APPLIED PHYSICS SHORT NOTES (STUDY MATERIAL)

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                                 APPLIED PHYSICS
          MEASUREMENTS-UNITS
AND DIMENSION
The
comparison of any physical quantity with its standard unit is called  
measurement.
Physical Quantities
All the quantities in terms of which laws of physics are described,
and
whose measurement is necessary are called physical quantities.

Units

 ·   A definite amount of a physical
quantity is taken as its standard unit.

 ·   The standard unit should be
easily reproducible, internationally accepted.

Fundamental Units
Those physical quantities which are independent to each other are called
fundamental quantities and their units are called fundamental units.
S.No. Fundamental Quantities Fundamental Units Symbol
1.
Length
metre
m
2.
Mass
kilogram
kg
3.
Time
second
S
4.
Temperature
kelvin
kg
5
Electric
current
ampere
A
6
Luminous
intensity
candela
cd
7
Amount
of substance
mole
mol
Supplementary Fundamental Units
Radian and steradian are two supplementary fundamental units. 
It
measures plane angle and solid angle respectively.
S.No. Supplementary Fundamental Quantities Supplementary
Unit Symbol
1
Plane
angle
radian
rad
2
Solid
angle
steradian
Sr
Derived Units
Those physical quantities which are derived from fundamental quantities 
are called derived quantities and their units are called derived units.
e.g.,
velocity, acceleration, force, work etc.


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Definitions of Fundamental Units
The seven
fundamental units of SI have been defined as under.
1.    
1 kilogram A cylindrical prototype mass made
of platinum and 
iridium alloys of height
39 mm and diameter 39 mm. It is mass 
of 5.0188 x 1025 atoms of carbon-12.
2.    
1 metre 1 metre is the distance that
contains 1650763.73
 wavelength of orange-red light of Kr-86.
3.    
1 second 1 second is the time in which
cesium atom
 vibrates 9192631770 times in an
atomic clock.
4.    
1 kelvin 1 kelvin is the (1/273.16) part
of the thermodynamics
 temperature of the triple point of water.
5.    
1 candela 1 candela is (1/60) luminous
intensity of an ideal 
source by an area of cm’ when source is at melting point of 
platinum (1760°C).
6.    
1 ampere 1 ampere is the electric current
which it maintained
 in two straight parallel conductor of infinite length and of negligible 
cross-section area
placed one metre apart in vacuum will produce 
between them a force 2 x 10-7 N per metre length.
7.    
1 mole 1 mole is the amount of substance
of a system which
 contains a many elementary entities (may be atoms, molecules,
ions, electrons or group of
particles, as this and atoms in 0.012 kg 
of carbon isotope 6C12.
Systems of Units
A system of units is the complete set of units, both fundamental and 
derived, for all kinds of physical quantities. The common system of 
units which
is used in mechanics are given below:
1.    
CGS System In this system, the unit of
length is centimetre, 
the unit of mass is gram and the unit of time is second.
2.    
FPS System In this system, the unit of
length is foot, the unit 
of mass is pound and the unit of time is second.
3.    
MKS System In this system, the unit of
length is metre,
 the unit of mass is kilogram and the unit of time is second.
4.    
SI System This system contain seven
fundamental
 units and two supplementary fundamental
units.
Relationship between Some Mechanical SI Unit
 and Commonly
Used Units
S.No. Physical Quantity
Unit
1
Length
(a) 1 micrometre = 10-6 m
(b) 1 angstrom =10-10 m
2
Mass
(a) 1 metric ton = 103 kg
                                                    
                                           (b) 1 pound =
0.4537 kg
                                         (c)
1 amu = 1.66 x10-23 kg



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3
Volume
  (a) 1 litre = 10-32 m3
4.
Force
(a) 1 dyne = 10-5 N
(b) 1
kgf = 9.81 N
(a) 1
kgfm2 = 9.81Nm-2
5.
Pressure
(b) 1 mm of Hg = 133 Nm-2
(c) 1 pascal = 1 Nm-2
(d) 1 atmosphere pressure = 76
cm of Hg = 1.01 x 105 pascal
(a) 1 erg =10-7 J
6.
Work
and energy
(b) 1
kgf-m = 9.81 J
(c) 1 kWh = 3.6 x 106 J
(d) 1 eV = 1.6 x 10-19 J
7.
Power
(d) 1 kgf- ms-1 =
9.81W
1 horse
power = 746 W
Some Practical Units
1.    
1 fermi =10-15 m
2.    
1 X-ray unit = 10-13 m
3.     
1 astronomical unit = 1.49 x 1011 m (average distance between sun
and earth)
4.    
1 light year = 9.46 x 1015 m
5.    
1 parsec = 3.08 x 1016 m = 3.26 light year
Some Approximate Masses
Object
Kilogram
Our
galaxy
2 x 1041
Sun
2 x 1030
Moon
7 x 1022
Asteroid
Eros 5 x 1015
Dimensions
Dimensions
of any physical quantity are those powers which are 
raised on fundamental units
to express its unit. The expression 
which shows how and which of the base
quantities represent the
 dimensions of a physical quantity, is called the
dimensional formula.



 Dimensional Formula of Some Physical Quantities

             Physical                                Dimensional         MKS
S.No.
   Quantity                               Formula                Unit
1
Area
[L2]
metre2
2
Volume
[L3]
metre3
3
Velocity
[LT-1]
ms-1
4
Acceleration
[LT-2]
ms-2
5
Force
[MLT-2]
newton
(N)
6
Work or
energy
[ML2T-2]
joule
(J)
7
Power
[ML2T-3]
J s-1 or watt
8
Pressure
or stress
[ML-1T-2]
Nm-2
9
Linear momentum or Impulse [MLT-1]
kg ms-1
10
Density
[ML-3]
kg m-3
11
Strain
Dimensionless    Unit less
12
Modulus
of elasticity
[ML-1T-2]
Nm-2
13
Surface
tension
[MT-2]
Nm-1
14
Velocity
gradient
T-1
second-1
15
Coefficient
of velocity
[ML-1T-1]
kg m-1s-1
16
Gravitational
constant
[M-1L3T-2]
Nm2/kg2
17
Moment
of inertia
[ML2]
kg m2
18
Angular
velocity
[T-1]
rad/s
19
Angular
acceleration
[T-2]
rad/S2
20
Angular
momentum
[ML2T-1]
kg m2S-1
21
Specific
heat
L2T-2θ-1
kcal kg-1K-1
22
Latent
heat
[L2T-2]
kcal/kg
23
Planck’s
constant
ML2T-1
J-s
24
Universal
gas constant
[ML2T-2θ-1]
J/mol-K
Homogeneity Principle
If the
dimensions of left hand side of an equation are equal to the
dimensions of
right hand side of the equation, then the equation is 
dimensionally correct.
This is known as homogeneity
principle.
Mathematically
[LHS] = [RHS]
Applications of Dimensions
1.    
To check the accuracy of physical
equations.
2.    
To change a physical quantity
from one system of units to 
     another system of units.
3.    
To obtain a relation between
different physical quantities.



   
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Significant Figures
In the measured value of a physical quantity, the number of digits 
about
the correctness of which we are sure plus the next doubtful digit, 
are called
the significant figures.
Rules for Finding Significant Figures
1.    
All non-zeros digits are
significant figures, e.g., 4362 m has
     4 significant figures.
2.    
All zeros occuring between
non-zero digits are significant 
     figures, e.g., 1005 has 4 significant figures.
3.    
All zeros to the right of the
last non-zero digit are not significant,
     e.g., 6250 has only 3 significant
figures.
4.    
In a digit less than one, all
zeros to the right of the decimal point 
     and to the left of a non-zero digit are
not significant,
     e.g., 0.00325 has only 3 significant figures.
5.    
All zeros to the right of a
non-zero digit in the decimal part
     are significant, e.g., 1.4750 has 5
significant figures.
Significant Figures in Algebraic Operations
(i) In Addition or Subtraction In addition or subtraction of the 
numerical values the final result should retain the least decimal 
place as in
the various numerical values. e.g.,
If l1= 4.326 m
and l2 = 1.50 m
Then, l1 + l2 = (4.326
+ 1.50) m = 5.826 m
As l2 has measured
upto two decimal places, therefore
l1 + l2 = 5.83 m
(ii) In Multiplication or Division In multiplication or division of the 
numerical values, the final result should retain the least significant 
figures
as the various numerical values. e.g., If length 1= 12.5 m 
and breadth b =
4.125 m.
Then, area A = l x b = 12.5 x
4.125 = 51.5625 m2
As l has
only 3 significant figures, therefore
A= 51.6 m2
Rules of Rounding Off Significant Figures
1.    
If the digit to be dropped is
less than 5, then the preceding 
     digit is left unchanged. e.g.,
1.54  is rounded off to 1.5.
2.    
If the digit to be dropped is
greater than 5, then the 
     preceding digit is raised by one. e.g.,
2.49  is rounded off to 2.5.
3.    
If the digit to be dropped is 5
followed by digit other than zero, 
     then the preceding digit is raised by one.
e.g., 3.55 is rounded off to 3.6.
4.    
If the digit to be dropped is 5
or 5 followed by zeros, then the 
     preceding digit is raised by one, if it is odd
and left unchanged if it is 
     even. e.g., 3.750 is rounded off to 3.8 and 4.650 is
rounded off to 4.6.
Error
The lack in accuracy in the measurement due to the limit of accuracy of
 the instrument or due to any other cause is called an error.
1. Absolute Error
The difference between the true value and the measured value of 
a
quantity is called absolute error.
2. Mean Absolute Error
The
arithmetic mean of the magnitude of absolute errors in all the 
measurement is
called mean absolute error.
3.  Relative Error The ratio of mean absolute error to the true 
value
is called relative

4. Percentage Error The
relative error expressed in percentage
   is called percentage error.
Propagation of Error
(i) Error
in Addition or Subtraction Let x = a + b or x = a – b
If the
measured values of two quantities a and b are 
(a ± Δa and (b ± Δb), then
maximum absolute error in their
 addition or subtraction.
Δx = ±(Δa
+ Δb)
(ii)
Error in Multiplication or Division Let x = a x b or x = (a/b).
 If the
measured values of a and b are (a ± Δa) and (b ± Δb), 
 then maximum relative
error

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