Units and Measurements Notes for CET | JEE | NEET
Introduction:
What is a Unit?
The standard measure of any quantity is called the unit of that quantity.
System of Units:
There are three main systems in an early period which are following
(i) CGS: Centimetre Gram Second system
(ii) (ii) MKS: Metre Kilogram Second system
(iii) (iii) FPS: Foot Pound Second system.
In 1971, the 14th International general conference on weights and measures recommended the use of the ‘International system' of units
Fundamental Quantites :
The physical quantities which do not depend on any other physical quantities for their measurements are known as fundamental quantities.Fundamental Quantity
SI Units
Symbol
Length
Metre
m
Mass
Kilogram
Kg
Time
Second
S
Temperature
Kelvin
K
Electric Current
Ampere
A
Luminous Intensity
Candela
Cd
Amount of Substance
mole
Mol
Fundamental Units:
The units used to measure fundamental quantities are called fundamental units.
Derived Quantities :
The physical quantities which depend on any Fundamental quantities for their measurements are known as Derived quantities.Derived Units :
The units used to measure Derived quantities are called Derived units
For Eg,
Unit of momentum = (Unit of mass)×(Unit of velocity)
= kg m/s = kg m s-1
Supplementary units :
Besides, the seven fundamental or basic units, there are two more units called supplementary units
v Plane Angle: Plane angle Is the ratio of the length of an arc of a circle to the radius of circle.
Ø It is measured in radian and denoted by Theta
Ø Formula
v Solid Angle: Solid angle is the 3 dimensional analog of d theta and is defined as the area of a portion of the surface of a sphere to the square of the radius of the sphere
v Unit of every physical quantity should be represented by its symbol
v Full name of a unit always starts with a smaller letter even if the name is after a person, e.g., 1 newton, etc. But the symbol for a unit named after a person should be in capital letters, e.g., N after scientist Newton.
v Symbols for units do not take the plural form. Eg 20N not 20Ns
v Symbols for units do not contain any full stops at the end of the recommended letter.
v The units of physical quantities in numerator and denominator should be written as one ratio
v Use of the combination of units and symbols for units is avoided when physical quantity is expressed by a combination of two. e.g., The unit J/kg K is correct while joule/kg K is not correct.
v A prefix symbol is used before the symbol of the unit.
v Space or hyphen must be introduced while indicating the multiplication of two units.
Parallax is defined as the apparent change in position of an object due to a change in the position of the observer
Sun is the closest star to earth. the next closest star is at a distance of 4.29 Light years which is Proxima Centauri.
Measurement of the size of a planet or a star:
if d is the diameter of a planet, the angle subtended by it at any single point on the Earth is called the angular diameter of the planet.
Vernier caliper or screw gauge is not usefull to measure very small distance Therefore we need electron microscope or tunneling electron Microscope.
Some Important units :
Measurement of mass:
1. In an earlier period a kilogram was the mass of a shiny piece of platinum-iridium alloy kept on the special glass.
2. On 20th May 2019 the carefully kept Platinium iridium piece is seen to pick up microparticles of dirt.
3. Thus the kilogram mass can be described in terms of the amount of current which has to be passed through an electromagnet so that it can pull down one side of an extremely sensitive balance to balance the other side which holds one standard kg mass
The (1/12)th mass of an unexcited atom of C12 is called the atomic mass unit (AMU). 1 amu = 1.6605402 10^-27 kg
SI unit of time is the second (s)
Solar day = 24 Hours = 24x60x60=86400s. Accordingly, a second was defined as 1/86400 of a mean Solar day Cesium atomic clock is used to get more standard and conveying.
Part 2 soon.....................
For Eg,
Unit of momentum = (Unit of mass)×(Unit of velocity)
= kg m/s = kg m s-1
Supplementary units :
Besides, the seven fundamental or basic units, there are two more units called supplementary units
v Plane Angle: Plane angle Is the ratio of the length of an arc of a circle to the radius of circle.
Ø It is measured in radian and denoted by Theta
Ø Formula
v Solid Angle: Solid angle is the 3 dimensional analog of d theta and is defined as the area of a portion of the surface of a sphere to the square of the radius of the sphere
Conventions for the use of SI Units:
v Unit of every physical quantity should be represented by its symbol
v Full name of a unit always starts with a smaller letter even if the name is after a person, e.g., 1 newton, etc. But the symbol for a unit named after a person should be in capital letters, e.g., N after scientist Newton.
v Symbols for units do not take the plural form. Eg 20N not 20Ns
v Symbols for units do not contain any full stops at the end of the recommended letter.
v The units of physical quantities in numerator and denominator should be written as one ratio
v Use of the combination of units and symbols for units is avoided when physical quantity is expressed by a combination of two. e.g., The unit J/kg K is correct while joule/kg K is not correct.
v A prefix symbol is used before the symbol of the unit.
v Space or hyphen must be introduced while indicating the multiplication of two units.
Parallax Method
Parallax is defined as the apparent change in position of an object due to a change in the position of the observer
Measurement of the distance to star:
Sun is the closest star to earth. the next closest star is at a distance of 4.29 Light years which is Proxima Centauri.
Measurement of the size of a planet or a star:
if d is the diameter of a planet, the angle subtended by it at any single point on the Earth is called the angular diameter of the planet.
Measurement of Very small Distance
Vernier caliper or screw gauge is not usefull to measure very small distance Therefore we need electron microscope or tunneling electron Microscope.
Some Important units :
Measurement of mass:
1. In an earlier period a kilogram was the mass of a shiny piece of platinum-iridium alloy kept on the special glass.
2. On 20th May 2019 the carefully kept Platinium iridium piece is seen to pick up microparticles of dirt.
3. Thus the kilogram mass can be described in terms of the amount of current which has to be passed through an electromagnet so that it can pull down one side of an extremely sensitive balance to balance the other side which holds one standard kg mass
Atomic mass unit :
The (1/12)th mass of an unexcited atom of C12 is called the atomic mass unit (AMU). 1 amu = 1.6605402 10^-27 kg
Measurement of Time :
SI unit of time is the second (s)
Solar day = 24 Hours = 24x60x60=86400s. Accordingly, a second was defined as 1/86400 of a mean Solar day Cesium atomic clock is used to get more standard and conveying.
Part 2 soon.....................
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