Nature Of Physical World And Measurement Online Test 11th Science Part 2

The word ‘science’ has its root in the Latin verb scientia, meaning “to know”.

In Tamil language, science is ‘அறிவியல்’ (Ariviyal) meaning ‘knowing the truth’. The human mind is always curious to know and understand different phenomena like the bright celestial objects in nature, cyclic changes in the seasons, occurrence of rainbow, etc.

Science is the systematic organization of knowledge gained through observation, experimentation and logical reasoning. The knowledge of science dealing with non-living things is physical science (Physics and Chemistry), and that dealing with living things is biological science (Botany, Zoology etc.).

According to part IV Article 51A (h) of Indian Constitution “It shall be the duty of every citizen of India to develop scientific temper, humanism and spirit of inquiry and reform’’. This is the aim of our Science Education.

The scientific method is a step-by-step approach in studying natural phenomena and establishing laws which govern these phenomena. Any scientific method involves the following general features. Systematic observation, Controlled experimentation, Qualitative and quantitative reasoning, Mathematical modeling and Prediction and verification or falsification of theories.

The name Physics was introduced by Aristotle in the year 350 BC

The study of nature and natural phenomena is dealt with in physics. Hence physics is considered as the most basic of all sciences.

The word ‘physics’ is derived from the Greek word “Fusis”, meaning nature.

Unification and Reductionism are the two approaches in studying physics. Attempting to explain diverse physical phenomena with a few concepts and laws is unification. An attempt to explain a macroscopic system in terms of its microscopic constituents is reductionism.

Newton’s universal law of gravitation explains the motion of freely falling bodies towards the Earth, motion of planets around the Sun, motion of the Moon around the Earth, thus unifying the fundamental forces of nature.

Relativity: One of the branches of theoretical physics which deals with the relationship between space, time and energy particularly with respect to objects moving in different ways.

Discoveries in physics are of two types; accidental discoveries and well-analyzed research outcome in the laboratory based on intuitive thinking and prediction. For example, magnetism was accidentally observed but the reason for this strange behavior of magnets was later analyzed theoretically. This analysis revealed the underlying phenomena of magnetism. With this knowledge, artificial magnets were prepared in the laboratories. Theoretical predictions are the most important contribution of physics to the developments in technology and medicine.

The famous equation of Albert Einstein, E=mc2 was a theoretical prediction in 1905 and experimentally proved in 1932 by Cockcroft and Walton. Theoretical predictions aided with recent simulation and computation procedures are widely used to identify the most suited materials for robust applications.

Physics has a huge scope as it covers a tremendous range of magnitude of various physical quantities (length, mass, time, energy etc.). It deals with systems of very large magnitude as in astronomical phenomena as well as those with very small magnitude involving electrons and protons.

Range of time scales: astronomical scales to microscopic scales, 10¹⁸s to 10^-22s.

Range of masses: from heavenly bodies to electron, 1055 kg (mass of known observable universe) to 10-31 kg (mass of an electron) [the actual mass of an electron is 9.11×10–31 kg].

Technology is the application of the principles of physics for practical purposes. The application of knowledge for practical purposes in various fields to invent and produce useful products or to solve problems is known as technology. Thus physics and technology can both together impact our society directly or indirectly.

Basic laws of electricity and magnetism led to the discovery of wireless communication technology which has shrunk the world with effective communication over large distances.

In physics we study the structure of atom, radioactivity, X-ray diffraction etc. Such studies have enabled researchers in chemistry to arrange elements in the periodic table on the basis of their atomic numbers. This has further helped to know the nature of valency, chemical bonding and to understand the complex chemical structures. Inter-disciplinary branches like Physical chemistry and Quantum chemistry play important roles here.

The invention of the electron microscope has made it possible to see even the structure of a cell. X-ray and neutron diffraction techniques have helped us to understand the structure of nucleic acids, which help to control vital life processes. X-rays are used for diagnostic purposes.

Radio-isotopes are used in radiotherapy for the cure of cancer and other diseases. In recent years, biological processes are being studied from the physics point of view.

Diffraction techniques help to study the crystal structure of various rocks. Radioactivity is used to estimate the age of rocks, fossils and the age of the Earth.

Oceanographers seek to understand the physical and chemical processes of the oceans. They measure parameters such as temperature, salinity, current speed, gas fluxes, and chemical components.

The comparison of any physical quantity with its standard unit is known as measurement. Measurement is the basis of all scientific studies and experimentation. It plays an important role in our daily life. Physics is a quantitative science and physicists always deal with numbers which are the measurement of physical quantities.

Quantities that can be measured, and in terms of which, laws of physics are described are called physical quantities. Examples are length, mass, time, force, energy, etc.

Physical quantities are classified into two types. They are fundamental and derived quantities.

Fundamental or base quantities are quantities which cannot be expressed in terms of any other physical quantities. These are length, mass, time, electric current, temperature, luminous intensity and amount of substance.

Quantities that can be expressed in terms of fundamental quantities are called derived quantities. For example, area, volume, velocity, acceleration, force, etc.

The process of measurement is basically a process of comparison. To measure a quantity, we always compare it with some reference standard. For example, when we state that a rope is 10 meter long, it is to say that it is 10 times as long as an object whose length is defined as 1 meter. Such a standard is known as the unit of the quantity. Here 1 meter is the unit of the quantity ‘length’.

The f.p.s. system is the British Engineering system of units, which uses foot, pound and second as the three basic units for measuring length, mass and time respectively.

The c.g.s system is the Gaussian system, which uses centimeter, gram and second as the three basic units for measuring length, mass and time respectively.

The m.k.s system is based on metre, kilogram and second as the three basic units for measuring length, mass and time respectively.

The c.g.s, m.k.s and SI are metric or decimal system of units. The fps system is not a metric system.

The system of units used by scientists and engineers around the world is commonly called the metric system but, since 1960, it has been known officially as the International System, or SI (the abbreviation for its French name, Système International).

The SI with a standard scheme of symbols, units and abbreviations, were developed and recommended by the General Conference on Weights and Measures in 1971 for international usage in scientific, technical, industrial and commercial work.

The advantages of the SI system are, this system makes use of only one unit for one physical quantity, which means a rational system of units. In this system, all the derived units can be easily obtained from basic and supplementary units which means it is a coherent system of units. It is a metric system which means that multiples and submultiples can be expressed as powers of 10.

One kilogram is the mass of the prototype cylinder of platinum iridium alloy (whose height is equal to its diameter), preserved at the International Bureau of Weights and Measures at Serves, near Paris, France. (1901)

One kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of the water. (1967)

One mole is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kg of pure carbon-12. (1971)

Luminous intensity, candela (cd) One candela is the luminous intensity in a given direction, of a source that emits monochromatic radiation of frequency 5.4 × 10 14 Hz and that has a radiant intensity of 1/683 watt/steradian in that direction. (1979)

Triple point of water is the temperature at which saturated vapor, pure water and melting ice are all in equilibrium. The triple point temperature of water is 273.16K

π radian = 180°
1 radian = ¬180°/ π = 57.27°

1° (degree of arc) = 60′ (minute of arc) and 1′ (minute of arc) = 60″ (seconds of arc)

The SI unit of length is metre. The objects of our interest vary widely in sizes. For example, large objects like the galaxy, stars, Sun, Earth, Moon etc., and their distances constitute a macrocosm.

The Radian (rad): One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

The Steradian (sr): One steradian is the solid angle subtended at the center of a sphere, by that surface of the sphere, which is equal in area, to the square of radius of the sphere.

On the contrary, objects like molecules, atoms, proton, neutron, electron, bacteria etc., and their distances constitute microcosm, which means a small world in which both objects and distances are small-sized.

The supplementary quantities of plane and solid angle were converted into Derived quantities in 1995 (GCWM).

The screw gauge is an instrument used for measuring accurately the dimensions of objects up to a maximum of about 50 mm.

Screw gauge: The principle of the instrument is the magnification of linear motion using the circular motion of a screw. The least count of the screw gauge is 0.01 mm

Vernier caliper: A Vernier caliper is a versatile instrument for measuring the dimensions of an object namely diameter of a hole, or a depth of a hole. The least count of the Vernier caliper is 0.01 cm

For measuring larger distances such as the height of a tree, distance of the Moon or a planet from the Earth, some special methods are adopted. Triangulation method, parallax method and radar method are used to determine very large distances.

Solution: Angle θ = 60°, The distance between the tree and a point x = 100 m

Height of the tree (h), for triangulation method tan θ = h/ x

h = x tan θ = 100 × tan 60° = 100 × 1.732. The height of the tree is 173.2 m.

Very large distances, such as the distance of a planet or a star from the Earth can be measured by the parallax method. Parallax is the name given to the apparent change in the position of an object with respect to the background, when the object is seen from two different positions.

The word RADAR stands for radio detection and ranging. A radar can be used to measure accurately the distance of a nearby planet such as Mars. In this method, radio waves are sent from transmitters which, after reflection from the planet, are detected by the receiver. By measuring, the time interval (t) between the instants the radio waves are sent and received, the distance of the planet can be determined.

Range and Order of Lengths

Some Common Practical Units

Fermi = 1 fm = 10^-15m

1 angstrom = 1 Å = 10^-10m

1 nanometer = 1 nm = 10^-9 m

1 micron = 1μm = 10^-6m

1 Light year (Distance travelled by light in vacuum in one year) 1 Light Year = 9.467 × 10¹⁵ m

1 astronomical unit (the mean distance of the Earth from the Sun) 1 AU = 1.496 × 10¹¹ m

1 parsec (Parallactic second) (Distance at which an arc of length 1 AU subtends an angle of 1 second of arc)

1 parsec = 3.08 × 10¹⁶ m =3.26 light year

Chandrasekhar Limit (CSL) is the largest practical unit of mass.

1 CSL = 1.4 times the mass of the Sun

The smallest practical unit of time is Shake. One Shake = 10^-8 s

Mass is a property of matter. It does not depend on temperature, pressure and location of the body in space. Mass of a body is defined as the quantity of matter contained in a body. The SI unit of mass is kilogram (kg). The masses of objects which we shall study in this course vary over a wide range.

For measurement of small masses of atomic/subatomic particles etc., we make use of a mass spectrograph. Some of the weighing balances commonly used are common balance, spring balance, electronic balance, etc.

A clock is used to measure the time interval. An atomic standard of time is based on the periodic vibration produced in a Cesium atom. Some of the clocks developed later are electric oscillators, electronic oscillators, solar clock, quartz crystal clock, atomic clock, decay of elementary particles, radioactive dating etc.

Order of Time Intervals

In India, the National Physical Laboratory (New Delhi) has the responsibility of maintenance and improvement of physical standards of length, mass, time, etc.

Systematic errors: Systematic errors are reproducible inaccuracies that are consistently in the same direction. These occur often due to a problem that persists throughout the experiment.

Systematic errors can be classified as follows, Instrumental error, Imperfections in experimental technique or procedure, Personal errors, Errors due to external causes, Least count error.

Instrumental errors: When an instrument is not calibrated properly at the time of manufacture, instrumental errors may arise. If a measurement is made with a meter scale whose end is worn out the result obtained will have errors. These errors can be corrected by choosing the instrument carefully.

Random errors may arise due to random and unpredictable variations in experimental conditions like pressure, temperature, voltage supply etc.

Errors may also be due to personal errors by the observer who performs the experiment. Random errors are sometimes called “chance error”.

Gross Error: The error caused due to the shear carelessness of an observer is called gross error. For example, Reading an instrument without setting it properly. Taking observations in a wrong manner without bothering about the sources of errors and the precautions. Recording wrong observations. Using wrong values of the observations in calculations.

Minimizing Experimental Error

Systematic error: Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is in the same direction. (Either too high or too low)

Absolute Error: The magnitude of 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.

Mean Absolute error: The arithmetic mean of absolute errors in all the measurements is called the mean absolute error.

If am is the true value and Δa_m is the mean absolute error then the magnitude of the quantity may lie between a_m + Δa_m and a_m – Δa_m

Relative error: The ratio of the mean absolute error to the mean value is called relative error. This is also called as fractional error. Thus Relative error=Mean absolute error / Mean value

Percentage error: The relative error expressed as a percentage is called percentage error. Percentage error = Δam/am×100% . A percentage error very close to zero means one is close to the targeted value, which is good and acceptable. It is always necessary to understand whether error is due to impression of equipment used or a mistake in the experimentation.

A number of measured quantities may be involved in the final calculation of an experiment. Different types of instruments might have been used for taking readings. Then we may have to look at the errors in measuring various quantities, collectively. The error in the final result depends on the errors in the individual measurements and on the nature of mathematical operations performed to get the final result. So we should know the rules to combine the errors.

The number of meaningful digits which contain numbers that are known reliably and first uncertain number.

In mechanics, we deal with the physical quantities like mass, time, length, velocity, acceleration, etc. which can be expressed in terms of three independent base quantities such as M, L and T. So, the dimension of a physical quantity can be defined as ‘any physical quantity which is expressed in terms of base quantities whose exponent (power) represents the dimension of the physical quantity’.

On the basis of dimension, we can classify quantities into four categories.

Dimensional variables: Physical quantities, which possess dimensions and have variable values, are called dimensional variables. Examples are length, velocity, and acceleration.

Dimensionless variables: Physical quantities which have no dimensions, but have variable values are called dimensionless variables. Examples are specific gravity, strain, refractive index etc.

Dimensional Constant: Physical quantities which possess dimensions and have constant values are called dimensional constants. Examples are Gravitational constant, Planck’s constant etc.

Dimensionless Constant: Quantities which have constant values and also have no dimensions are called dimensionless constants. Examples are π, e (Euler’s number), numbers etc.

Application of the Method of Dimensional Analysis method is used to convert a physical quantity from one system of units to another. Check the dimensional correctness of a given physical equation. Establish relations among various physical quantities.

Limitations of Dimensional analysis: This method gives no information about the dimensionless constants in the formula like 1, 2, ……..π, e (Euler number), etc. This method cannot decide whether the given quantity is a vector or a scalar. This method is not suitable to derive relations involving trigonometric, exponential and logarithmic functions. It cannot be applied to an equation involving more than three physical quantities. It can only check on whether a physical relation is dimensionally correct but not the correctness of the relation.