‘I’ Scheme Basic Physics (22102) ) INTRODUCTION 1.1 UNIT Basic Physics (22102) Chapter 1 :- Unit and Measurement CO102.1:- Estimate errors in measurement of physical quantities Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of a physical Quantity is expressed by a number (or numerical measure) accompanied by a unit. Although the number of physical quantities appears to be very large, we need only a limited number of units for expressing all the physical quantities, since they are inter-related with one another. The units for the fundamental or base quantities are called fundamental or base units. The units of all other physical quantities can be expressed as combinations of the base units. Such units obtained for the derived quantities are called derived units. A complete set of these units, both the base units and derived units, is known as the system of unit Unit: The standard used to measurement of a physical quantity is called as unit. For example Mile is used as a unit to measure the distance. Liter is used as a unit to measure the capacity of something. Kilogram is used as a unit to measure the weight.
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‘I’ Scheme Basic Physics (22102)
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INTRODUCTION
1.1 UNIT
Basic Physics (22102)
Chapter 1 :- Unit and Measurement
CO102.1:- Estimate errors in measurement of physical quantities
Measurement of any physical quantity involves comparison with a certain
basic, arbitrarily chosen, internationally accepted reference standard called
unit. The result of a measurement of a physical Quantity is expressed by a
number (or numerical measure) accompanied by a unit. Although the number
of physical quantities appears to be very large, we need only a limited number
of units for expressing all the physical quantities, since they are inter-related
with one another. The units for the fundamental or base quantities are called
fundamental or base units. The units of all other physical quantities can be
expressed as combinations of the base units. Such units obtained for the
derived quantities are called derived units. A complete set of these units, both
the base units and derived units, is known as the system of unit
Unit: The standard used to measurement of a physical quantity is called as unit.
For example Mile is used as a unit to measure the distance. Liter is used as a
unit to measure the capacity of something. Kilogram is used as a unit to measure the weight.
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Derived Units Fundamental Units
Units
PHYSICAL QUANTITIES
Derived Quantities Fundamental Quantities
Physical Quantities
A physical quantity is a quantity that can be measured, OR Any Quantities, which can be measured, is called Physical Quantities
For Examples physical quantities are mass, amount of substance, length,
time, temperature, electric current, light intensity, force, velocity, density,
and many others
Fundamental quantity: -
Defination
The quantity which does not depend upon any other quantity for its measurement
is called fundamental quantity
For example: - mass, length, time etc.
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Sr.No. Fundamental
Quantities
Fundamental
Units
Symbol
1 Length Meter m
2 Mass Kilogram kg
3 Time Second s
4 Electric current Ampere A
5 Temperature Kelvin K
6 Amount of
substance
Mole mol
7 Luminous intensity Candela cd
There are two Supplementary quantities to fundamental quantities
Sr. No. Supplementary quantity Unit Symbol
1. Plane angle Radian rad
2. Solid Angle Steradian sr
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Requirement of standard unit:
Fundamental unit: -The unit of Fundamental quantity is called
fundamental unit. OR the unit used to measures fundamental
quantity is called fundamental Unit.
For Example:-meter, kilogram, second, Ampere, Kelvin,
Derived quantity: -
Defination
The quantity which depends upon one or more fundamental quantity
for its measurement is called Derived quantity.
For example: -. Area, volume, velocity, acceleration. etc.
Derived unit: -The unit of derived quantity is called derived unit. Or
the unit used to measure derived quantity is called derived unit
For example: - m2, m/s2, kg/m3
1. It should be well defined.
2. It should be of convenient size, i.e. neither too small nor too
large in comparison with the measurable physical quantity.
3. It should not change with the time.
4. It should be easily reproducible.
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1.2 SYSTEM OF UNIT
5. It should be imperishable or indestructible.
6. It should not be affected by the change in physical conditions
such as pressure, temperature etc.
7. It should be internationally acceptable.
8. It should be easily accessible.
The System of units based on seven base units is at present
internationally accepted unit system and is widely used throughout the
world. We use first three Fundamental quantities Length, Mass & Time
1.CGS System:- In this system, the unit of length is “centimeter”, the
unit of mass is “gram” and the unit of time is “second”.
2.FPS System:- In this system, the unit of length is “foot”, the unit of
mass is “pound” and the unit of time is “second”.
3.MKS System:- In this system, the unit of length is “meter”, the unit of
mass is “kilogram” and the unit of time is “second”.
4.SI System:- This system contain seven fundamental units and two
supplementary fundamental units. 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 India National
Physical Laboratory maintains the standards of measurements. The
system of units used around the world is International System of SI.
This system is used in all over the world. This system is consisting
of seven fundamental units and two supplementary units.
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1.3 DIMENSIONS AND DIMENSIONAL FORMULA
Dimension (Definition) : The dimensions of physical quantity are the powers to which
fundamental (base) units must be raised to obtain the unit of a given
physical quantity.
Or
The exponent of a base quantity which enters into the expression, is
called dimension of the quantity in that base.
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1.3.1 DIMENSIONAL FORMULA
length -'L'
mass by 'M'
time by 'T'
Dimensional formula (equation)
An equation, which gives the relation between fundamental units and
derived units in terms of dimensions is called dimensional formula.
Examples :-
Dimensional formula (equation) for area :
We have,
Area = length x breadth
= length x length
= [L] x [L]
= [ L2
]
Dimensional formula for area (A) = [L2
M0
T0
]
Thus, [L2
M0
T0
] is called dimensional formula
[2 0
0
] are called dimensions.
Dimensional formula for,
Density (ρ) = Mass ÷ Volume
The dimensional formula of mass = [L0
M1 T
0]
And,
The dimensional formula of volume = [L3 M
0 T
0]
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we get,
Density = Mass ÷ Volume
(ρ) = [L0
M1 T
0] ÷ [L
3 M
0 T
0]
= [ L-3
M1 T
0]
Therefore,
density is dimensionally represented as [L-3
M1 T
0]
It is an expression which shows how and which of the fundamental units
are required to represent the unit of physical quantity. Dimensional
Formula is a standardized method to express the Physical quantities in
terms of Fundamental quantities as chosen in the SI system of
measurement.
These are denoted with symbols in square brackets [ ] For Example : Force (Quantity) = mass × acceleration
= mass ×velocity/time
= mass ×displacement/ time2
= mass × length/time2
So dimensions of force : 1 in length, 1 in mass, –2 in time
Dimensional formula for Force is : [L1 M
1T
-2]
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Physical Quantities and their Units
Quantities Symbol SI units Symbol Dimension Unit
Dimensions
Distance D Meter m [L1 M0 T0] m
Mass M Kilogram kg [L 0M1 T0] kg
Time T Second s [L0 M0 T 1] s
Area A Square meter m2 [L0 M2 T0] m2
Volume V Cubic meter m3 [L3 M0 T0] m3
Density D Kilogram per
cubic meter
kg/m3 [L-3 M1 T0] kg/m3
Kinetic
energy
K.E. Joule J [L2 M1 T-2] Kg.m2/s2
Potential
energy
P. E. Joule J [L2 M1 T-2] Kg.m2/s2
Acceleration A Meter per
second square
m/s2 [L1 M0 T-2] m/s2
Power P Watt W [L2 M1 T-3] kg.m2/s3
Pressure P Pascal Pa [L-1 M1 T-2] kg/m.s2
Velocity V Meter per
second
m/s [L1 M0 T-1] m/s
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Frequency F Hertz Hz [L0 M0 T-1] s-1
Force F Newton N [L1 M1 T-2] kg.m/s2
Wavelength λ Meter m [L1 M0 T0 ] m
Heat Q Joule J [L2 M1 T-2] kg.m2/s2
Impulse Newton second Ns [L1 M1 T-1] Kg .m/s
Work w Joule J [L2 M1 T-2] Kg.m2/s2
Electric
current
I Ampere A --- C/s
Electric
Intensity E Newton per
coulomb
N/C --- kg.m/C.s2
Electric
resistance
R Ohm Ω --- kg.m2/C2.s
Emf E Volt V --- kg.m2/C.s2
Energy E Joule J --- kg.m2/s2
Capacitance C Farad F --- C2.s2/kg.m2
Magnetic flux ϕ Weber Wb --- kg.m2/C.s
Potential
difference
V Volt V --- kg.m2/C.s2
Amount of
substance N Mole mol --- mol
Luminous
intensity
I Candela cd --- cd
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ERRORS
1.4 ERROR AND TYPES OF ERROR
Error: - An error is fault or deficiency which may occur in most
careful observation. OR
Error is deviation of measurement from standard value. Errors cannot
be eliminated but can be reduced. There are three types of error
1)Instrumental error:-This error is due to faulty instruments e. g.
If the vernier having error is used for the measurement then an error
will occur in each and every reading. This type of error can be
reduced by taking same measurement with different instruments.
2)Systematic error: - This error is due to the defective setting or
adjustment of the experiment or due to human limitations. e.g. In the
experiment of magnetometer if the pointer is not adjusted to zero
exactly, then systematic error will arise. The errors can be reduced
by avoiding causes with the help of skillful experimenter.
Ssystematic errors may be divided into following sub-categories
Random error Systematic error Instrumental error
Errors
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1.4.1 ESTIMATION OF ERROR
1) Constructional Error:- a manufacturers always mention the
minimum possible errors in the construction of the instruments
2) Errors in Reading or Observation:- for Example Construction of
the Scale
3) Determination Error:- It is due to the indefiniteness in final
adjustment measuring apparatus.
3)Random error: - This error is due to the change in environmental
condition such as humidity, temperature, pressure etc. This type of
error can be minimized by performing experiment in controlled
conditions. These are random error and their magnitudes are not
constant. Persons performing the experiment have no control over
the origin of these errors. These errors are due to so many reasons
such as noise and fatigue in the working persons. These errors may
be either positive or negative
The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted.
1) True value:- True value (Am) is the mean of all the observed readings.
2) Corrected reading = given reading Zero error
3) Absolute error:- It is the difference between the individual
measured value and the true value.
Absolute error (∂A) = Measured value - True value (Am)
∂A1 = A1 - Am
∂A2 = A2 - Am
∂An = An - Am
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Numerical:
The diameter of a wire as measured by a screw gauge was found to
be 1.002cm,1.004cm and 1.006cm. Calculate The absolute error in
the readings.
Solution: Mean =
Am =1.004cm
Hence, absolute errors
∂ A1=1.002−1.004 =0.002cm
∂ A2=1.004−1.004 =0.000cm
∂ A3=1.006−1.004 =0.002cm
4)Average Absolute Error (∂Am):- The mean of all values of absolute
error is known as average absolute error.
∂A mean =
(∂Am)=
=
Average Absolute Error = 0.001333
5) Relative error = it is the ratio of the mean absolute error to the true
value.
Relative error =R = 𝐨 𝐨
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= 𝛛 mean
𝐦 𝐧
=
=0.001324
Percentage error :-When the relative error is expressed in percent, it is
called the percentage error
Percentage error = Relative error x 100
% Error = Relative error x 100
= 0.001327 x 100
Percentage error= 0.1327 %
Significant Figures Significant Figures in a measured or observed value is the number of
Reliable digits. Each of
the digits of a number that are used to express it to the required degree
of accuracy, starting from the first non-zero digit.
Definition :-
significant figures are the numbers which are responsible
meaningful or trustworthy
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Rules to identify the significant figures
(i) All non- zero digits are significant figure.
Eg. 25 has two significant figures (2 and 5),
while 123.45 has five significant figures (1, 2, 3, 4 and 5).
(ii) All zero between two non-zero digits are significant figure.
101.203 has six significant figures: 1, 0, 1, 2, 0 and 3.
(iii) All zeros to the right of a non-zero digit but to the left of an
understood decimal point are not significant. But such zeros are
significant if they come from a measurement.
Eg.
0.070140 Significant figures=5
(iv) All zeros to the right of a non-zero digit but to the left of a
decimal point are significant.
10.2104 Significant figures=6
(v) All zeros to the right of a decimal point are significant.
Eg. 1.000 Significant figures=4
(vi) All zeros to the right of a decimal point but to the left of a
non-zero digit are not significant. Single zero conventionally
placed to the left of the decimal point is not significant.
0.12345 Significant figures=5
05.01234 Significant figures=6
1.5 x 102 has 2 significant figures
Where as
1.50 x 102 has 3 significant figures.
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Significant Figures Worksheet
Indicate how many significant figures there are in each of the following
measured values
Sr.No Values Number of
significant figure
1 246.32 5
2 107.854 6
3 100.3 4
4 0.678 3
5 1.008 4
6 0.0034 2
7 14.6 3
8 0.0009 1
9 700000 1
10 350.67 5
11 0.4 1
12 320001 6
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Find the number of significant figure in each of the following:-
