Units and measurements chapter 1 converted

Class 11 Physics chapter one notes. simplified and reduced for better understanding and quick revisions.
Notes on Units, physical Quantities, errors, calculation of errors, and dimension analysis.

1. UNITS AND
MEASUREMENTS
PHYSICS
CLASS XI

2. PHYSICAL QUANITY
•Measurement of any physical quantity
involves comparison with a certain basic
arbitrarily chosen internationally accepted
reference standard called unit
•Any measurable quantity is called physical
quantity.
•Physical Quantity is of two types:
❑Fundamental Quantity.
❑Derived Quantity.

3. FUNDAMENTAL QUANTITY
•It is a physical quantity which is independent
of other physical quantity.
•Eg: Length, Mass , time….
DERIVED QUANTITY
❖It is a physical quantity which depends upon
other physical quantities.
❖Eg : acceleration, Area, Velocity…..
A complete set of both the base units and
derived units is known as System of Units

4. INTERNATIONAL SYSTEM OF UNITS
The base units for length, mass and time in these system are as follows.
❑In CGS system they were centimeters, grams and seconds
respectively.
❑In FPS system they were Foot, pound and second respectively.
❑In MKS system they were meter, kilogram and second respectively.
International
system of
units
CGS FPS MKS

5. Measurement of Length
•Lengthcanbemeasureddirectlyusingsomeof
themethodslikeusingaverniercallipersfor
lengthtoanaccuracyof1/(10,000)orusinga
meterscaleforanaccuracyof1/1000.
•Formeasurementsoflengthbeyondthisrange
weusesomeindirectmethods.
•Onesuchmethodisparallaxmethod,this
methodistypicallyusedtodeterminethe
distancefromearthtootherplanets.

6. Parallax method
•TomeasurethedistanceDofafarawayplanet
Sbytheparallaxmethodweobserveitfrom
twodifferentpositionsAandBontheearth
separatedbythedistanceAB=b.
•Wemeasuretheanglebetweenthetwo
directionsalongwhichtheplanetisviewedat
thesetwopoints.
•The<ASBisrepresentedbythesymbolθis
calledtheparallaxangleorparallacticangle.

7. •AfterdeterminingthedistanceDwecanusea
similarmethodtocalculatethesizeorangular
diameteroftheplanet.
•IfdisthediameteroftheplanetandαCanbe
measuredfromthesamelocationonearth.

8. D = b/θ
θ
α
Parallax Method

9. Q . 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 upto B, a distance of
100m 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=40°estimate the distance of the
tower C from the original position A

11. Q.Thesunsangulardiameterismeasuredtobe1920”.
ThedistanceDofthesunfromtheearthis1.496×10
11
m.
Whatisthediameterofthesun.
Answer: The suns angular diameter α= 1920”
= 1920 ×4.85 ×10
-6
rad.
= 9.31 ×10
-3
rad
Suns diameter,
d = αD
=(9.31×10
-3
rad)×(1.496×10
11
m)
=1.39×10
9
m

12. Range of Lengths

13. MEASUREMENT OF MASS
•Massisabasicpropertyofmatter.
•TheSIunitofmassisKg.
•Whiledealingwiththemassofatomsand
moleculesKgisinconvenientsoweuseanother
unitcalledunifiedatomicmassunit(u).
•1 unified mass = 1u
= (1/12) of the mass of an atom of
carbon -12 isotope including the mass of
electrons
= 1.66 ×10
-27
kg

14. MEASUREMENT OF MASS
•Massofcommonlyavailableobjectscanbe
measuredusingaweighingmachineusedin
groceryshops.
•Largemasseslikemassofstarsandplanetscanbe
measuredusingNewton'slawofgravitation
whichwillbediscussedlateron.
•Smallmasseslikemassofatomsandmolecules
canbemeasuredusingMassSpectrographin
whichtheradiusofthetrajectoryisproportional
tothemassofachargedparticlemovingin
uniformelectricandmagneticfield.

15. Range of mass

16. MEASUREMENT OF TIME
•Tomeasureanytimeintervalweneedaclock.
•Wenowuseatomicstandardoftime.
•Itisbasedontheperiodicvibrationsproduced
inacaesiumatom.
•Thisisthebasisofthecesiumclock
sometimescalledatomicclockusedinthe
nationalstandards.

17. ACCURACY AND PRECISION
•Accuracyishowcloseameasurementistothe
correctvalueforthatmeasurement.
•Theprecisionofameasurementsystemis
referstohowclosetheagreementisbetween
repeatedmeasurements(whicharerepeated
underthesameconditions).
•Measurementscanbebothaccurateand
precise,accuratebutnotprecise,precisebut
notaccurate,orneither.

19. ERRORS
•Theresultsofanymeasurementfromany
measuringinstrumentcontainssome
uncertainty.Thisuncertaintyiscallederror.
•Thuseverymeasurementsisapproximatedue
toerrorsinmeasurements.
•Ingeneralerrorsisclassifiedintothreetypes:
❖SystematicErrors
❖RandomErrors.

20. SYSTEMATIC ERRORS
•Systematicerrorsarethoseerrorsthattendtobe
inonedirectioneitherpositiveornegative.
•Someofthesourcesofsystematicerrorsare:
i.InstrumentalErrors:Thisareerrorsthatarise
fromimperfectdesignorcalibrationofthe
instrumentitincludeszeroerrors.
ii.Imperfectioninexperimentaltechniquesor
procedure:Externalconditionsactsasafactor
formeasurement.
iii.PersonalErrors:Thisareerrorsthatarisedueto
individualsbias,lackofpropersettingofthe
apparatusorindividualscarelessness.

21. RANDOM ERROR
•Thisareerrorsthatoccurrandomlyandhence
arerandomwithrespecttosignandsize.
•Thesecanariseduestorandomand
unpredictablefluctuationsinexperimental
conditions.
•Forexamplewhenthesamepersonrepeatsthe
sameobservationitisverylikelythathegets
differentreadingseverytime.

22. LEAST COUNT ERRORS
•Thesmallestvaluethatcanbemeasuredbythe
measuringinstrumentiscalleditsleastcount.
•Theleastcounterroristheerrorassociatedwiththe
resolutionoftheinstrument.
Eg:Averniercalliperhastheleastcountof0.01cm;
Aspherometermayhavealeastcountof0.001cm.
•Leastcounterrorscanoccurwithbothsystematicand
randomerrors.
•Usinginstrumentsofhigherprecision,improving
experimentaltechniques..Canreducetheleastcount
error.
•Repeatingtheobservationseveraltimesandtakingthe
meanvalueoftheobservationscangiveyoutheresult
veryclosetothetruevalueofthemeasuredquantity.

23. ABSOLUTE ERROR, RELATIVE
ERROR AND PERCENTAGE ERROR
•AbsoluteError:TheMagnitudeofdifference
betweentheindividualmeasurementsandthetrue
valueofthequantityiscalledabsoluteerrorofthe
measurement.
•RelativeError:Itistheratioofthemeanabsolute
errortothemeanvalueofthequantitymeasured.
•PercentageError:Whenrelativeerroris
expressedinpercentitiscalledpercentageerror.

25. ABSOLUTE ERROR, RELATIVE
ERROR AND PERCENTAGE ERROR
Q.Wemeasurethetimeperiodofoscillationofa
simplependulum.Insuccessivemeasurementsthe
readingsturnouttobe2.63s,2.56s,2.42s,2.71sand
2.80s.Calculatetheabsoluteerror,relativeerroror
percentageerror.
Solution:
Given:Successivemeasurementreadings
=2.63s,2.56s,2.42s,2.71sand2.80s.
Numberofobservations=5

28. DIMENSIONS OF PHYSICAL
QUANITIES.

29. DIMENSIONAL ANALSYSIS AND
ITS APPLICATIONS
•Thestudyoftherelationshipbetweenphysicalquantities
withthehelpofdimensionsandunitsofmeasurementis
termedasdimensionalanalysis.
•Dimensionalanalysisisessentialbecauseitkeepstheunits
thesame,helpingusperformmathematicalcalculations
smoothly.
•Dimensionalanalysisisafundamentalaspectof
measurementandisappliedinreal-lifephysics.
•Wemakeuseofdimensionalanalysisforthreeprominent
reasons:
–Tochecktheconsistencyofadimensionalequation
–Toderivetherelationbetweenphysicalquantitiesinphysical
phenomena
–Tochangeunitsfromonesystemtoanother