International system of units
* A unit is an internationally accepted basic reference standard against which the measurements of any physical quantity are compared.
* The units of fundamental or base quantities are called base units or fundamental units.
* The units of derived quantities, expressed as a combination of base units are called derived
units.
* A system of units is a generally accepted set of units of measurement, which comprises base and derived units.
Measurement of length
* To measure large distances, we employ an important method called the parallax method.
*Distance between two viewpoints or points of observation is called basis.
* The distance of the star from the earth, D=b/⍬ (where ⍬ is in radiance)
* Diameter of the star, d=D⍺ (⍺ is in radiance).
* For the purpose of measurements, degree can be converted into radiance.
10= 1.75x 10-2 rad (60’)
1’ = 2.91x 10-4 rad (60”)
1” = 4.85x 10-6 rad
Measurement of mass and time
* Mass is the basic property of matter and a fundamental unit of measurement since its
measurement does not depend on any other physical quantity.
* The SI unit of mass is Kilogram (kg).
* One unified atomic mass unit is defined as mass of one twelfth the mass of an isolated atom of 12 C isotope, at rest and in its ground state, including the mass the electrons.1u=1.66 x 10-27 kg.
* Measuring time is measuring the time interval between two events.
* To have the most accuracy in measuring time, an atomic standard of time is used, which is
based on periodic vibrations produced in a ceasium atom.
Accuracy and errors in measurement
* Accuracy is the degree of closeness of a measured value to the true or actual value.
* Precision is the degree of resolution of a measured value when the same quantity is measured with different devices.
* Any uncertainty in a measured value is called an error.
* Errors are classified as systematic errors and random errors.
* The magnitude of difference between the true value and each measured value of a quantity is called the absolute error of that measurement.
* Mean absolute error is the arithmetic mean of absolute errors of all measurements.
* Food adulteration is the act of intentionally deteriorating food quality by mixing cheap, low quality, inedible and toxic substances with it.
* The APGM Act provides grade specifications for different qualities of food and ensures good quality food products for the people.
* A quality certification scheme for food is being implemented under the ‘AGMARK’ label is a statutory symbol for purity and quality.
* Consumers of Agmarked products have the advantages of guaranteed quality and consumer protection.
* The Government of India and Andhra Pradesh have set up several offices and laboratories in different parts of the state.
Significant figures
* The number of digits in a measurement, which are certain, plus one additional digit, which
is uncertain, are together known as significant figures.
* Rules to determine significant figures in a given number:
• All non zero digits are significant.
• All the digits, including zeroes, are significant for a decimal number greater than one.
• If the decimal number lies between zero and one, the zeroes to the right of the decimal point but left of the first non zero digit, are non significant figures.
• If the measurement is a whole number, then the case becomes ambiguous if there are zeroes to the left of an understood decimal point but to the right of a non zero digit. To remove this ambiguity, the number should be reported in scientific notation (⍺ x 10b).
• All the final zeroes in a decimal number obtained by rounding off a decimal to a given number of decimal places are significant.
* The result of an arithmetic operation should not have more significant figures than the original data from which it was obtained.
* In multiplication or division, the result should retain as many significant figures as there are in the original number with the least significant figures.
* In addition or subtraction, the result should retain as many decimal places as there are in
the number with the least decimal places.
* If the original data is specified to n significant figures, the result obtained by combining
the data will also be valid to n significant figures.
* The relative error of a value of a number specified to significant figures depends not only
on n but also on the number itself.
* Intermediate results in a multi step calculation should be taken to an additional significant
figure in every measurement than the number of digits in the least precise measurement.
Dimensions and Dimensional equations
* The dimensions of a physical quantity are the powers or the exponents to which its base quantities are raised to represent that quantity.
* An expression for a physical quantity in terms of its base quantities is called the dimensional formula.
* An equation which equates quantity with a substance’s dimensional formula is called the’dimensional equation.
Dimensional analysis and its applications
* The dimensional formulae of physical quantities are useful in checking the dimensional consistency of equations.
* Dimensional formulae are useful in deriving expressions for a physical quantity given that the other physical quantities on which it is dependent and the constants involved are known.
* Dimensional formulae are used to find the conversion factors for a unit of a physical quantity from one system to another.
* Dimensionless quantities cannot be found by using dimensional analysis.
* The exact relationship between different physical quantities that have the same dimensions cannot be found by using dimensional analysis.
* Dimensional analysis cannot be applied to derive equations involving additive or subtracting terms, logarithmic functions, trigonometric functions and exponential functions.