Combination of Errors – Units and Measurement

Combination of Errors
(i) Error in Addition or Subtraction :
Let x = a + b or x = a- b
If the measured values of two quantities a and b are (a ± Δa) and (b ± Δb), then maximum absolute error in their addition or subtraction is

Δx = ± (Δa + Δb)

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Combination of Error Formula, Definition, Rules

(ii) Combination of Errors in Multiplication or Combination of Errors in Division:
Let x = a x b or x = \(\frac{a}{b}\)
If the measured values of a and b are (a ± Δa) and (b ± Δb), then maximum relative error

\(\left(\frac{\Delta a}{a}+\frac{\Delta b}{b}\right)\)

(iii) Error in case of a measured quantity raised to a Power:
Let z = apbq / cr
If the measured values of a, b and c are (a ± Δa), (b ± Δb) and (c ± Δc), then maximum error

\(\frac{\Delta z}{z}=p\left(\frac{\Delta a}{a}\right)+q\left(\frac{\Delta b}{b}\right)+r\left(\frac{\Delta c}{c}\right)\)

Note: The smallest value that can be measured by a measuring instrument is called least count of that instrument, eg. A metre scale having graduation at 1 mm division scale spacing, has a least count of 1 mm or 0.1 cm.

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors

Physics Notes | Physics – Definitions, Laws, Formula, Derivation, Example

Physics notes are provided here for students, in PDF format, which can be easily downloaded. Students who are preparing for Class 11 and Class 12th Board exam 2021, can download these materials and learn offline as well. The notes provided here are prepared by our subject experts, based on the CBSE syllabus and NCERT curriculum.

Physics – Definitions, Laws, Formula, Derivation, Example

The Physics notes include chapter-wise solutions for all the questions, given in the book. Learning from these notes, students will be able to score good marks in the final exam.

Free Physics Study Material

Free Physics study materials are provided here for students who are preparing for CBSE 11th and 12th examination. With the help of these materials they can have a quick revision before the exam and save their time. Also, these materials are helpful for students who are preparing for competitive exams such as AIEEE and JEE.

Topic-wise notes for Physics subjects are available. Below are the links given for individual topics. Students need to click on the respective link to get the notes. Each topic has been explained with the help of solved problems, to make each student understand better. Go through the notes of Physics subject and enhance your learning skills here.

Units and Measurement

In this chapter, students are going to learn about measurements of different physical quantities and their respective units. Also, the symbol of each unit and definition will be explained.

The unit explains the measure of type of quantity. For example, to measure the length we use meter, centimeter, inches as units. But to measure distances we use kilometers, meters, yards, etc. To measure the weight of any object the fundamental unit is kilogram. These are the standard quantities. Also, there are many derived quantities such as velocity, force, acceleration, derived from fundamental quantities. All these quantities and their units will be discussed in this chapter, along with the error which is included within the measurement.

Scalars and Vectors

The vectors and scalars are defined in three dimension space. A vector is a quantity which has both magnitude and direction whereas a scalar quantity has only magnitude. The example of vector quantity is velocity, where the speed of the object is measured based on its direction. The example of scalar quantity is speed, which only depends on distance travelled by the object in a particular time.

Learn here different types of vectors such as equal vectors, negative vectors, zero vectors, unit vectors, coplanar vectors, etc. Along with that learn how to add, subtract, multiply and divide any two vectors. Also, check the scalar product and the vector product of two vectors. Solve questions based on vectors here.

Motion in a Straight Line

An object is either in rest position or in motion state. In this unit, you will learn about the rest and motion state of objects and how it is stated in Physics. Also, learn the difference between distance and displacement of objects, how to measure speed, velocity and acceleration, difference between uniform and nonuniform motion along with their graphs.

Whenever an object is in uniform motion, we can represent this in the graph and also the equation for the motion can be derived from it. We will learn here how to derive the equation for such uniform motion along with motion under gravity.

Motion in a Plane (Projectile and Circular Motion)

In this chapter or under this topic, we are going to come across the motion of the object when it is thrown from one end to another end. This practice is said to be projection. Also, when an object is moved in a circular motion, then the equation of the motion is derived here.

When an object is moved in circular motion then a centrifugal force acts on it, because of which it moves around a center in a constant manner. It is also called centripetal force. We will learn here about centripetal force and centripetal acceleration in detail with formulas. Also learn the force applied in everyday life motion of the particle in a vertical circle.

Laws of Motion

There are various laws in Physics which define the motion of the object. When an object is in motion whether it is linear or circular there is some force which is always imposed on it. Newton’s laws of motion explains the linear momentum and moment of inertia of moving objects. There are three laws discussed by Newton, where the relation between motion of the object and force imposed on it is explained.

In its first law, Newton’s state that the object stays in steady state or in motion until and unless an external force is applied on it. In second law, the rate of change of momentum is directly proportional to the force acted on the object. And in the third law, we will learn that for every action there is an equal and opposite reaction.

Work, Energy and Power

Work, energy and power are the three quantities which are inter-related to each other. The rate of doing work is called power. An equal amount of energy is consumed to do a work. So, basically the power is the rate at which energy is consumed to complete a work.

The unit of work in SI is Joule (J), the unit of energy is also joules (J) and the unit of power is watt (W). Learn in detail more about these three quantities in the below given sub-topics.

Rotational Motion

In this portion, we will learn about the rotational motion of the objects. A body moves completely in rotational motion when each particle of the body moves in a circle about a single line. When a force is applied on a body about an axis it causes a rotational motion. The force applied here is called the torque. The axis of the rotation usually goes through the body.

All the concepts related to rotational motion are covered here such as center of mass, moment of inertia, radius of gyration, torque, center of gravity, angular momentum, angular impulse and rotational kinetic energy. Also, learn the two theorems such as parallel axes and perpendicular theorem explained with respect to rotational motion of objects.


Have you ever thought, when we throw a ball above the ground level, why it returns back to the ground. It’s because of gravity. When a ball is thrown above the ground in the opposite direction, a gravitational force acts on it which pulls it downwards and makes it fall. This phenomena is called gravitation.

Newton’s law is explained for gravitational force also. Here we will cover acceleration of the object due to gravity and what are the factors affecting the object due to gravitational force. Learn relation between gravitational field and potential field, Kepler’s law of planetary, weightlessness of objects in absence of gravitation, etc.


Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. For example, a rubber band has the elastic property because of which it retains its shape whenever we stretch it.

Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity. Also, learn the types of modulus of elasticity along with Poisson’s ratio.


Hydrostatics is a property of liquid or fluid in mechanics. A fluid is a material which flows at room temperature, because its upper molecule overlaps the inner molecule, which tends to flow the liquid in forward direction. In hydrostatics, we will learn about the condition of fluids when it is in rest or exerted by an external force. Here we will study the fluids in motion.

There will be different laws and principles explaining the motion of the fluid and also in rest state, such as Pascal’s law, Archimedes’ principle, laws of floatation. Also learn the density of a fluid and relativity.


In physics, hydrodynamics of fluid dynamics explains the mechanism of fluid such as flow of liquids and gases. It has a wide range of applications such as evaluating forces and momentum on aircraft, prediction of weather, etc.

Below are the theories and explanations given to explain the motion of fluids. Learn all the sub-topics here by just one click.

Surface Tension

In Physics, the tension of the surface film of a liquid because of the attraction of the surface particles by the bulk of the liquid, which tries to minimize surface area is called surface tension.
When the surface of the liquid is strong enough, then surface tension is applicable. It is strong enough to hold a weight. Like the surface of water can hold droplets at the surface in a ball shape. Because of the property of water, some insects can run on the surface of the water without getting drowned.

Learn the different forces applied on a fluid surface here.

  1. Surface Tension
  2. Adhesive Force
  3. Cohesive Force
  4. Molecular Range
  5. Factors Affecting Surface Tension
  6. Surface Energy
  7. Angle of Contact
  8. Capillarity
  9. Jurin’s Law

Thermometry and Calorimetry

The thermometer is a device used to check the temperature of an object. This branch of measurement of temperature of a substance is called thermometry. It is measured in degrees or fahrenheit, usually.

Calorimetry also means the measurement of heat but in joules. It states the amount of heat lost by the body is the amount of heat gained by its surrounding.

Learn more on how to calculate heat and temperature here with the given sub-topics.

Kinetic Theory of Gases

In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.


In thermodynamics, we deal with the relationship between heat and other forms of energies. It explains the conversion of thermal energy into another form of energy and vice-versa. There are three basic laws that define thermodynamics. They are the First Law, Second Law and Zeroth Law. The thermodynamic shows its major application when the heat is transferred from a body to its surrounding environment, till the temperature of the body is equivalent to the temperature of the atmosphere. This is called thermal equilibrium.

  • Thermodynamical Terms
  • Work done Internal Energy (U)
  • Zeroth Law of Thermodynamics
  • First Law of Thermodynamics
  • Thermodynamic Processes
  • Second Law of Thermodynamics Entropy
  • Heat Engine
  • Carnots Cycle Refrigerator

Transmission of Heat

The transfer of heat is classified in many types of mechanism such as thermal radiation, thermal conduction, thermal convention, and heat transfer by change of phase. The transmission of heat is also termed as heat conduction where the kinetic energy of particles of the two systems are exchanged through their boundaries.

  • Heat Transmission
  • Ingen Hausz Experiment
  • Reflectance or Reflecting Power
  • Absorptance or Absorbing Power
  • Transmittance or Transmitting Power
  • Emissive Power
  • Emissivity
  • Perfectly Black Body
  • Kirchhoff’s Law
  • Stefan’s Law
  • Wien’s Displacement Law
  • Solar Constant


When an object is moving back and forth in a regular rhythm, then it is said to be in a state of oscillation. For example, a pendulum oscillates from one end to another end continuously in a periodic motion, until any external force stops it. It repeats itself over and over for a period of time. The types of oscillations are explained in this chapter.

  • Periodic Motion
  • Oscillatory Motion
  • Harmonic Oscillation
  • Simple Harmonic Motion
  • Some Important Formulae of SHM
  • Graphical Representation of SHM
  • Force in SHM
  • Energy in SHM
  • Simple Pendulum
  • Second’s Pendulum
  • Conical Pendulum
  • Compound Pendulum
  • Torisonal Pendulum
  • Spring Pendulum
  • Oscillations of liquid in a
  • U-tube
  • Lissajou’s Figures

Waves and Sound

When an object vibrates or shakes, then it produces a sound. This sound comes in the form of longitudinal waves. It passes through a medium like air, by the vibration of the particles in the medium. Sound wave is also called a pressure wave. Low pressure areas are called rarefactions and areas of higher density are called compressions or condensations.

Sound waves can travel through the different medium like water, wall, etc. depending on the density of the medium.

  • Waves
  • Sound Waves
  • Velocity of Longitudinal (Sound) Wave
  • Shock Waves
  • Speed of transverse Motion
  • Simple Harmonic Wave
  • Superposition of Waves
  • Interference
  • Beats
  • Echo
  • Stationary or standing
  • Waves
  • Vibrations in a stretched
  • string
  • Organ Pipes
  • Resonance Tube
  • Melde’s Experiment
  • Doppler’s Effect


The study of electric charges at rest position is called electrostatic. The word itself explains the phenomena. Electro means electric and statics means constant.

It also states the phenomena of slow-moving electric charges. This phenomena arises when electric charges exert forces on each other. It is well described by Coulomb’s law.

  • Charge
  • Coulomb’s Law in Vector Form
  • Electric Field
  • Electric Potential
  • Equipotential Surface
  • Electric Flux
  • Gauss’s Theorem
  • Electric Dipole
  • Work Done
  • Dipole in Non-Uniform
  • Electric Field
  • Van-de-Graaff Generator

Current Electricity

When the electrons move through a conductive metallic wire, then this movement is called electric current. It is measured in Amperes (A). The value of current electricity is measured in terms of number of charges that move through the wire per second. For the flow of current, it is very necessary that the circuit is closed. Voltage is the electric potential, measured in volts. Resistance is the force that opposes the free flow of the current. It is measured in Ohms.

  • Electric Current
  • Current Density
  • Mobility
  • Ohm’s Law
  • Electrical Resistance
  • Resistivity
  • Electrical Conductivity
  • Superconductors
  • Resistors
  • Combination of Resistors
  • Electric Cell
  • Kirchhoff’s Laws
  • Wheatstone Bridge
  • Meter Bridge
  • Potentiometer

Heating and Chemical Effects of Current

According to the fundamental law of conservation, energy can never be destroyed nor it can be created. The total energy in an isolated system remains constant. Therefore, it can only be transferred from one form to another.

In the same way, when we speak about the heating and chemical effects of current, the electric current passes through a conductor generating heat, after sometime. So here electrical energy is converted into thermal energy through the medium.

  • Electric Energy
  • Electric Power
  • Heating Effects of Current
  • Electric Fuse
  • Short Circuiting
  • Overloading
  • Rating of Electrical
  • Appliances
  • Fusing of Bulb When it is Switched On
  • Chemical Effect of Electric Current
  • Faraday’s Laws Electrolysis
  • Thermoelectric Effect
  • Thermoelectric Power
  • Peltier Effect
  • Thomson’s Effect
  • Thermopile

Magnetic Effect of Current

The magnetic effect of current is called electromagnetic effect. When a current carrying conductor is brought near to a compass, its needle gets deflected due to flow of electricity. Hence, the electric current generates the magnetic field.

  • Oersted’s Experiment
  • Biot Savart’s Law
  • Magnetic Field Due to a Straight Current Carrying Conductor
  • Right Hand Thumb Rule
  • Solenoid
  • Toroid
  • Fleming’s Left Hand Rule
  • Motion of a Charged Particle in a Uniform Magnetic Field
  • Cyclotron
  • Magnetic Dipole
  • Moving Coil Galvanometer
  • Ammeter
  • Voltmeter

Magnetism and Matter

The behavioural property of matter can be understood by magnetism, in Physics. When a matter is placed in a magnetic field it generates different properties which defines different types of magnetic materials such as paramagnetic, diamagnetic, etc.

  • Natural Magnet
  • Artificial Magnet
  • Magnetic Dipole
  • Coulomb’s Law
  • Gauss’s Law in Magnetism
  • Earth’s Magnetism
  • Magnetic Map
  • Neutral Points
  • Tangent Law
  • Deflection Magnetometer
  • Tangent Galvanometer
  • Vibration Magnetometer
  • Hysteresis
  • Coercivity

Electromagnetic Induction

In Physics, when a magnetic field is kept constant and a conductor is moving or a conductor is positioned fixed and the magnetic field keeps changing, then this process is called electromagnetic induction. Because of this action, an electromotive force is produced across the conductor, which is called Voltage.

  • Magnetic Flux
  • Faraday’s Laws of Electromagnetic Induction
  • Lenz’s Law
  • Fleming’s Right Hand Rule
  • Eddy Currents
  • Self-Induction
  • Mutual Induction
  • Grouping of Coils

Alternating Current

An electric current that reverses its direction, periodically and its magnitude continuously with time is called alternating current. It is just opposite to the direct current (DC), that flows in one direction only.

  • Alternating Current
  • Reactance
  • Impedance
  • Power in an AC Circuit
  • Resonance in an AC Circuit
  • Wattless Current
  • Choke Coil
  • AC Generator or Dynamo
  • DC Motor
  • Transformer
  • Transformation Ratio

Electromagnetic Waves

When there is a vibration between electric field and magnetic field it generates a wave called Electromagnetic wave or EM wave. It is made up of oscillating magnetic and electric fields. It can travel through the vacuum of outer space at a speed of 3 x 10^8 m/s. It is used to transmit long/short/FM wavelength radio waves, and TV/telephone/wireless signals or energies.

  • Displacement Current
  • Electromagnetic Waves
  • Electromagnetic Spectrum

Ray Optics

The propagation of light in terms of rays is explained in the ray optics model. There are two types of optics, geometrical optics and physical optics. When light travels in a straight line it is called geometrical optics and if the light travels in the form of electromagnetic it is generalised as physical optics or wave optics. Learn more about light travel, reflection and refraction of light, etc.

  • Light
  • Important Terms
  • Reflection of Light
  • Types of Reflection
  • Mirror
  • Linear Magnification
  • Areal and Axial
  • Magnification
  • Refraction of Light
  • Refractive Index
  • Cauchy’s Formula
  • Critical Angle
  • Total Internal Reflection (TIR)
  • Optical Fibres
  • Lens
  • Cutting of a Lens
  • Aberration of Lenses
  • Prism
  • Dispersion of Light
  • Angular Dispersion
  • Scattering of Light
  • Human Eye
  • Simple Microscope
  • Astronomical Telescope
  • Reflecting Telescopes

Wave Optics

In wave optics, also called physical optics, we will learn about interference, diffraction, polarization, and other phenomena. Here the geometrical optics is not considered valid. The physical optics is an approximation used in electrical engineering and applied Physics. It is an intermediate between geometrical optics and full wave electromagnetism. Learn here in detail about wave optics based on Newtons’ theory, Huygens principle, Young’s double slit experiment, etc.

  • Newtons Corpuscular Theory of light
  • Huygens’ Wave Theory of light
  • Huygens’ Principle
  • Superposition of Waves
  • Interference of Light
  • Young’s Double Slit Experiment (YDSE)
  • Fringe Width
  • Fresnel’s Biprism
  • Diffraction
  • Polarisation
  • Polaroid
  • Doppler’s Effect in Light

Electrons, Photons and X-rays

X-rays are the form of radiation that comes from electrons. It is also a type of light. Just like the light, it is also waveo form of electromagnetic energy carried by the particles present in the air. These particles carrying the electromagnetic energy are called photons. Both the photons, present in x-ray and visible light, are generated by motion of electrons in atoms. Learn in detail the photoelectric effect, how x-ray light works and what are its applications here.

  • Cathode Rays
  • Positive Rays
  • Photoelectric Effect
  • Compton Effect
  • Matter Waves on de-Broglie Waves
  • Davisson-Germer Experiment • X-rays
  • X-rays Spectrum

Atomic Physics

The field of physics, where atoms are studied as an isolated system of electrons and an atomic nucleus is Atomic Physics. Here, it basically focuses on the arrangement of electrons around the nucleus. Also, the process by which the electrons change their positions around the nucleus. This physics is used to study the behaviour of photons, electrons, atoms, light and simple molecules. The collision and splitting of atoms are also studied under this topic.

  • Dalton’s Atomic Theory
  • Thomson’s Atomic Model
  • Rutherford’s Atomic Model
  • Bohr’s Atomic Model
    Hydrogen Spectrum Series
  • Wave Model

Nuclear Physics

In nuclear physics, you will learn about protons and neutrons present at the center of the atom and their behavior. Also, you will come across what holds them together in a space which is only a few femtometer distant from the nucleus. The radioactive decay, fission, and fusion of nuclei are studied in nuclear physics. Ernest Rutherford is said to be the father of Nuclear Physics.

  • Nucleus
  • Isotopes
  • Isobars
  • Isotones
  • Isomers
  • Nuclear Force
  • Mass Defect
  • Nuclear Binding Energy
  • Nuclear Reaction
  • Nuclear Fission
  • Nuclear Fusion
  • Radioactivity
  • Radioactive Decay Law


In Physics, electronics is the study of flow of electrons and control of electrons through a medium or matter. The electrical circuit made up of components is responsible to control the flow of electricity. Physical electronics is a part of electrical engineering. Also, technology and home-used electronic devices are the application of electronics, where emission, flow and control of electrons in medium (vacuum or matter) are dealt with.

  • Solid
  • Energy Bands of Solids
  • Types of Semiconductor
  • p-n Junction and Diode
  • Zener Diode
  • Light Emitting Diodes (LED)
  • p-n Junction Diode as
  • Rectifier
  • Transistor
  • Logic Gate
  • Truth Table
  • Basic Logic Gates
  • Combination of Gates


One of the applications of applied branches of Physics is communication. Here we will deal with various types of communication systems such as electronic communication, optical communication, computer communication, telephone, telegraphs, television, radio and mobile phone. All these are communicating devices through which an information is transmitted from one to another.

  • Communication
  • Communication System
  • Modulation
  • Demodulation
  • Antenna
  • Earth’s Atmosphere
  • Propagation of Radio Waves
  • Microwave Propagation
  • Satellite Communication
  • Merits of Satellite Communication
  • Demerits of Satellite Communication
  • Optical Communication
  • Internet Telephony
  • Mobile Telephony
  • Global Positoining System (GPS)


In physics, the universe is defined as all about space time and their contents. These contents include various forms of energy which also consist of electromagnetic radiation and matter. Hence, the celestial bodies, planets, sun, stars, moons, galaxies, solar system, etc. are considered to be the contents of spacetime.

The great big bang theory is also explained here in the physical universe, where the evolution of the solar system is been described.

  • Solar System
  • Sun Planets
  • Inner Structure of the Earth
  • Stars
  • Life Cycle of a Star
  • Death of a Star Black Hole
  • Galaxy Constellation
  • The Big-Bang Theory

Error – Units and Measurement

Error: The lack in accuracy in the measurement due to the limit of accuracy of the measuring instrument or due to any other cause is called an error. The difference between the measured value and the true value of a quantity is known as the error in the measurement.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Error – Types of Errors, Expressions

Errors are usually classified as
1. Absolute Error
The difference between the true value and the measured value of a quantity is called absolute error. If a1, a2, a3,…, an are the measured values of any quantity a in an experiment performed n times, then the arithmetic mean of these values is called the true value (am) of the quantity.


The absolute error in measured values is given by

Δa1 = am – a1
Δa2 = am – a2
Δan = am – an

2. Mean Absolute Error
The arithmetic mean of the magnitude of absolute errors in all the measurement is called mean absolute error.

\(\overline{\Delta a}=\frac{\left|\Delta a_{1}\right|+\left|\Delta a_{2}\right|+\ldots+\left|\Delta a_{n}\right|}{n}\)

3. Relative Error or Fractional Error
The ratio of mean absolute error to the true value is error.

Realtive Error = \(\frac{\text { Mean absolute error }}{\text { True value }}=\frac{\overline{\Delta a}}{a_{m}}\)

4. Percentage Error
The relative error expressed in percentage is called percentage error.

Percentage error = \(\frac{\overline{\Delta a}}{a_{m}}\) x 100%

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors

Significant Figures – Units and Measurement

Significant Figures: In the measured value of a physical quantity, the number of digits about the correctness of which we are sure plus the next doubtful digit, are called the significant figures.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to Understand the Basic Physics Concepts.

Significant Figures – Units and Measurement

Rules for Finding Significant Figures

  1. All non-zeros digits are significant figures, e.g. 4362 m has 4 significant figures.
  2. All zeros occuring between non-zero digits are significant figures, e.g. 1005 has 4 significant figures.
  3. All zeros to the right of the last non-zero digit are not significant, e.g. 6250 has only 3 significant figures.
  4. In a digit less than one, all zeros to the right of the decimal point and to the left of a non-zero digit are not significant, e.g. 0.00325 has only 3 significant figures.
  5. All zeros to the right of a non-zero digit in the decimal part are significant, e.g. 1.4750 has 5 significant figures.

Significant Figures in Algebraic Operations
(i) In Addition or Subtraction:
In addition or subtraction of the numerical values, the final result should retain as many decimal places as there are in the number with the least places. e.g.
If l1 = 4.326 m and l2 = 1.50 m
Then, l1 + l2 =(4.326 + 1.50) m = 5.826 m
As l2 has measured upto two decimal places, therefore
l1 + l2 = 5.83 m

(ii) In Multiplication or Division:
In multiplication or division of the numerical values, the final result should retain as many significant figures as there are in the original number with the least significant figures, e.g. If length l = 12.5 m and breadth b = 4.125 m.
Then, area A = l x b = 12.5 x 4.125 = 51.5625 m²
As l has only 3 significant figures, therefore
A = 51.6 m²

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors

Dimensions – Units and Measurement

Dimensions of any physical quantity are those powers to which the fundamental quantities are raised to express that quantity. The expression of a physical quantity in terms of its dimensions, is called its dimensional formula.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Dimensions – Units and Measurement

Dimensional Formula of Some Physical Quantities

S.No. Physical Quantities Dimensional Formula MKS Units
1. Area [L2] m2
2. Volume [L3] m3
3. Velocity [LT-1] ms-1
4. Acceleration [LT-2] ms-2
5. Force [MLT-2] Newton (N)
6. Work energy [ML2T-2] joule (J)
7. Power [ML2T-3] J s-1 or W (watt)
8. Pressure or stress [ML-1T-2] Nm-2
9. Linear momentum or impulse [MLT-1] Kg ms-1
10. Density [ML-3] Kg ms-3
11. Strain dimensionless unitless
12. Modulus of elasticity [ML-1T-2] Nm-2
13. Surface tension [MT-2] Nm-1
14. Velocity gradient [T-1] s-1
15. Coefficient of viscosity [ML-1T-1] Kg ms-1 s-1 
16. Gravitational constant [M-1L3T-2] Nm2Kg2
17. Moment of inertia [ML2] Kg-m2
18. Angular velocity  [T-1] rad/s
19. Angular acceleration  [T-2] rad/s2
20. Angular momentum [ML2T-1] kg m2s-1
21. Specific heat [L2T-2θ-1] kcal Kg-1K-1
22. Latent heat [L2T-2] kcal/kg
23. Planck’s constant [ML2T-1] J-s
24. Universal gas [ML2T-2θ-1] J/mol-K

Homogeneity Principle
If the dimensions of left hand side of an equation are equal to the dimensions of right hand side of the equation, then the equation is dimensionally correct. This is known as homogeneity principle.
Mathematically, [LHS] =[RHS].
Applications of Dimensions

(i) To check the accuracy of physical equations.
(ii) To change a physical quantity from one system of units to another system of units.
(iii) To obtain a relation between different physical quantities.

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors

Systems of Units – Units and Measurement

Systems of Units
A system of units is the complete set of units, both fundamental and derived, for all kinds of physical quantities.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to Understand the Basic Physics Concepts.

Systems of Units – Units and Measurement

Systems of Units, Measurements, Quantities

The common system of units which is used in mechanics are given below:
(i) CGS System:
In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.

(ii) FPS System:
In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.

(iii) MKS System:
In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.

(iv) SI System:
The system of units, which is accepted Internationally for measurement is the System Internationaled units abbreviated as SI. This system contains seven fundamental units and two supplementary fundamental units.

Relationship between Some Mechanical SI Unit and Commonly Used Units

S.No. Physical Quantities Units
1. Length (a)     1 micrometre = 10-6 m

(b)     1 nanometre = 10-9 m

(c)      1 angstorm =  10-10

2. Mass (a)     1 metric ton = 103  kg

(b)     1 pound = 0.4537 kg

(c)     1 amu = 1.66 x 10-23

3. Volume (a)     1 litre = 10-3 m3
4. Force (a)     1 dyne = 10-5 N

(b)     1 kgf = 9.81 N

5. Pressure (a)     1 kgf-m²= 9.81 Nm-2

(b)     1 mm of Hg = 133 Nm-2

(c)     1 pascal = 1 Nm-2

(d)     1 atmosphere pressure = 76 cm of Hg = 1.01 x 105 Pascal

6. Work and energy (a)    1 erg = 10-7 J

(b)    1 kgf-m = 9.81 J

(c)    1 kWh = 3.6 x 106 J

(d)    1 eV = 1.6 x 10-19 J

7. Power (a)    1 kgf-ms-1 = 9.81 W

(b)    1 horse power = 746 W

Some Practical Units of Length

  • 1 fermi = 10-15 m
  • 1 X-ray unit = 10-13 m
  • 1 astronomical unit = 1.49 x 1011 m (average distance between sun and earth)
  • 1 light year = 9.46 x 1015 m
  • 1 parsec = 3.08 x 1016 m = 3.26 light year

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors

Physical Quantities and their Units

Physical Quantities
All the quantities which can be measured directly or indirectly in terms of which the laws of Physics are described are called physical quantities.

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Physical Quantities and their Units, Symbols, Definition

A standard amount of a physical quantity chosen to measure the physical quantity of the same kind is called a physical unit. It should be easily reproducible, internationally accepted.

Fundamental Quantities and Their Units
Those physical quantities which are independent to each other are called fundamental quantities and their units are called fundamental units.
Physical Quantities and Their Units

Physical Quantities and Their Units

Supplementary Fundamental Quantities and Their Units

Radian and steradian are two supplementary fundamental units. It measures plane angle and solid angle respectively.

Physical Quantities and Their Units
Derived Quantities and Their Units
Those physical quantities which are derived from fundamental quantities are called derived quantities and their units are called derived units e.g. Velocity, acceleration, force, work etc.

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors