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:
Characteristics of Fundamental Units:
- Fundamental Units are well defined and are of suitable
- They are easily reproducible.
- They do not vary with temperature , pressure and time.
- Meter: The distance traveled by light in Vaccum in 1/299,792,458 second is called 1m.
- Kilogram: 1 kg is the mass of the cylinder made of the platinum-iridium alloy at the international bureau of weights .
- 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
They are the powers to which the fundamental quantities are being raised to represent given physical quantities.
Force = Mass x Acceleration
= mass x velocity /time
= mass x length / (time ) 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
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:
- Zeros occurring between now- zero digits are significant.
- 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.
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.
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
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
The lack of accuracy in the measurement due to the limit of the accuracy of the instrument.
Types of Error :
- Absolute Error : The difference between the true value and measured value is called absolute error.
am = a1 +a2 + a3 +—-/n
- Relative Error : The ratio of the mean absolute error to the true value is called relative error.
- Percentage Error: The relative error expressed in percentage is called percentage error.
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