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Mechanics and

properties of matter

Measurements

By: Dr. Nitin Oke.

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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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Need of system of units• It must be convenient• Easily reproducible• Must be uniform and constant• Internationally accepted.

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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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SI system• Base units are

– Meter : it is defined as 165076373 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 1/299792458 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 9192631770 vibrations

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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 1/600000 m2 of black body in the normal direction to its surface at temperature of freezing platinum under the pressure of 101325 N/m2

– Kelvin : It is the fraction 1/ 273.16 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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• 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.

SI system

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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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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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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/timekg. m/s

– Pressure mass/length.time2 kg/ms2

– room temperature temperature K

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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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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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More about UnitsFundamental

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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More about UnitsDerived

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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Always remember - - -• Full names of units are NOT written

starting with capital initial letter. Meter meter Kilogramkilogram

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.

newton N nkilogramKg kg

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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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Dimensions of derived units

[T-1]frequency

[L1T-1]speed

[L1T-2]acceleration

[M1L1T-1]momentum

[M1L1T-2] Force

[M1L2T-3]Power

[M1L2T-2]Work/ Energy

dimension

Derived Quantities

[IT]Electric charge

[M1L1T-3 I-1]potential

[M1L1T-3 I-2]resistance

[ ]Radian, refractive index etc

[M1L-3]Density

dimensionDerived

Quantities

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Application of dimensional equation

• Dimensional analysis can be used —1. to check whether the given equation is

dimensionally correct. ( If an equation is dimensionally correct then it can differ only in numerical constants.)

2. To find the relation between same unit in different systems. For example let 1N = c dyne1[M1L1T-2] = c [M1L1T-2]kg.m.s-2 = c gm.cm.s-2

1cm

100cm

gm

1000gm

2

2

s

s

cm

m

gm

kg = 10000 = c

105

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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:

0 1 2 3 4

4.8

4.85

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Significant figure• Significant figure:• The number of all nonzero digits are significant.

– 234 has 3 significant digits– 17065001 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– 0.0102 has 3 significant digits– 0.0120 has 3 significant digits– 0.00 has 2 significant digit– 0.000012 has 2 significant digits

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Need and notation of scientific numbers• If reading is • 2.320m = 232.0cm = 2320mm

=0.002320km• Here 2320mm has 3 significant digits and

2.320 has 4 significant digits • To avoid above contradiction we use

scientific notation in which the number will be written as – 2.320m = 2.320 x 102cm

= 2.320 x 103mm = 2.320 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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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 987.231+ 34.3+456.096

1477.61477.627

Multiples and divisorsPrefix Symbol Multiples

deca da 10hecto 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