ICSE Class 9 Physics Chapter 01 Measurements and Experimentation

Measurements and Experimentation

Syllabus

International system of units (the required S.I. units with correct symbols are given at the end of this syllabus). Other commonly used system of units - FPS and CGS.

Measurements using common instruments, Vernier calipers and micrometer screw gauge for length and simple pendulum for time. Scope - Measurement of length using vernier calipers and micrometer screw gauge. Decreasing least count leads to an increase in accuracy; least count (L.C.) of vernier calipers and screw gauge, zero error (basic idea) (no numerical problems on calipers and screw gauge). Simple pendulum; time period, frequency, graph of length l vs. T² only; slope of the graph. Formula T = 2π √(l/g) (No derivation). Only simple numerical problems.

Systems of Unit and Units in S.I. System

Need of Unit for Measurement

Physics, like other branches of science require experimental studies which involve measurements. For the measurement of a physical quantity, we consider a constant quantity of same nature as a standard and then we compare the given quantity with the standard quantity i.e. we find the number which expresses, how many times the standard quantity is contained in the given physical quantity. Thus

Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature.

The standard quantity used to measure the given physical quantity is called the unit. For quantities of different nature, we use different units.

Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature.

The result of measurement of a physical quantity is expressed in terms of the following two parameters:

(i) The unit in which the quantity is being measured, and

(ii) The numerical value which expresses, how many times the above selected unit is contained in the given quantity.

Thus the magnitude of a physical quantity is expressed as:

Physical quantity = (numerical value) × (unit)

Examples: (i) If the length of a piece of cloth is 10 metre, it means that the length is measured in the unit metre and this unit is contained 10 times in the length of that piece of cloth.

(ii) If the mass of a given quantity of sugar is 5 kilogram, it means that the mass is measured in the unit kilogram and this unit is contained 5 times in the given quantity of sugar.

Choice of unit

To measure a physical quantity, the unit chosen should have the following properties:

(i) The unit should be of convenient size.

(ii) It should be possible to define the unit without ambiguity.

(iii) The unit should be reproducible.

(iv) The value of unit should not change with space and time. (i.e., it must always remain same everywhere).

The last three conditions (ii), (iii) and (iv) are essential for the unit to be accepted internationally.

Kinds of unit

Units are of two kinds: (i) Fundamental or basic units, and (ii) Derived units.

Fundamental or basic units

A fundamental (or basic) unit is that which is independent of any other unit or which can neither be changed nor can be related to any other fundamental unit.

Examples: The units of mass, length, time, temperature, current and amount of substance are independent of each other. They can not be obtained from any other unit. These are the fundamental units.

Derived units

The units of quantities other than those measured in fundamental units, can be expressed in terms of the fundamental units and they are called the derived units. Thus

Derived units are those which depend on the fundamental units or which can be expressed in terms of the fundamental units.

Examples: (i) For the measurement of area, we need to measure length and breadth in the unit of length and then express area in a unit which is length × length or (length)².

(ii) The volume is expressed in a unit which is length × length × length or (length)³.

(iii) The unit of speed of a moving body is obtained by dividing the unit of distance (i.e., length) by the unit of time i.e., it can be expressed in terms of the units of length and time.

Thus the units used to measure area, volume, speed, etc. are the derived units. More examples of derived units are given ahead in article 1.6.

Systems of Unit

In mechanics, length, mass and time are the three fundamental quantities. For the units of these three basic quantities, following systems have been used:

(i) C.G.S. system (or French system): In this system, the unit of length is centimetre (cm), of mass is gram (g) and of time is second (s).

(ii) F.P.S. system (or British system): In this system, the unit of length is foot (ft), of mass is pound (lb) and of time is second (s).

(iii) M.K.S. system (or metric system): In this system, the unit of length is metre (m), of mass is kilogram (kg) and of time is second (s).

The above mentioned systems are now no longer in use and are only of historical importance. Now we use the S.I. system of units which is an enlarged and modified version of the metric system.

Systeme Internationale d'Unites (or S.I. system)

In 1960, the General Conference of Weights and Measures recommended that in addition to the units of length, mass and time, the units of temperature, luminous intensity, current and the amount of substance also be taken as fundamental units and the units of angle and solid angle as the complementary fundamental units. Thus in all, now there are seven fundamental units and two complementary fundamental units.

For S.I. system, the following table gives the fundamental quantities, their units and their standard symbols.

Use of prefix with a unit

For expressing large measurements, we use deca, hecto, kilo etc., as prefixes with the units.

Nowadays 1 mol means 1 kg mol equal to 6.02 × 10²⁶ entities (i.e., atoms or molecules or ions).

The symbol and meaning of each prefix are given below.

The various small measurements are expressed by using the prefixes deci, centi, milli, micro, etc., with the units. The symbol and meaning of each such prefix are given below.

Example: 2.5 GHz will mean 2.5 × 10⁹ Hz, 5.0 pF will mean 5.0 × 10⁻¹² F, 5.0 MΩ will mean 5.0 × 10⁶ Ω, 2.0 ms will mean 2.0 × 10⁻³ s and so on.

Units of Length

S.I. unit of length

The S.I. unit of the length is metre (m).

A metre was originally defined in 1889 as the distance between two marks drawn on a platinum-iridium (an alloy with 90% platinum and 10% iridium) rod kept at 0°C in the International Bureau of Weights and Measures at Sevres near Paris.

Later, in 1960, the metre was re-defined as 1,650,763.73 times the wavelength of a specified orange-red spectral line in the emission spectrum of Krypton-86. It is also defined as: 'one metre is 1,553,164.1 times the wavelength of the red line in the emission spectrum of cadmium'.

In 1983, the metre was re-defined in terms of speed of light according to which one metre is the distance travelled by the light in 1/(299,792,458) of a second in air (or vacuum).

Sub units of metre

For the measurement of small lengths, the metre is considered too big a unit. The most commonly used sub units of metre are (i) centimetre (cm), (ii) millimetre (mm), (iii) micron (μ) and (iv) nanometre (nm).

(i) centimetre (cm): One centimetre is one-hundredth part of a metre. i.e., \(1 \text{ cm} = \frac{1}{100} \text{ m} = 10^{-2} \text{ m}\)

(ii) millimetre (mm): One millimetre is one-thousandth part of a metre. i.e., \(1 \text{ mm} = \frac{1}{1000} \text{ m} = 10^{-3} \text{ m} = \frac{1}{10} \text{ cm}\)

(iii) micrometre or micron: It is one-millionth (10⁻⁶) part of a metre. It is expressed by the symbol μ. It is also called micrometre (symbol μm). \(1 \text{ micron} (\mu) = 10^{-6} \text{ metre}\) \(= 10^{-4} \text{ cm} = 10^{-3} \text{ mm}\)

(iv) nanometer (nm): It is one-billionth (10⁻⁹ th) part of a metre. i.e., \(1 \text{ nm} = 10^{-9} \text{m}\)

Multiple units of metre

For the measurement of large lengths (or distances), the metre is considered as too small a unit. The most commonly used multiple unit of metre is kilometre.

kilometre (km): One kilometre is the one-thousand multiple of a metre. i.e., \(1 \text{ km} = 1000 \text{ m (or } 10^3 \text{ m)}\)

Non-metric units of length

Bigger units: For the measurement of distance between two heavenly bodies, the kilometre is considered a too small unit. The commonly used units for this purpose are: (i) astronomical unit (A.U.), (ii) light year (ly) and (iii) parsec.

(i) Astronomical unit (A.U.): One astronomical unit is equal to the mean distance between the earth and the sun. i.e., \(1 \text{ A.U.} = 1.496 \times 10^{11} \text{ metre}\)

(ii) Light year (ly): A light year is the distance travelled by light in vacuum, in one year. i.e., \(1 \text{ light year} = \text{speed of light} \times \text{time 1 year}\) \(= 3 \times 10^8 \text{ m s}^{-1} \times (365 \times 24 \times 60 \times 60 \text{ s})\) \(= 9.46 \times 10^{15} \text{ m}\)

The distance of stars from earth is generally expressed in light years. However, light minute and light second are its smaller units.

\(1 \text{ light minute} = 3 \times 10^8 \text{ m s}^{-1} \times 60 \text{ s} = 1.8 \times 10^{10} \text{ m}\)

and \(1 \text{ light second} = 3 \times 10^8 \text{ m s}^{-1} \times 1 \text{ s} = 3 \times 10^8 \text{ m}\)

(iii) Parsec: One parsec* is the distance from where the sun major axis of orbit of earth (1 A.U.) subtends an angle of one second. i.e., Parsec × 1 = 1 A.U. or \(1 \text{ Parsec} = \frac{1.496 \times 10^{11} \text{ m}}{(1/3600) \times (\pi/180)}\) \(= \frac{3.08 \times 10^{16}}{9.46 \times 10^{15}} \text{ ly } = 3.26 \text{ ly}\)

Smaller units: To express the wavelength of light, size and separation between two molecules (or atoms), radius of orbit of electron, etc. a small size unit called the Angstrom (Å) is used, while the size of the nucleus is expressed by a still smaller unit called fermi (f).

(i) Angstrom (Å): It is 10⁻¹⁰th part of a metre. It is expressed by the symbol A. i.e., \(1 \text{ Angstrom (Å)} = 10^{-10} \text{ metre}\) \(= 10^{-8} \text{ cm} = 10^{-1} \text{ nm}\) \(\therefore 1 \text{ micron} = 10,000 \text{ Å}\) and \(1 \text{ nm} = 10 \text{ Å}\)

Nowadays, Å is outdated and nm is preferred over the Å. The wavelength of light, inter-atomic or inter-molecular separation, etc. are now commonly expressed in nm.

(ii) fermi (f): It is 10⁻¹⁵ th part of a metre. i.e., \(1 \text{ fermi (f)} = 10^{-15} \text{ m}\)

The commonly used smaller and bigger units of length are summarized in the following table.

* Parsec is constituted from the combination of two words, parallax (par) and arc-second (sec).

Teacher's Note

The metre was originally defined using a physical standard bar, which could wear or break. Modern definitions use universal constants of nature - first light wavelengths, then the speed of light itself - ensuring that the standard is always available and unchanging anywhere in the universe.

This is a preview of the first 3 pages. To get the complete book, click below.