆x=absolute error in 𝑥  X=a-b  ∆x= ∆a+ ∆b
  • 25. Error in product  X=A/B  X= x∓∆𝑥 A= 𝑎 ∓ ∆𝑎 B=𝑏 ∓ ∆𝑏  x=a/b  ∆𝑥 x = ∆𝑎 𝑎 + ∆𝑏 𝑏 Error in quotient  X=A*B  X= x∓∆𝑥 A= 𝑎 ∓ ∆𝑎 B=𝑏 ∓ ∆𝑏  x=a*b  ∆𝑥 x = ∆𝑎 𝑎 + ∆𝑏 𝑏
  • 26. Error when a quantity raised to a power  X=𝐴 𝑚/𝐵 𝑛  X= x∓∆𝑥 A= (a ∓ ∆𝑎) 𝑚 B=(𝑏 ∓ ∆𝑏) 𝑛  X= a 𝑚 / 𝑏 𝑛  Error Δ𝑥 𝑥 = 𝑚 × Δ𝑎 𝑎 + 𝑛 × Δ𝑏 𝑏  Let x=𝑎2  Here error Δ𝑥 𝑥 = 2Δ𝑎 𝑎
  • 27.
  • 28.
  • 29.
  • 30. Significant figures significant figures are the number of digits required to report the result of an experiment or calculation accurately  All non zero digits are significant  123.56 has 5 significant figure  All zeros in between nan zero are significant  120.56 has 5 sig fig  All the non zero after decimal but before a non zero digit are significant  0.00855 has 3 sig fig
  • 31.  All zero right side to decimal and right side of a non-zeo digit are significant  0.8200 has 4 sig fig  All zeros,right of anon zero digit in a whole non are not significant  11500 has 3 sig fig  If there are a decimal at end in the above case then all no are significant  11500. has 5 sig fig  If a number has integral part and decimal part then all zeros in the number are significant  30.10 has 4 significant fig
  • 32.  7447—  4  23.07----  4  0.083----  2  5500----  2  0.04350------  4  10.30-----  4