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Contents
Units and measurements class 11 notes
Units
The term is used to define the physical quantity having a similar nature to that of the physical quantity.
Types of Units
- Fundamental Units
- Derived units
System of Units
A complete set of units that are used to measure all kinds of fundamental and derived quantities is known as a system of units.
- K.S system
- G.S system
- P.S system
- SI system
The fundamental unit of measurement
It is a defined unit that cannot be described as a function of any other unit. The S.I Unit (International System of Units) defines seven fundamental units of measurement. They can be applied to the various areas of studying physical science.
SI Base Units
The International units defined seven basics units of measurement from which all other SI units can be derived. SI system is a common system of the unit which is adopted globally. SI System is also called Rationalised M.K.S system.
Properties of SI System
- SI system is a coherent system
- SI system is a rational system
- It is an absolute system
- It is a metric system
Definition of Basic and Supplementary SI Units
There are 7 basic SI unit and 2 supplementary SI units are the following:
Metre (m): Metre is the SI unit of length. The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 of a second.
Kilogram (kg): The kilogram is the mass of the platinum-iridium prototype which was approved by the conference Generale de Poids et Measures, held in Paris in 1889, and kept by the Bureau International des Poids et Measures at Paris in France.
Second (s): Second is the SI unit of time. It is the duration of 9 192 631 770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
Ampere (A): It is the intensity of a constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would be produced between these conductors a force equal to 2 x 10^{-7} Newton per meter of length.
Kelvin (k): It is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Candela (cd): It is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10^{12} hertz and that has a radiant intensity in the direction of 1/683 watt per steradian.
Mole (mol): The amount is the amount of the substance of a system that contains as many elementary entities as there is an atom in 0.012 gram of carbon 12.
List of 7 Basic SI Unit in Tabular Form
Basic Physical Quantity | Basic Unit | Symbol |
Length | Metre | m |
Mass | Kilogram | kg |
Time | Second | s |
Temprature | Kelvin | K |
Electric current | Ampere | A |
Luminous intensity | Candela | cd |
Quantity of matter | Mole | mol |
Supplementary SI Units
Supplementary quantity | Basic Unit | Symbol |
Plane Angle | radian | rad |
Solid Angle | steradian | sr |
Radian (rad): Radian is defined as the plane angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
Steadian (sr): It is defined as the solid angle subtended at the center of the sphere by a surface of the sphere equal in area to that of the square, having each side equal to the radius(r) of the sphere.
Units and Measurements Notes With Easy Concepts
Derived Units
The physical quantities whose defining operations are based on other physical quantities are known as derived quantities.
Example: force, momentum, velocity, acceleration, etc.
Physical Unit
The standard amount of a physical quantity chosen to measure the physical quantity of the same kind is known as a physical unit.
Desirable characteristics of a physical unit
- The physical unit should not change with time.
- The physical unit should be easily reproducible.
- It should be internationally acceptable.
- It should be not accepted by the change in the physical condition such as temperature, pressure, etc.
- The physical unit should be well defined.
- It should be imperishable or indestructible.
- It should be of convenient size.
Some common Practical Units
Angstrom: Angstrom is used to express the wavelength of light.
1 Angstrom = 10^{-10}m = 10^{-8}cm
Fermi: Fermi is the small practical unit of distance used for measuring nuclear sizes. It is also known as femtometre.
1 Fermi = 10^{-15}m
Nanometre: It is also used for expressing the wavelength of light.
1 nanometre = 10^{-9}m
Micron: It is the unit of distance defined as a micrometer.
1 micron = 10^{-6}m
Light year: Light travels a distance in 1 year is known as a light-year.
1 light year = 9.46 x 10^{15}m
Astronomical unit: Astronomical unit is defined as the mean distance of the earth from the sun.
1 AU = 1.496 x 10^{11}m
Parsec: It is defined as the distance at which an arc of 1 AU subtends an angle of 1 second of arc. It is the largest practical unit used in astronomy.
1 parsec = 3.08 x 10^{16}m
1 parsec = 3.26 light year
Parallax
It is the apparent shift in the position of an object which respects another when we shift our eye sidewise.
Different between mass and weight
MASS | WEIGHT |
Mass is the measure of inertia. | Weight is measure of gravity. |
It is scalar quantity. | It is vector quantity. |
It is a constant quantiity. | It varies from place to place. |
Mass cannot be zero for a body. | Weight of a body is zero at the centre of the earth. |
It is an essential property of material bodies. | It is not a essential property. |
It is not affected by the presence of material bodies. | It is afferected by the presence of material bodies. |
Its units are gram, kilogram, etc. | Its units are dyne, newton, etc. |
Internal and Gravitational Masses
Internal mass: The mass of a body that determines its inertia in translator motion is known as its inertial mass.
Gravitational mass: The mass of a body that determines the gravitational pull acting upon it due to the earth is known as its gravitational mass.
Dimensions of a physical quantity
There are seven dimensions of the world, which are denoted by square brackets [].
Dimension of mass = [M]
Dimension of length = [L]
Dimension of time = [T]
Dimension of electric current = [A]
Dimension of temperature = [K]
Dimension of amount of substance = [mol]
Dimension of luminous intensity = [cd]
Dimensional formula
The dimensional formula is the term that tells about the power with which a fundamental quantity is contained in a physical quantity.
Dimensional equation
It is obtained when a physical quantity is equated with its dimensional formula.
Example:-
[X] = [ M^{a }L^{b }T^{c }]
The right-hand side represents the dimensional formula of physical quantity X, whose dimensions in mass, length, and time are a, b, and c respectively.
When speed is defined using the fundamental units of mass, length, and time,
Speed = distance/time = LT^{-1} = M^{0}LT^{-1}
Where there is no mass, M^{0} = 1
Unit of speed depends on the unit of length and time and is independent of mass.
Dimensional formula (of a physical quantity) can be represented by its relation with other physical quantities and then expressing these quantities in terms of mass [M], length [L], and time [T].
Dimensional formula of all important Units
Physical Quantity | Relation with other Quantity | Dimensional Formula |
Area | Length x breadth | L x L = L^{2} = [M^{0}L^{2}T^{0}] |
Volume | Length x breadth x height | L x L x L = L^{3} = [M^{0}L^{3}T^{0}] |
Speed or Velocity | Dist./time or Displ./time | L/T = [M^{0}LT^{-1}] |
Momentum | Mass x velocity | M x LT^{-1} = [MLT^{-1}] |
Force | Mass x acceleration | M x LT^{-2} = [MLT^{-2}] |
Work or Energy | Force x Displacement | MLT^{-2} x L = [ML^{2}T^{-2}] |
Electric Power | Work/time | ML^{2}T^{-2}/T = [ML^{2}T^{-3}] |
Frequency | 1/time period | 1/T = [M^{0}L^{0}T^{-1}] |
Impulse | Force x time | MLT^{-2} x T = [MLT^{-1}] |
Application of dimensional formula
- To check the correctness of the given equation. This use is based on the principle of homogeneity that is only quantities of the same dimension can be added, subtracted, and equated.
- To convert one system of units into another system of units.
- To derive the equations showing the relationship between different physical quantities.
Limitation of the dimensional system
- Dimensionless quantities cannot be determined by this method. They can be found either by theory or experiment.
- This method is not applicable to trigonometric, logarithmic, and exponential functions.
- In the case of physical quantities that are independent of more than three physical quantities, this method is difficult.
- In some cases, the constant of proportionality also possesses dimensions. In such cases, one cannot use this system.
- If one side of the equation contains the addition or subtraction of physical quantities, one cannot use this method.
Types of variables and constants
Dimensional variables: Those Physical quantities which possess dimensions and have variable values known as dimensional variables.
Dimensionless variables: Those Physical quantities which have no dimensions but have variable values known as dimensionless variables.
Dimensional constants: Physical quantities that have no dimensions but have variable values known as dimensional constants.
Dimensionless constants: Constant quantities having no dimensions
Significant figures
The significant figures are normally those digits in a measured quantity that is known reliably or about which we have confidence in our measurement plus one additional digit that is uncertain.
For example, if one writes 3.0 it means that he is stating that he is able to estimate the first decimal place of the quantity and he is implying an error of 0.05 units. If one writes 3, he is unable to determine the first decimal place, hence, implying an error of 0.5 units.
Rules for determining the number of significant figures
- All non-zero digits are significant.
- All zeros (0) between two non-zero digits are significant.
- All zeros to the right of a non-zero digit but to the left of an understood decimal point are not.
- All zeros to the right of a non-zero digit but to the left of a decimal point are significant.
- All zeros (0) to the right of a decimal point are significant.
- All zeros to the right of a decimal point but to the left of a non-zero digit are non-significant.
- The number of significant figures does not depend on the system of units.
Rules for rounding off a measurement
- When the digit to be dropped is smaller than 5, then the preceding digit is left unchanged.
- When the digit to be dropped is greater than 5, then the preceding digit is increased by 1.
- If the digit to be dropped is 5 followed by non-zero digits, then the preceding digit is increased by 1.
- When the digit to be dropped is 5, then the preceding digit is left unchanged if it even.
- When the digit to be dropped is 5, then the preceding digit is increased by 1 if it is odd.
Accuracy
Accuracy of a result or experiment procedure can refer to the percentage difference between the experimental result and the accepted value.
It is also associated with the inherent uncertainty in a measurement.
Reliability
Reliability can be defined as repeatability or consistency. If an experiment is repeated many times and gives an identical result each time it is reliable.
Nature of errors
Errors occur in all physical measurements. If a measurement is used in a calculation, the error in the measurement is carried forward in the result.
Types of errors
Random error
It occurs in any measurement as a result of variations in the measurement technique. For example, parallax error, the limit of reading, etc).
Absolute Error
The magnitude of the difference between the true value of the quantity measured and the individual measured value is known as absolute error.
Mean Absolute Error
The arithmetic mean of the positive magnitudes of all the absolute errors is known as mean absolute error.
Relative Error
The ratio of the mean absolute error to the true value of the measured quantity is known as a relative error.
Experimental Error
Variations occur in any series of measurements taken with a suitably sensitive measuring instrument. These variations in the different readings of the measurement are known as experimental error.
Percentage Error
The relative error is expressed in percentage is known as a percentage error.
Systematic Error
Systematic errors occur to the same extent in each of a series of measurements. Causes of systematic error include:
- Using the instrument wrongly on a consistent basis.
- Built-in error in the instrument may be zero error.
- The external condition can introduce systematic errors such as a metallic rule calibrated for use at 25 degrees Celsius will only be accurate at that temperature.
Systematic errors can drastically affect the accuracy of a set of measurements.
Frequently Asked Question (FAQ) of Units and Measurements class 11
All important questions of units and measurement chapter:
What is a dimensional formula?
The expression which shows how and which of the fundamental quantities represent the dimensions of a physical quantity is known as the dimensional formula.
What is a dimensional equation?
The equation obtained by equating a physical quantity with its dimensional formula is known as a dimensional equation.
What are the units of measuring time?
The unit of measuring time is second.
What are the 7 basic units of measurement?
The 7 basic units of measurement are:
- Length = metre (m)
- Time = second (s)
- Mass = kilogram (kg)
- Electric current = ampere (A)
- Temperature = kelvin (K)
- Luminous intensity = candela (cd)
- Amount of substance = mole (mol)
What is the full form of the SI unit?
The International System of Units universally abbreviated SI, is the modern metric system of measurement.
What is the SI unit of weight?
Weight is the measure of gravity. The SI unit of weight is Newton and the CGS unit of weight is dyne.
Also Read –
- Motion in a straight line class 11
- Newton’s laws of motion
- Complete notes of surface tension
- Circular motion class 11
- Thermodynamic Notes Class 11
- Laws of thermodynamic class 11
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