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Measurement- Never Been so Easy!

measurement

Physical Quantities:   All quantities  that can be measured are called physical quantities. 

Eg: Time, Length.

Measurement: It is the comparison of a quantity with a standard of the  same physical quantity.

Units:  All physical  quantities  are measured  as compared to  the standard magnitude of  same physical quantities  and  these standards are called units.

Types of  Physical Quantities:

 

Fundamental Quantities: There are seven fundamental quantities:

 

measurement

Characteristics of Fundamental Units:

  1. Fundamental Units are well  defined and are of suitable 
  2. They are  easily reproducible.
  3. They do not vary with temperature , pressure and time.

Fundamental Units

  1. Meter: The distance traveled by light  in Vaccum in   1/299,792,458 second is called 1m.
  2. Kilogram: 1 kg is the mass of the  cylinder  made of the platinum-iridium alloy   at  the international  bureau of   weights .
  3. Second: Electromagnetic radiation by Cesium -133 are emitted at several wavelengths. Radiation  is  selected  which  corresponds to the transition between the two levels of  ground state of Cs -133.

Principal System  of Units:

CGS System: Centimetre , gram and second .

FPS System: Foot , Pound and Second

MKS System:  Meter,  Kilogram and Second

Dimensions:

They are the powers to which the  fundamental quantities  are  being  raised  to represent given physical quantities. 

For  Example:

Force = Mass x  Acceleration

        =  mass x velocity /time

        =  mass x length / (time ) 2

         =  MLT-2

2. Derived Units:  Physical Quantities which depend on fundamental  quantities  or  which can be derived from fundamental  quantities  are known as derived quantities.

The principle of Homogeneity:  The dimension of the quantities  on the left side is equal to the right side. This is the principle of homogeneity.

E = ½ mv2  (Kinetic Energy)

E= mass x (velocity )2

½ is a number and has no dimensions.

E = M x [  L/T ] 2

 E   = ML2T -2

Significant Figures:

Measurements  made by an instrument  are  not correct . The degree of precision is given by the  significant figures  to which measurement has been recorded.  The number of  figures requires specifying a  certain measurement perfectly  are  called significant figure .

Rules for the Significant Figures:

  1. Zeros  occurring between now- zero digits are significant.
  2. All zeros to the right of a decimal point and to the left of the no – zero digits are not significant figures.

If a measurement contains no decimal point , the number of final zeros are ambiguous and are not counted are significant. Eg:  In 5x 10 3 Significant figure is 1 .

Vernier Callipers and Screw Gauge:

It is used for measuring length.

Vernier Calipers:

It is used to measure accurately up to 1/10 of a millimeter.  It consists of Main scale and Vernier Scale. The main scale is fixed and Vernier scale is movable. 

Vernier Constant:

The size of one main scale division is S and that of Vernier scale is V units. 

(n-1 ) S =  nV

nS – S  =  nV

S-V = S/n

n = Length of one division of main scale / Number of divisions on Vernier Scale

Screw Guage: 

It is used to measure small lengths like the diameter of a wire or thickness of the sheet. It consists of a U shape metal frame.  The main scale is also called pitch scale.

Pitch: It is the defined as the linear distance moved by the screw forward or backward  when one complete rotation is given to the circular cap.

L.C. =  Pitch/  Total number of divisions on the circular scale.

If there are 50 divisions on the circular scale, then least count :

Distance traveled  on the pitch scale is 2 mm

So Pitch is 2 mm/4 = 0.5 mm

LC =  0.05/50 =  0.01 mm

Error:

The lack of accuracy in the measurement  due to the limit of the accuracy of the instrument.

Types of Error :

  1. Absolute Error : The difference between the true value and measured value is called absolute error.

       am =  a1 +a2 + a3 +—-/n

  1. Relative Error : The ratio of the mean absolute error to the true value is called relative error.
  1. Percentage Error: The relative error expressed in percentage is called percentage error.

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