Units and Measurement
Units and Measurement
Units and Measurement
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The International System of units or S.I. system - It was adopted and accepted in the international
conference of weights and measurement held at Geneva in 1960.
• In fact, S.I system is extended and modifiied form of the MKS System.
• In S.I. System there are Seven Fundamental Quantities. They do not depend on other Physical
Quantity i.e. Independent to each other.
Length – metre
Mass – kg
Time – second
Electric current – Ampere
Temperature – kelvin
Amount of substance – mole
Luminous intensity – candela
Measurement of Lengths
The sizes of the objects we come across in the universe vary over a very wide range.
• The nucleus takes up only 10-14 metres of the space of the atom. As a result, size (radius) of
nucleus is measured in fermi also called femtometre.
• The diameter of a nucleus varies in the range of 4 -15 fm for a lighter nucleus to a heavy nucleus.
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Cosmic Distance
Astronomical unit (average distance of the Sun from the Earth)
• 1 AU = 1.496 x 10¹¹ m = 150 million kilometres (93 million miles) or ~8 light minutes
The astronomical unit is used primarily for measuring distances within the Solar System or around
other stars
A light-year is the distance that light travels in vacuum in one year (365.25 days)
• 1 light year = 1 ly= 9.46 × 1015 m. 1 light year = 63240 A.U. / 63000 A.U.
The parsec is a unit of length used to measure the large distances to astronomical
objects outside the Solar System.
• 1 persec equal to 3.26 light-years or 206,000 astronomical units (au) = 3.0857×1016 m .
MEASUREMENT OF MASS
Mass is a basic property of matter. It does not depend on the temperature, pressure or location of the
object in space.
Measurement of Time
To measure any time interval, we need a clock. We now use an atomic standard of time, which is based on
the periodic vibrations produced in a cesium atom. This is the basis of the caesium clock, sometimes called
atomic clock. A cesium atomic clock is used at the National Physical Laboratory (NPL), New Delhi to
maintain the Indian standard of time.
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luminous intensity is a measure of the wavelength-weighted power emitted by a light
source in a particular direction per unit solid angle, based on the sensitivity of the human eye .
The luminous intensity (in candelas) is a measure of how bright the beam in a particular direction
is.
• The SI unit of luminous intensity is the candela (cd).
luminous flux or luminous power is the measure of the perceived power of light.
Luminous flux (in lumens) is a measure of the total amount of light a lamp puts out.
The SI unit of luminous flux is the lumen (lm).
• The lumen (symbol: lm) is the SI derived unit of luminous flux, a measure of the total
quantity of visible light emitted by a source per unit of time.
illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how
much the incident light illuminates the surface with human brightness perception.
• In SI units illuminance is measured in lux (lx), or equivalently in lumens per square
metre (lm·m−2). In the CGS system, the unit of illuminance is the phot, which is equal
to 10000 lux.
Luminance levels indicate how much luminous power could be detected by the human
eye looking at a particular surface from a particular angle of view. Luminance is thus an
indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid
angle subtended by the eye's pupil.
• The SI unit for luminance is candela per square metre (cd/m2)
The amount of substance is simply the number of particles that constitute the substance.
The particles may be molecules, atoms, ions, electrons, or other, depending on the context.
• The mole is a unit of amount of substance.
• 1 mole is defined as exactly 6.022×1023 particles, which may be atoms, molecules, ions,
or electrons. This number is also called Avogadro's Number. In other words, 1 mole is equal to
Avogadro's number.
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Derived Units:
Units which are derived from basic units and bear a constant relationship with the fundamental units. They
depend on the other physical quantity.
Except for 7 fundamental quantities, all other quantities are derived quantities. Example: Volume, velocity,
force, speed, area, density, power, etc.
Dimensional Formula - The formula that indicates how and which fundamental quantities are there
in a physical quantity.
ক োন ো ক ৌতরোশিনত (Physical quantities) মূল রোশিগুশল ী োনে উপশিত থোন তো ওই রোশির মোত্রো (Dimensions)
শ র্োরণ
ধ নর ।
Length – [L]
Mass – [M]
Time - [T]
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The Planck's constant - is a fundamental physical constant denoted h, and is of fundamental importance in
quantum mechanics.
A photon's energy is equal to its frequency multiplied by the Planck constant.
Due to mass–energy equivalence, the Planck constant also relates mass to frequency.
In SI units, it has the exact value = 6.62607015×10−34 J⋅Hz−1
The Planck–Einstein relation connects the particular photon energy E with its associated wave
frequency f:
E = hf
Dimension – ML2 T -1
Dimension of The Planck's constant is same with the Dimension of Angular Momentum.
Torque - is the measure of the force that can cause an object to rotate about an axis.
Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes
an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force.
The point where the object rotates is called the axis of rotation.
Torque depends on the magnitude of the force and the perpendicular distance between the point
of axis of rotation and the point of application of force.
In physics, torque is simply the tendency of a force to turn or twist.
Different terminologies such as moment or moment of force are interchangeably used to describe
torque.
The unit of torque is Newton–meter (N-m).
Dimension – ML2 T -2
Dimension of Torque is same with the Dimension of any form of energy or work.
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Dimensionless Quantity
Dimensionless quantity is the ratio of two similar physical quantity
Example – atomic weight, specific gravity, refractive index, poison’s ratio
These physical quantities are of two types (a) scalars (b) vectors.
(a) Scalars - Those physical quantities which have magnitude only and whose direction is not taken into the
consideration are called scalars.
Example: Mass, temperature, density, volume, electric current, work etc.
(b) Vectors - Those physical quantities which have both magnitude and direction and which are obeying
the triangle law of vectors/parallelogram law of vectors are called vectors.
Example: Displacement, linear momentum, angular velocity, torque, magnetic field intensity, electric
displacement, current density etc.
A physical quantity which has both magnitude and direction but which doesn't obey vector laws of
addition/subtraction is not a vector quantity, like. electric current, pressure etc.
Nautical mile
A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of
territorial waters.
• The Dobson Unit is the most common unit for measuring ozone concentration.
• One DU is also equivalent to 2.687×1020 molecules per square metre.
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• The Dobson spectrophotometer, also known as Dobsonmeter, Dobson spectrometer,
or just Dobson is one of the earliest instruments used to measure atmospheric ozone.
• The Dobson spectrometer was invented in 1924 by Gordon Dobson.
Fathometer
The fathometer is an echo sounding system (active sonar instruments) for measurement of
water depth.
• The fathom is a unit of water depth.
• One fathom is equal to 6 feet.
• It is also used to locate fish under the water by detecting reflected pulses of sound
energy. Hence it is also called fish finder. Fish finders were derived from fathometers.
A furlong is a measure of distance, equal to one eighth of a mile, equivalent to 660 feet or
approximately 201 metres. It is now almost obsolete, except in horse racing, where in many
countries it is the standard measurement of race lengths.
Jiffy can be an informal term for any unspecified short period, as in "I will be back in a jiffy".
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