Unit And Measurement Class 11 Notes

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· Unit

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law that is used for the standard measurement of different quantities.

· Fundamental units

Those units which are independent of other units are called fundamental units. Metre, Kilogram, second, mole, Ampere, Kelvin, and Candela are fundamentals units.

_{Physical Quantities}	_Units	_Symbol
_Length	_Meter	_m
_Mass	_Kilogram	_kg
_Time	_Second	_s
_Temperature	_Kelvin	_K
_{Electric Current}	_Ampere	_A
_{Luminous Intensity}	_Candela	_cd
_{Amount of Substance}	_Mole	_mol

· Derived units

Those units which are dependent on fundamental units are called derived units. m/s²,m/s,Nm₂/kg², etc are derived units.

· Supplementary units

Those dimensionless units that are used along with the base units to form derived units are called supplementary units.

· Dimension

The dimension of a physical quantity indicates how that quantity is linked with fundamental units. The power of fundamental units involved in the unit of that quantity represents the dimensions of that quantity.

Application of Dimensions of a Physical quantity:
1. Helps to find the unit of a physical quantity

2. Helps to convert the units from one system to another system

3. Helps to check the correctness of a given equation

4. Helps to derive an equation

Limitations of Dimensional Analysis:

● It can't give the values of numbers.

● It doesn't give the value of trigonometric functions.

● It can't derive the physical relation which contains more terms.

● It doesn't give information about the signs.

Accuracy :
Accuracy is the extent to which a reported measurement approaches the true value of the quantity measured.

Precision:
Precision is the degree of exactness or refinement of a measurement. Basically, it describes the limitations of the measuring instrument.

Error:
Measurement is the foundation of all experimental science and technology. The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error.

Errors of Measurements:
It is the difference between the true value and the measurement of the value of the quantity is known as the error of measurement.

Types of Errors:

In general, the errors in measurement can be broadly classified as

a) Systematic errors
Systematic errors are those errors that tend to be in one direction, either positive or negative. Basically, these are the errors whose causes are known.

b) Random errors
The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions (e.g. unpredictable fluctuations in temperature, voltage supply, mechanical vibrations of experimental set-ups, etc, personal (unbiased) errors by the observer taking readings, etc. For example, when the same person repeats the same observation, it is very likely that he may get different readings every time.

c) Least count error

The least count is the smallest value that can be measured by the measuring instrument.

The least count error is the error associated with the resolution of the instrument.

Significant Figures:

Significant figures in the measured value of a physical quantity tell the number of digits in which we have confidence.

The larger the number of significant figures obtained in a measurement, the greater is the accuracy of the measurement. The reverse is also true.