CBSE Class 11 Physics Unit and Measurement Notes Set 02

UNITS AND MEASUREMENT

CONCEPTS INVOLVED

• The International system of units

• Measurement of length

• Measurement of mass

• Measurement of Time

• Accuracy, Precision of instruments and errors in measurement

• Significant figures

• Dimensions of physical quantities

• Dimensional formulae and dimensional equations

• Dimensional analysis and its applications

Main points

√ Physics is a quantitative science, based on measurement of physical quantities.Certain physical quantities have been chosen as fundamental or base quantities. The fundamental quantities that are chosen are Length, Mass, Time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

√ Each base quantity is defined in terms of a certain basic arbitrarily chosen but properly standardized reference standard called unit (such as metre,kilogram,second,ampere,kelvin,mole,and candela. The units for the fundamental base quantities are called fundamental or base units and two supplementary units in relation to quantities plane angle and solid angle radian, Ste radian..

√ Other physical quantities derived from the base quantities can be expressed as a combination of the base units and are called derived units. A complete set of units both fundamental and derived units are called a system of units.

√ The International System of units based on seven base units is at present internationally accepted unit system and is widely used throughout the world

√ The SI units are used in all physical measurements, for both the base quantities and the derived quantities obtained from them. Certain derived units are expressed by means of SI units of special names such as joule, newton, watt etc.

√ In computing any physical quantity the units for derived quantities involved in the relationships are treated as though they were algebraic quantities till the desired units are obtained

√ In SI system that is System Internationale d’ Units there are 7 base units’ and two supplementary units.

√ Direct and indirect methods can be used for the measurement of physical quantities. In measured quantities while expressing the result, the accuracy and precision of measuring instruments along with errors in measurement should be taken into account. 

√ In measured and computed quantities proper significant figures only should be retained. Rules for determining the number of significant figures, carrying out arithmetic operations with them and rounding off the uncertain digits must be followed.

√ The dimensions of base quantities and combination of these dimensions describe the nature of physical quantities .Dimensional analysis can be used to check the dimensional consistency of equations, deducing relations among physical quantities etc. A dimensionally consistent equation need not be actually an exact equation, but a dimensionally wrong or inconsistent equation must be wrong.

√ The uncertainty in the measurement of a physical quantity is called an error.

√ The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity

√ Precision tells us to what limit the quantity is measured.

√ The errors in measurement can be classified as

(i) Systematic errors and (ii) Random errors

√ SYSTEMATIC ERRORS: These are the errors that tend to be either positive or negative.Sources of systematic errors are

(i) Instrumental errors

(ii) Imperfection in experimental technique or procedure

(iii) Personal errors

√ RANDOM ERRORS :Those errors which occur irregularly .These errors arise due to unpredictable fluctuations in experimental conditions

√ Least count error is the error associated with the resolution of the instrument.

√ The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement.
Ex: Δa = I a-a_meanI

√ The relative error or the percentage error is the ratio of the mean absolute error to the mean value of the quantity measured. When the relative error is expressed in per cent it is called the percentage error.

Ex: (i) Relative error = Δa_mean/a_mean (ii) % error = ( Δa_mean/a_mean) X 100

COMBINATION OF ERRORS

√ ERROR OF A SUM OR A DIFFERENCE When two quantities are added or subtracted, the absolute error in the final result is the sums of the absolute errors in the individual quantities.

IF Z=A+ B then the max possible error in Z, ΔZ =ΔA + ΔB

IF Z=A- B then the max possible error in Z, ΔZ =ΔA + ΔB

√ ERROR OF A PRODUCT OR A QUOTIENT

When two quantities are multiplied or divided the relative error is the sum of the relative errors in the multipliers Suppose Z= A*B or Z=A/B then the max relative error in ‘Z’ = ΔZ/Z= (ΔA/A) + (ΔB/B)  

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