# Chapter 2 – Units and Measurements

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Units and measurements form the basis of how our world functions, and it is practically impossible to imagine working without them. Measurement is the quantification of a thing or event by giving it a number. This is also useful in comparing a value to a given particular, chosen value along with an internationally accepted standard reference called a unit.

Though the things to measure are innumerable, there are a limited number of units. The units used for fundamental quantities are called base units, and these are used in various combinations for expressing other quantities. Such units that are used for the derived quantities are called derived units. Together, the base or fundamental and derived units form a system of units.

#### Systems of Units

There are different systems of units that were being used by scientists and researchers in different countries of the world. Three of the common systems of units and measurements are:

• CGS System: The base unit of length, mass, and time in this system are Centimetre, Gram, and Second.
• FPS/British System: The base unit of length, mass, and time in this system are Foot, Pound, and Second.
• MKS System: The base unit of length, mass, and time in this system are Meter, Kilogram, and Second.

However, in order to unify the units and measurements across the world for the measurement of time, length, and mass, a new system was developed called the Système Internationale d’ Unites or SI unit system.

The system of units that is at present internationally accepted for measurement is the Système Internationale d’ Unites (French for International System of Units), abbreviated as SI.

#### SI Unit System

The SI unit system for measurement allows conversions within the system that makes it very easy to quantify, calculate, and measure. The seven base units used in the SI unit system are:

• Length: Meter (m)
• Mass: Kilogram (Kg)
• Time: Second (s)
• Electric Current: Ampere (A)
• Thermodynamic Temperature: Kelvin (K)
• Amount of substance: mole (mol)
• Luminous intensity: Candela (cd)

Two dimensionless quantities that have been given SI units are radian or (rad) for plane angle and steradian(str) for a solid angle. Apart from these basic units in SI, some other units and symbols are routinely used but can be easily converted into SI units. Some of these include minute, hour, Pascals(atmospheric pressure), hectare(ha), etc.

#### Measurement of Length

The commonly used direct measurement unit of length is a meter. Depending upon whether the length you wish to measure is short or long, different tools are helpful. For example:

• For lengths 10-3 to 103 m, a meter scale is very useful
• A Vernier Caliper can be used to measure lengths up to an accuracy of 10-4 m
• For lengths as short as 10-5, a screw gauge with a spherometer can be helpful

If you wish to measure lengths outside these ranges, there are some special methods that you can use.

To measure lengths beyond these ranges, we make use of some special, indirect methods such as using an optical microscope and utilizing the wavelength of light to determine the distance. Similarly, if you wish to measure large lengths like distances between planets or between Earth and a star, you can use the parallax method.

#### Measurement of Mass

Of the many units and measurements, the measurement of mass is what we deal with regularly, along with length and time. Mass, as we all know, is the property of matter and is not affected by any external factors like temperature, pressure, or location. Mass is measured in its SI unit, Kilogram or Kg. However, when it comes to atoms and molecules that are way too tiny to be measured in Kilograms, a standard unit of mass is used called Atomic Mass Unit(u).

It has been standardized internationally and 1u=1/12 of the mass of C-12 isotope, i.e., 1.66×10-27Kg. Weighing scales are used to determine the weight of an object that is actually the mass of an object multiplied by the gravitational force on the object.

#### Measurement of Time

Time is another component that we measure in our daily lives. When we measure time, we measure the time interval. For this, we need a clock. Today, we use an atomic standard of time that uses the periodic vibrations produced in a Caesium atom. In earlier days and some places, even today, a pendulum is used to measure time. One of the first devices used to measure time is the sand clock.

In a caesium clock, one second is defined as the time needed for 9,192,631,770 vibrations of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Atom clocks are very accurate and provide a portable measurement standard. A caesium clock is used at the National Physical Laboratory (NPL) to maintain the Indian Standard Time(IST).

#### Accuracy, Precision, and Errors in Measurement

Accurate, precise, and error-free measurement is the basis of scientific experiments, technology, constructions, and everything under the Sun. Every measurement contains some uncertainty called as errors. Accuracy of measurement is basically how close a measured value is to the true value of what we are measuring. Precision, on the other hand, informs us of what limit a quantity is measured. For example, if the measured length of a piece of cloth is said to be 4.5 cm, but you have measured it as 4.6 cm. Your friend measured the same cloth and said it is 4.48cm long. Your friend is then said to have measured the length with more accuracy.

Measurement errors can be of different types:

• Systematic Errors: Errors that occur in one direction. Can be of the following types:-
• Instrumental Errors
• Errors due to the improper technique used in the experiment
• Personal Errors
• Random Errors: Errors that occur irregularly and randomly.

Other important concepts you need to know about errors are:

• Least Count Errors: Occurs due to the inaccuracy of the instrument’s resolution.
• Absolute Errors: The error between the real value of a quantity and the value measured is called absolute error.
• Relative Errors: The ratio between mean absolute error to the arithmetic mean value for the quantity measured using a series of readings is called a relative error. When this relative error is expressed in percentage, it is called a percentage error.

#### Significant Figures

There are many cases where a combination of errors can occur. However, the result of an experiment must always be given as precisely as possible. If the mass of an object is 3.42, then digits 3 and 4 are reliable, but 2 is uncertain. The value measures, therefore, has three significant figures. Some rules that you can follow to determine the number of significant figures are:

• All non-zero digits are important.
• The zeros between any two non-zero digits are important and must be considered, irrespective of where the decimal is placed.
• If the measured value is less than 1, then the zeros on the right of the decimal point and left of the first non-zero digit are not important.
• The last zero in the number without any decimal point is insignificant.

#### Dimensions of Physical Quantities

In order to describe a physical substance or quantity, apart from units and measurements, we also require dimensions. Dimensions can be defined as the power to which the base value or quantities are raised to represent that said quantity.

Dimensional Formulae and Equations

Dimensions of a physical quantity are expressed using dimensional formulae and equations.

Most physical quantities in physics are written in terms of the dimensions [L], [M] and [T].

For example, the volume is written as [L]x[L]x[L]= [L]3.

Similarly, Force= Mass x Acceleration

Or, F= mass x (length)/(time)2

So, the dimensions can be written as: [M] x [L]/[T]2

Another example where dimensional formulas can be used to form an equation is:

½ mv2=mgh where m= mass, v= velocity, g= acceleration due to gravity, and h=height

So, the dimensions of ½ mv2= [M] x [LT-1]2

=[M L2 T-2]

The dimensions of mgh= [M] x [LT-2] x [L]

=[M] x [L2T-2]

= [ML2T-2]

If you notice, the dimensions of the left and right-hand-side of the equation are the same. So, the equation is dimensionally correct.

Dimensional Analysis and Its Applications

Once you are aware of the dimensions, you will be able to judge a substance’s physical behavior. The dimensional analysis helps you deduce the relations between various quantities and determine how they are derived accurately. While performing dimensional analysis or applying it to experiments, you must remember that when one or more physical quantities are multiplied, their units must also be treated in the same manner. Having the same units on both sides cancel out each other.

#### FAQs

• What are the units in physics?

Many quantities are measured in physics, and these need to have a standard of measurement. Units are standardised values, and measurement of physical quantities are expressed in these units.

• What are the 7 basic units of measurement?

In the SI unit system, there are 7 basic units of measurement. These seven base units used in the SI units system are:

• Length: Meter (m)
• Mass: Kilogram (Kg)
• Time: Second (s)
• Electric Current: Ampere (A)
• Thermodynamic Temperature: Kelvin (K)
• Amount of substance: mole (mol)
• Luminous intensity: Candela (cd)

Apart from these seven units, two dimensionless quantities have also been given SI units. These include – radian or (rad) for plane angle and steradian (str) for a solid angle.

• What are the two classification systems of units?

Many classification systems of units are prevalent. However, the two most widely used are the SI unit system and the CGS unit system.

• What are the types of units?

Units are of two types– fundamental and derived. The units used for fundamental quantities are called base or fundamental units. These are used in various combinations for expressing other quantities. Units that are used for the derived quantities are called derived units. The fundamental and derived units together form a system of units.

Without units and measurements, our world would have never progressed. There isn’t a thing that is not measured or quantified and forms the basis of how we live, eat, work, etc. Want more clarity on the topic? Hop on to our app or MSVGo app for some interactive videos. MSVgo is an e-learning app which has been developed to embark conceptual learning in the students from grade 6-12. MSVgo has been providing the students with a core understanding of the concepts. It is a video library which is a wondrous collaboration of concepts with animations and explanatory visualization. This app contains high-quality videos based on the curriculum, ICSE, ISC, IGCSE and IB curriculum in India. You must check out the videos on MSVgo to understand concepts in-depth on this topic.

### High School Physics

• Alternating Current
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• Acids, Bases and Salts
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• Algebra – Arithmatic Progressions
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### Middle School Math

• Addition
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• Time
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