This presentation covers measurement of physical quantities, system of units, dimensional analysis & error analysis. I hope this PPT will be helpful for instructors as well as students.
Physical Quantities--Units and Measurement--Conversion of UnitsKhanSaif2
This presentation covers physical quantities and their types, units and their types, conversion of units and order of magnitude in a very interactive manner. I hope this presentation will be helpful for teachers as well as students.
1.1 Introduction to physics
1.2 Physical quantities
1.3 International system of units
1.4 Prefixes (multiples and sub-multiples)
1.5 Scientific notation/ standard form
1.6 Measuring instruments
• meter rule
• Vernier calipers
• screw gauge
• physical balance
• stopwatch
• measuring cylinder
An introduction to significant figures
Physical Quantities--Units and Measurement--Conversion of UnitsKhanSaif2
This presentation covers physical quantities and their types, units and their types, conversion of units and order of magnitude in a very interactive manner. I hope this presentation will be helpful for teachers as well as students.
1.1 Introduction to physics
1.2 Physical quantities
1.3 International system of units
1.4 Prefixes (multiples and sub-multiples)
1.5 Scientific notation/ standard form
1.6 Measuring instruments
• meter rule
• Vernier calipers
• screw gauge
• physical balance
• stopwatch
• measuring cylinder
An introduction to significant figures
This presentation covers scalar quantity, vector quantity, addition of vectors & multiplication of vector. I hope this PPT will be helpful for Instructors as well as students.
This is a summary of the topic "Physical quantities, units and measurement" in the GCE O levels subject: Physics. Students taking either the combined science (chemistry/physics) or pure Physics will find this useful. These slides are prepared according to the learning outcomes required by the examinations board.
This presentation covers scalar quantity, vector quantity, addition of vectors & multiplication of vector. I hope this PPT will be helpful for Instructors as well as students.
This is a summary of the topic "Physical quantities, units and measurement" in the GCE O levels subject: Physics. Students taking either the combined science (chemistry/physics) or pure Physics will find this useful. These slides are prepared according to the learning outcomes required by the examinations board.
This presentation covers vertical motion under gravity, effect of air resistance on free fall & graphs of free fall. I hope this PPT will be helpful for instructors as well as students.
Effect of Phasor Measurement Unit (PMU) on the Network Estimated VariablesIDES Editor
The classical method of power measurement of a
system are iterative and bulky in nature. The new technique
of measurement for bus voltage, bus current and power flow is
a Phasor Measurement Unit. The classical technique and PMUs
are combined with full weighted least square state estimator
method of measurement will improves the accuracy of the
measurement. In this paper, the method of combining Full
weighted least square state estimation method and classical
method incorporation with PMU for measurement of power
will be investigated. Some cases are tested in view of accuracy
and reliability by introducing of PMUs and their effect on
variables like power flows are illustrated. The comparison of
power obtained on each bus of IEEE 9 and IEEE 14 bus system
will be discussed.
GPS helps us identify exact location of a place/feature in the globe. Now-a-days we can carry out survey, enter data and process data. GPS is very helpful in soil survey
This presentation covers internal structures of heart like atria and ventricles & external structures like emerging blood vessels and grooves on the heart. I hope this PPT will be helpful for instructors as well as teachers.
AWS and Mechanical Turk for the automotive industry. Contains AWS automotive case studies, AWS overview, Mechanical Turk use case and application examples in automotive industry, Mechanical Turk background.
Force, types of forces and system of forcesKhanSaif2
This presentation covers concept of force and different types of forces as well as different system of forces. I hope this PPT will be helpful for instructors as well as students.
MAHARASHTRA STATE BOARD
CLASS XI
PHYSICS
CHAPTER 1
UNITS AND MEASUREMENT
Introduction
The international system of
units
Measurement of length
Measurement of mass
Measurement of time
Accuracy, precision of
instruments and errors in
measurement
Significant figures
Dimensions of physical
quantities
Dimensional formulae and
dimensional equations
Dimensional analysis and its
applications
Units and Dimensions notes for physics. Here is the complete notes for unit and dimensions. Mechanics, physics notes for students. All abou unit and dimension. units and measurements class 11. dimensions of physical quantities.
Introduction to physics--Branches of Physics--Importance of physicsKhanSaif2
This presentation covers about physics, branches of physics and importance of physics in a very interactive manner. I hope this presentation will be helpful for teachers as well as students.
This presentation covers concepts such as surface tension, surface energy, liquid drops and bubbles, wetting, capillarity at the elementary school level. Comment down in a box for improvement.
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
This PPT covers curvilinear motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
This PPT covers projectile motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructors as well as students.
This PPT covers linear motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
This ppt covers composition and functions of blood in a systematic and interactive manner. I hope this PPT will be helpful for instructor's as well as students.
This presentation covers basics of cell structure and functions of different cell organelles in detail with interactive illustrations. I hope this presentation will be beneficial for instructor's as well as students.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
4. Need for measurement in physics
• To understand any phenomenon in physics we have to
perform experiments.
• Experiments require measurements, and we measure
several physical properties like length, mass, time,
temperature, pressure etc.
• Experimental verification of laws & theories also needs
measurement of physical properties.
5. Physical Quantity
A physical property that can be measured and
described by a number is called physical quantity.
Examples:
• Mass of a person is 65 kg.
• Length of a table is 3 m.
• Area of a hall is 100 m2.
• Temperature of a room is 300 K
6. Types of physical quantities
1. Fundamental quantities:
The physical quantities which do not depend on any
other physical quantities for their measurements
are known as fundamental quantities.
Examples:
• Mass
• Length
• Time
• Temperature
7. Types of physical quantities
The physical quantities which depend on one or more
fundamental quantities for their measurements are
known as derived quantities.
Examples:
• Area
• Volume
• Speed
• Force
2. Derived quantities:
8. Units for measurement
The standard used for the measurement of
a physical quantity is called a unit.
Examples:
• metre, foot, inch for length
• kilogram, pound for mass
• second, minute, hour for time
• fahrenheit, kelvin for temperature
9. Characteristics of units
Well – defined
Suitable size
Reproducible
Invariable
Indestructible
Internationally acceptable
10. • This system was first introduced in France.
• It is also known as Gaussian system of units.
• It is based on centimeter, gram and second
as the fundamental units of length, mass and
time.
CGS system of units
11. MKS system of units
• This system was also introduced in France.
• It is also known as French system of units.
• It is based on meter, kilogram and second as
the fundamental units of length, mass and
time.
12. FPS system of units
• This system was introduced in Britain.
• It is also known as British system of units.
• It is based on foot, pound and second as the
fundamental units of length, mass and time.
13. International System of units (SI)
• In 1971, General Conference on Weight and Measures
held its meeting and decided a system of units for
international usage.
• This system is called international system of units and
abbreviated as SI from its French name.
• The SI unit consists of seven fundamental units and
two supplementary units.
14. Seven fundamental units
FUNDAMENTAL QUANTITY SI UNIT 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
15. Definition of metre
The metre is the length of the
path travelled by light in a
vacuum during a time interval of
1/29,97,92,458 of a second.
16. Definition of kilogram
The kilogram is the mass of prototype
cylinder of platinum-iridium alloy
preserved at the International Bureau
of Weights and Measures, at Sevres,
near Paris.
21. Rules for writing SI units
1
Full name of unit always starts with small
letter even if named after a person.
• newton
• ampere
• coulomb
not
• Newton
• Ampere
• Coulomb
22. Rules for writing SI units
2
Symbol for unit named after a scientist
should be in capital letter.
• N for newton
• K for kelvin
• A for ampere
• C for coulomb
23. Rules for writing SI units
3
Symbols for all other units are written in
small letters.
• m for meter
• s for second
• kg for kilogram
• cd for candela
24. Rules for writing SI units
4
One space is left between the last digit of
numeral and the symbol of a unit.
• 10 kg
• 5 N
• 15 m
not
• 10kg
• 5N
• 15m
25. Rules for writing SI units
5
The units do not have plural forms.
• 6 metre
• 14 kg
• 20 second
• 18 kelvin
not
• 6 metres
• 14 kgs
• 20 seconds
• 18 kelvins
26. Rules for writing SI units
6
Full stop should not be used after the
units.
• 7 metre
• 12 N
• 25 kg
not
• 7 metre.
• 12 N.
• 25 kg.
27. Rules for writing SI units
7
No space is used between the symbols for
units.
• 4 Js
• 19 Nm
• 25 VA
not
• 4 J s
• 19 N m.
• 25 V A.
28. SI prefixes
Factor Name Symbol Factor Name Symbol
10
24 yotta Y 10
−1 deci d
10
21 zetta Z 10
−2 centi c
10
18 exa E 10
−3 milli m
10
15 peta P 10
−6 micro μ
10
12 tera T 10
−9 nano n
10
9 giga G 10
−12 pico p
10
6 mega M 10
−15 femto f
10
3 kilo k 10
−18 atto a
10
2 hecto h 10
−21 zepto z
10
1 deka da 10
−24 yocto y
29. • 3 milliampere = 3 mA = 3 x 10
−3
A
• 5 microvolt = 5 μV = 5 x 10
−6
V
• 8 nanosecond = 8 ns = 8 x 10
−9
s
• 6 picometre = 6 pm = 6 x 10
−12
m
• 5 kilometre = 5 km = 5 x 10
3
m
• 7 megawatt = 7 MW = 7 x 10
6
W
Use of SI prefixes
30. Some practical units for measuring length
1 micron = 10
−6
m
Bacterias Molecules
1 nanometer = 10
−9
m
31. Some practical units for measuring length
1 angstrom = 10
−10
m
Atoms Nucleus
1 fermi = 10
−15
m
32. Some practical units for measuring length
• Astronomical unit = It is defined as the mean distance of
the earth from the sun.
• 1 astronomical unit = 1.5 x 10
11
m
Distance of planets
33. Some practical units for measuring length
• Light year = It is the distance travelled by light in vacuum in
one year.
• 1 light year = 9.5 x 10
15
m
Distance of stars
34. Some practical units for measuring length
• Parsec = It is defined as the distance at which an arc of 1 AU
subtends an angle of 1’’.
• It is the largest practical unit of distance used in astronomy.
• 1 parsec = 3.1 x 10
16
m
1 AU 1”
35. Some practical units for measuring area
• Acre = It is used to measure large areas in British system of
units.
1 acre = 208’ 8.5” x 208’ 8.5” = 4046.8 m2
• Hectare = It is used to measure large areas in French system
of units.
1 hectare = 100 m x 100 m = 10000 m2
• Barn = It is used to measure very small areas, such as nuclear
cross sections.
1 barn = 10
−28
m2
36. Some practical units for measuring mass
1 metric ton = 1000 kg
Steel bars Grains
1 quintal = 100 kg
37. 1 pound = 0.454 kg
Newborn babies Crops
1 slug = 14.59 kg
Some practical units for measuring mass
38. Some practical units for measuring mass
• 1 Chandrasekhar limit = 1.4 x mass of sun = 2.785 x 10
30
kg
• It is the biggest practical unit for measuring mass.
Massive black holes
39. Some practical units for measuring mass
• 1 atomic mass unit =
1
12
x mass of single C atom
• 1 atomic mass unit = 1.66 x 10
−27
kg
• It is the smallest practical unit for measuring
mass.
• It is used to measure mass of single atoms,
proton and neutron.
40. Some practical units for measuring time
• 1 Solar day = 24 h
• 1 Sidereal day = 23 h & 56 min
• 1 Solar year = 365 solar day = 366 sidereal day
• 1 Lunar month = 27.3 Solar day
• 1 shake = 10
−8
s
41. Seven dimensions of the world
Fundamental quantities
Length
Mass
Time
Temperature
Current
Amount of substance
Luminous intensity
Dimensions
[L]
[M]
[T]
[K]
[A]
[N]
[J]
42. Dimensions of a physical quantity
The powers of fundamental quantities
in a derived quantity are called
dimensions of that quantity.
43. =
Mass
length × breath × height
[Density] =
[M]
L × L × L
=
[M]
L3
= [ML−3
]
Dimensions of a physical quantity
Density =
Mass
Volume
Example:
Hence the dimensions of density are 1 in mass and − 3 in length.
44. Uses of Dimension
To check the correctness of equation
To convert units
To derive a formula
45. To check the correctness of equation
∆x = displacement = [L]
Consider the equation of displacement,
By writing the dimensions we get,
vit = velocity × time =
length
time
× time = [L]
at2
= acceleration × time2
=
length
time2
× time2
= [L]
The dimensions of each term are same, hence the equation is
dimensionally correct.
∆x = vit +
1
2
a t2
46. To convert units
Let us convert newton SI unit of force into dyne CGS unit of force .
The dimesions of force are = [LMT−2
]
So, 1 newton = (1 m)(1 kg)(1 s)−2
and, 1 dyne = (1 cm)(1 g)(1 s)−2
Thus,
1 newton
1 dyne
=
1 m
1 cm
1 kg
1 g
1 s
1 s
−2
=
100 cm
1 cm
1000 g
1 g
1 s
1 s
−2
= 100 × 1000 = 105
Therefore, 1 newton = 105 dyne
47. To derive a formula
The time period ‘T’ of oscillation of a
simple pendulum depends on length ‘l’
and acceleration due to gravity ‘g’.
Let us assume that,
T ∝ 𝑙a 𝑔b or T = K 𝑙a 𝑔b
K = constant which is dimensionless
Dimensions of T = [L0M0T1]
Dimensions of 𝑙 = [L1
M0
T0
]
Dimensions of g = [L1M0T−2]
Thus, L0M0T1 = K [L1M0T0]a [L1M0T−2]b
= K LaM0T0 LbM0T−2b
L0M0T1 = K La+bM0T−2b
a + b = 0 & − 2b = 1
∴ b = −
1
2
& a =
1
2
T = K 𝑙1/2 𝑔−1/2
∴ T = K
𝑙
𝑔
48. Least count of instruments
The smallest value that can be
measured by the measuring instrument
is called its least count or resolution.
49. LC of length measuring instruments
Ruler scale
Least count = 1 mm
Vernier Calliper
Least count = 0.1 mm
50. LC of length measuring instruments
Screw Gauge
Least count = 0.01 mm
Spherometer
Least count = 0.001 mm
51. LC of mass measuring instruments
Weighing scale
Least count = 1 kg
Electronic balance
Least count = 1 g
52. LC of time measuring instruments
Wrist watch
Least count = 1 s
Stopwatch
Least count = 0.01 s
53. Accuracy of measurement
It refers to the closeness of a measurement
to the true value of the physical quantity.
Example:
• True value of mass = 25.67 kg
• Mass measured by student A = 25.61 kg
• Mass measured by student B = 25.65 kg
• The measurement made by student B is more accurate.
54. Precision of measurement
It refers to the limit to which a physical
quantity is measured.
Example:
• Time measured by student A = 3.6 s
• Time measured by student B = 3.69 s
• Time measured by student C = 3.695 s
• The measurement made by student C is most precise.
55. Significant figures
The total number of digits
(reliable digits + last uncertain digit)
which are directly obtained from a
particular measurement are called
significant figures.
58. Rules for counting significant figures
1
All non-zero digits are significant.
Number
16
35.6
6438
Significant figures
2
3
4
59. 2
Zeros between non-zero digits are significant.
Rules for counting significant figures
Number
205
3008
60.005
Significant figures
3
4
5
60. Rules for counting significant figures
3
Terminal zeros in a number without decimal are
not significant unless specified by a least count.
Number
400
3050
(20 ± 1) s
Significant figures
1
3
2
61. Rules for counting significant figures
4
Terminal zeros that are also to the right of a
decimal point in a number are significant.
Number
64.00
3.60
25.060
Significant figures
4
3
5
62. Rules for counting significant figures
5
If the number is less than 1, all zeroes before the
first non-zero digit are not significant.
Number
0.0064
0.0850
0.0002050
Significant figures
2
3
4
63. 6
During conversion of units use powers of 10 to
avoid confusion.
Rules for counting significant figures
Number
2.700 m
2.700 x 10
2
cm
2.700 x 10
−3
km
Significant figures
4
4
4
64. Exact numbers
• Exact numbers are either defined numbers or the
result of a count.
• They have infinite number of significant figures
because they are reliable.
By definition
1 dozen = 12 objects
1 hour = 60 minute
1 inch = 2.54 cm
By counting
45 students
5 apples
6 faces of cube
65. Rules for rounding off a measurement
1
If the digit to be dropped is less than 5, then the
preceding digit is left unchanged.
Number
64.62
3.651
546.3
Round off up to 3 digits
64.6
3.65
546
66. 2
If the digit to be dropped is more than 5, then the
preceding digit is raised by one.
Number
3.479
93.46
683.7
Round off up to 3 digits
3.48
93.5
684
Rules for rounding off a measurement
67. 3
If the digit to be dropped is 5 followed by digits other
than zero, then the preceding digit is raised by one.
Number
62.354
9.6552
589.51
Round off up to 3 digits
62.4
9.66
590
Rules for rounding off a measurement
68. 4
If the digit to be dropped is 5 followed by zero or
nothing, the last remaining digit is increased by 1 if it is
odd, but left as it is if even.
Number
53.350
9.455
782.5
Round off up to 3 digits
53.4
9.46
782
Rules for rounding off a measurement
69. Significant figures in calculations
Addition & subtraction
The final result would round to the same decimal
place as the least precise number.
Example:
• 13.2 + 34.654 + 59.53 = 107.384 = 107.4
• 19 – 1.567 - 14.6 = 2.833 = 3
70. Significant figures in calculations
Multiplication & division
The final result would round to the same number
of significant digits as the least accurate number.
Example:
• 1.5 x 3.67 x 2.986 = 16.4379 = 16
• 6.579/4.56 = 1.508 = 1.51
71. Errors in measurement
Difference between the actual value of
a quantity and the value obtained by a
measurement is called an error.
Error = actual value – measured value
73. 1. Systematic errors
• These errors are arise due to flaws in
experimental system.
• The system involves observer, measuring
instrument and the environment.
• These errors are eliminated by detecting
the source of the error.
74. Types of systematic errors
Personal errors
Instrumental errors
Environmental errors
75. a. Personal errors
These errors are arise due to faulty procedures
adopted by the person making measurements.
Parallax error
77. c. Environmental errors
These errors are caused by external conditions like
pressure, temperature, magnetic field, wind etc.
Following are the steps that one must follow in order
to eliminate the environmental errors:
a. Try to maintain the temperature and humidity of the
laboratory constant by making some arrangements.
b. Ensure that there should not be any external magnetic or
electric field around the instrument.
79. 2. Gross errors
These errors are caused by mistake in using
instruments, recording data and calculating results.
Example:
a. A person may read a pressure gauge indicating 1.01 Pa
as 1.10 Pa.
b. By mistake a person make use of an ordinary electronic
scale having poor sensitivity to measure very low masses.
Careful reading and recording of the data can reduce the
gross errors to a great extent.
80. 3. Random errors
• These errors are due to unknown causes and
are sometimes termed as chance errors.
• Due to unknown causes, they cannot be
eliminated.
• They can only be reduced and the error can be
estimated by using some statistical operations.
81. Error analysis
For example, suppose you measure the oscillation period of
a pendulum with a stopwatch five times.
Trial no ( i ) 1 2 3 4 5
Measured value ( Xi ) 3.9 3.5 3.6 3.7 3.5
82. Mean value
The average of all the five readings gives the most probable
value for time period.
X =
1
n
Xi
X =
3.9 + 3.5 + 3.6 + 3.7 + 3.5
5
=
18.2
5
X = 3.64 = 3.6
83. Absolute error
The magnitude of the difference between mean value and
each individual value is called absolute error.
∆Xi = X − Xi
Xi 3.9 3.5 3.6 3.7 3.5
∆Xi 0.3 0.1 0 0.1 0.1
The absolute error in each individual reading:
84. Mean absolute error
The arithmetic mean of all the absolute errors is called
mean absolute error.
∆X =
1
n
∆Xi
∆X =
0.3 + 0.1 + 0 + 0.1 + 0.1
5
=
0.6
5
∆X = 0.12 = 0.1
85. Reporting of result
• The most common way adopted by scientist and engineers
to report a result is:
Result = best estimate ± error
• It represent a range of values and from that we expect
a true value fall within.
• Thus, the period of oscillation is likely to be within
(3.6 ± 0.1) s.
86. Relative error
The relative error is defined as the ratio of the
mean absolute error to the mean value.
relative error = ∆X / X
∆X / X =
0.1
3.6
= 0.0277
∆X / X = 0.028
87. Percentage error
The relative error multiplied by 100 is called as
percentage error.
percentage error = relative error x 100
percentage error = 0.028 x 100
percentage error = 2.8 %
88. Least count error
Least count error is the error associated with the
resolution of the instrument.
• The least count error of any
instrument is equal to its
resolution.
• Thus, the length of pen is likely
to be within (4.7 ± 0.1) cm.
89. Combination of errors
• Let ∆A be absolute error in measurement of A
• Let ∆B be absolute error in measurement of B
• Let ∆X be absolute error in measurement of X
In different mathematical operations like addition,
subtraction, multiplication and division the errors
are combined according to some rules.
90. When X = A ± B
∆X
X
=
∆A+∆B
A ± B
∆X = ∆A + ∆B
91. When X = A × B or A / B
∆X
X
=
∆A
A
+
∆B
B
∆X =
∆A
A
+
∆B
B
X
96. Order of magnitude
The approximate size of
something expressed in powers
of 10 is called order
of magnitude.
97. To get an approximate idea of the number, one may
round the coefficient a to 1 if it is less than or
equal to 5 and to 10 if it is greater than 5.
Examples:
• Mass of electron = 9.1 x 10
−31
kg
≈ 10 x 10
−31
kg ≈ 10
−30
kg
• Mass of observable universe = 1.59 x 10
53
kg
≈ 1 x 10
53
kg ≈ 10
53
kg