## Learning Objectives

## After completing the topic, the student will be able to:

- Understand the importance of fundamental units of physical quantities and distinguish between the two systems of units.
- Explore the rules for writing the units for any physical quantity.
- Estimate and measure very small and very large distances.
- Determine the dimensions of any physical quantity, using dimensional analysis.
- Understand the nature of errors and methods of analysis of the errors in measurement.
- Observe and understand the difference between accuracy and precision.
- Determine the number of significant figures in a numerical value.
- Analyse the least count of some measuring devices
- Differentiate between vectors and scalars and investigate the importance of vectors with relevance to daily life applications.
- Express vectors in different types of co-ordinate system.
- Identify the types of vectors and resolve them in to their corresponding components, based on the angle subtended.
- Employ methods for addition and multiplication of vectors, with reference to the properties of dot and cross products.

Einstein (1933) has said, "Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge starts from experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality". Standard measurements as part of experimentation is essential part of research as well as application of knowledge.

When you go to buy sugar, you do not say that "I want to buy a sugar", you will say "I want to buy **1kg** of sugar". The shopkeeper then weighs the sugar, against **STANDARD** weights and gives you 1 kg of sugar. Similarly, when you measure with a ruler, say length of a pencil, the markings on the ruler are **STANDARD** lengths. Take another physical quantity, say time. A second, a minute and an hour on your watch has been set to a **STANDARD**. Now you may ask, why this is so? The answer to this question is that anywhere on the earth, your measurements should match anybody else's measurements.

When you say that you have bought 10 kg of potatoes, whether you buy them in Pune, Paris or Portsmouth, 10 kg of potatoes have to be 10 kg of potatoes and nothing else. Therefore, whenever you measure any physical quantity, they are relative to or compared against some **STANDARD** measurements. The international community from time to time announces new, revised standards and all nations have to comply with these standards.

The basic quantity of the standard is known as a unit. The amount of a physical quantity that is used as a reference for the measurement of that quantity is called the unit of that quantity. The unit is invariable, easily reproducible and is internationally accepted while an actual measurement would be a fixed multiple of the unit. The multiple is called the magnitude of the unit. For example, if we decide unit length to be 1 meter, and if a length of the side of the table is 2.0 meters then magnitude of the measurement is 2.0.

Since the development of measuring processes, a number of systems of unit have been put forward. Here are a few:

**F P S System (Foot–Pound–Second)**

In this system of unit, length is measured in foot; mass in pound; and time in second. This is also known as British system of measurement.**C G S system (Centimeter–Gram–Second)**

In this system of unit, length is measured in centimeter; mass in gram; and time in second.**M K S system (Meter–Kilogram–Second) or Metric system**

Here, length is measured in meter; mass in kilogram; and time in second.**SI Units**

The representations or prototypes of units are maintained in many international centres worldwide, like the International Bureau of Weights and Measures at Sevres near Paris, National Institute of Standard Technology or National Physical Laboratory in the USA or Bureau of Indian Standards in New Delhi, India. Internationally everyone strictly follows a standard system of units. This system is called the S.I. units (Standard International). Calibrations used for measurement have to be standardized so that they remain constant, under normal everyday life. If this was not done, then there would be chaos in the world as everyone's measurement would be different!! In SI there are**seven fundamental units**and**two supplementary units**.

MKS units and the SI system of units are nearly similar and now-a-days used in most measurements. To know the difference between M.K.S and S.I systems click