UNIT AND DIMENSIONS

2. UNIT

1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS

Measurement: In our daily life, we need to express and compare the magnitude of different quantities; this can be done only by measuring them.

Measurement is the comparison of an unknown physical quantity with a known fixed physical quantity.

Unit: The known fixed physical quantity is called unit. OR

The quantity used as standard for measurement is called unit.

For example, when we say that length of the class room is 8 metre. We compare the length of class room with standard quantity of length called metre.

Length of class room = 8 metre

Q = UN

Physical Quantity = Numerical value × unit Q = Physical Quantity

n = Numerical value u = Standard unit

e.g. Mass of stool = 15 kg Mass = Physical quantity 15 = Numerical value Kg = Standard unit

Means mass of stool is 15 times of known quantity i.e. Kg.

Characteristics of Standard Unit: A unit selected for measuring a physical quantity should have the following properties

(i)  It should be well defined i.e. its concept should be clear.

(ii) It should not change with change in physical conditions like temperature, pressure, stress etc..

(iii) It should be suitable in size; neither too large nor too small.

(iv) It should not change with place or time.

(v) It should be reproducible.

(vi) It should be internationally accepted.

Classification of Units: Units can be classified into two categories.

1. Fundamental

2. Derived

Fundamental Quantity: The quantity which is independent of other physical quantities. In mechanics, mass, length and time are called fundamental quantities. Units of these fundamental physical quantities are called Fundamental units.

e.g. Fundamental Physical Quantity       Fundamental unit 

       Mass                                                     Kg, Gram, Pound

       Length                                                  Metre, Centimetre, Foot

       Time                                                      Second

Derived Quantity: The quantity which is derived from the fundamental quantities e.g. area is a derived quantity.

Area   = Length x Breadth

= Length x Length

= (Length)² 

Speed =Distance /Time

=Length / Time

The units for derived quantities are called Derived Units.

1.2.1 Table of Fundamental Units

Sr. No.	Name of Physical Quantity	Unit	Symbol
1 2 3 4 5 6 7	Length  Mass  Time Temperature  Electric Current  Luminous Intensity Quantity of  Matter	Metre  Kilogram  Second  Kelvin  Ampere  Candela  Mole	m  Kg  s  K  A Cd  mol

1.2.2Table of Supplementary unit

Sr. No	Name of Physical Quantity	Unit	Symbol
1 2	Plane angle Solid angle	Radian Steradian	rad sr