1. Mechanics and properties of matter
Measurements
By: Dr. Nitin Oke.
Safe Hands, Akola

2. Need of measurement
Physical theory need experimental verification and results of experimental verification involves measurement.
If every one decide to have his own way of measurement then it will not be possible to come to correct conclusion.
Thus a well defined, universally accepted system must be developed
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3. Need of system of units It must be convenient Easily reproducible
Must be uniform and constant
Internationally accepted.
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4. Different systems of units
FPS system: Used by Europeans, consist of three basic units for length, mass and time. The units were foot (ft), pound (lb) and for time it is second (s).
Metric system: MKSA system, it is system based on quantities for length, mass, time and current. Sub system of this system is more popular by name MKS.
SI system: Recent mostly accepted. It is abbreviation of ”System International de unites” (1960) It consist of six base units two supplementary units and derived units.
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5. SI system Base units are
Meter : it is defined as times the wavelength in vacuum of orange red line emitted by krypton 86.
Present definition is length of path traveled by light in vacuum during time interval 1/ of second.
Kilogram : It is the mass of prototype of iridium – platinum alloy kept in “ International Bureau of Weights and measures at serves, Near Paris in France
Second : It is the time taken by radiation from cesium- 133 atom to complete vibrations
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6. SI system Base units are
Ampere : it is defined as current flowing through each of two thin parallel conductors of infinite length kept in free space at a distance of a meter apart, produces a force of 2 x 10-7 N per unit length.
Candela : It is the luminous intensity of an area of 1/ m2 of black body in the normal direction to its surface at temperature of freezing platinum under the pressure of N/m2
Kelvin : It is the fraction 1/ of thermodynamic temperature of triple point of water.
Mole : It is defined as the amount of substance of a system which the same number of elementary entities as there are atoms in exactly 12 grams of pure carbon 12
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7. SI system Supplementary units are
Radian : It is the angle subtended by an arc length equal to radius of a circle at centre of circle.
Steradian : It is the solid angle subtended at the centre of a sphere by an area of a square on the surface of a sphere each side of square is of length equal to radius of sphere.
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8. Fundamental physical quantities
Fundamental physical quantities: The physical quantities which can not be expressed in terms of other physical quantities are called as fundamental physical quantities.
Fundamental physical quantities: The physical quantities which are chosen for base units are called as fundamental physical quantities.
Fundamental units: Units expressing fundamental quantities is called as fundamental units.
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9. Derived physical quantities
Physical quantities which can be expressed in terms of one or more fundamental quantities are called as derived quantities.
Speed , acceleration, density, volume, force, momentum, pressure, room temperature. charge, potential difference, KE, PE, resistance, work,
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10. Derived physical quantities
Speed length/time m/s
Acceleration length/time2 m/s2
Density mass/ length3 kg/m3
Volume length3 m3
Force mass.(length)/time2 kg.m/s2
Momentum mass. Length/time kg. m/s
Pressure mass/length.time2 kg/ms2
room temperature temperature K
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11. Short recall Force = mass. displacement Work = force . Displacement
KE = ½ mv2
PE = m. g. h
I = charge/time
pd = energy required to circulate the unit charge from terminal to terminal. = E/q
R = V/I
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12. Derived physical quantities
Charge = current x Time = A.s
Work = force . Displacement
= mass x (length)2/(time)2
KE = mass x (length)2/(time)2
PE = mass x (length)2/(time)2
potential difference
= energy per unit charge
= [mass x (length)2/(time)2] /current. time
= mass x (length)2 /current. time3
Resistance
= V/ I = (M.L2/I.T3)/I = ML2/I2T3
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13. Fundamental Quantities
More about Units
Fundamental Quantities
SI Units
Symbol
Length
meter m
Mass
kilogram kg
Time
second s
Electric current
ampere A
Luminous intensity
candela cd
Temperature
kelvin K
Mole
mole
mol
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14. More about Units Derived Quantities SI Units Symbol Force newton N
Work / Energy
joule J
Power
watt W
Electric charge
coulomb C
potential
volt V
resistance
ohm Ω
frequency
hertz Hz
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15. Always remember - - - Newton n kg Kg
Full names of units are NOT written starting with capital initial letter.
Kilogram
Meter
meter
kilogram
Newton
newton
Units named after person will NOT be written with capital initial letter. The symbol of the units in memory of a person will be in capital letters. This will not be for other units. n
newton N kg
kilogram Kg
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16. Dimensional Analysis
Dimensions of a physical quantity are the powers to which the fundamental units must be raised in order to get the unit of derived quantity.
Symbols used for fundamental quantities are
Length [ L ] , mass [ M ], time [ T ], current [I], Temperature [  ]
Using powers of these symbol we represent dimension of physical quantities.
In short the dimension is expression which shows the relation between the derived unit and the fundamental units.
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17. Dimensions of derived units
Derived Quantities
dimension
Derived Quantities
dimension
frequency
[T-1]
potential
[M1L1T-3 I-1]
speed
[L1T-1]
resistance
[M1L1T-3 I-2]
acceleration
[L1T-2]
Electric charge
[IT]
momentum
[M1L1T-1]
Force
[M1L1T-2]
Density
[M1L-3]
Work/ Energy
[M1L2T-2]
Radian, refractive index etc
[ ]
Power
[M1L2T-3]
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18. Application of dimensional equation
Dimensional analysis can be used —
to check whether the given equation is dimensionally correct. ( If an equation is dimensionally correct then it can differ only in numerical constants.)
To find the relation between same unit in different systems. For example
let 1N = c dyne
1[M1L1T-2] = c [M1L1T-2]
kg.m.s-2 = c gm.cm.s-2
c = = 105
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19. Significant figure
Order of magnitude: If a number is expressed as “n x 10m ” where 0.5 ≤ n < 5 then 10m is called as order of magnitude.
Significant figure:
Reliable figure :
Doubtful figure:
4.8
4.85
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20. Significant figure Significant figure:
The number of all nonzero digits are significant.
234 has 3 significant digits
has 8 significant digits
Decimal point is a problem as
If number is free of decimal point then zero on right of first nonzero digit are NOT significant means
200 has 1 significant digit
3700 has 2 significant digits
If number is with decimal point then zeros to the right of decimal point and on left of first nonzero number is non significant but zeros on right of last nonzero digit are significant
has 3 significant digits
has 3 significant digits
0.00 has 2 significant digit
has 2 significant digits
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21. Need and notation of scientific numbers
If reading is
2.320m = 232.0cm = 2320mm = km
Here 2320mm has 3 significant digits and has 4 significant digits
To avoid above contradiction we use scientific notation in which the number will be written as
2.320m = x 102cm
= x 103mm = x 10-3km
As power of ten does not contribute in significant figures thus even by changing units the number of significant digits will remain same.
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22. Operation with scientific figures
During addition or subtraction always express answer with number of digits after decimal point is same as the number with the least number of digits after decimal point.
For example
1477.6
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23. Multiples and divisors
Prefix
Symbol
Multiples
deca da 10
hecto h
102
kilo k
103
mega M
106
giga G
109
tera T
1012
peta P
1015
exa E
1018
zetta Z
1021
yotta Y
1024
Prefix
Symbol
Multiples
deci de
10-1
centi c
10-2
milli m
10-3
micro 
10-6
nano n
10-9
peco p
10-12
femto f
10-15
atto a
10-18
zepto z
10-21
yocto y
10-24