Introduction and its
importance
Measurement is the process of finding the value of unknown quantity with the
known quantity of same kind.
Fundamental quantities
The quantities which can neither be derived from nor be further resolved into
other simpler quantities are called fundamental quantities.
Length, mass, time,
electric current, temperature, luminous intensity of light and amount of
substance are some examples of fundamental quantities.
Derived quantities
Those physical quantities which depend on two or more fundamental quantities or
power of a fundamental quantity are called derived quantities.
Area, volume, density, force, speed, acceleration,
pressure etc. are some examples of derived quantities.
Unit
The reference standard quantity with which we carry out the measurement of any
physical quantity of the same kind is known as unit.
The unit selected for measuring a physical quantity
must have the following characteristics:
1. The unit
should be well-defined and accepted all over the world.
2. The unit should be easily reproducible.
3. The unit should change neither with time nor with physical conditions like temperature, pressure etc.
4. The unit should be universally agreed upon so that the results obtained in different countries are comparable.
2. The unit should be easily reproducible.
3. The unit should change neither with time nor with physical conditions like temperature, pressure etc.
4. The unit should be universally agreed upon so that the results obtained in different countries are comparable.
5. The unit should be of a
suitable size.
Standard system of units
1. MKS system: In this system, length is measured in meter, mass is measured in kilogram and time is measured in second. It is also called metric system.
2. CGS system: In this system, length is measured in centimeter, mass is measured in gram and time is measured in second. It is also called French system.
3. FPS system; In this system, length is measured in foot, mass is measured in pound and time is measured in second. It is also called British system.
4. SI system: The French name for this system is “Sestéme International d’ Unite’s” (International System of Units). This system is, in fact, the improved and extended version of MKS system of units. In the year 1960, the Eleventh General Conference of Weights and Measures in France held among the world-class scientists recommended SI system of units. This system is now used all over the world. Thus, the system of units is agreed by the international convention of scientists held in France in 1960 is called SI unit. In SI system, length is measured in meter, mass is measured in kilogram and time is measured in second.
1. MKS system: In this system, length is measured in meter, mass is measured in kilogram and time is measured in second. It is also called metric system.
2. CGS system: In this system, length is measured in centimeter, mass is measured in gram and time is measured in second. It is also called French system.
3. FPS system; In this system, length is measured in foot, mass is measured in pound and time is measured in second. It is also called British system.
4. SI system: The French name for this system is “Sestéme International d’ Unite’s” (International System of Units). This system is, in fact, the improved and extended version of MKS system of units. In the year 1960, the Eleventh General Conference of Weights and Measures in France held among the world-class scientists recommended SI system of units. This system is now used all over the world. Thus, the system of units is agreed by the international convention of scientists held in France in 1960 is called SI unit. In SI system, length is measured in meter, mass is measured in kilogram and time is measured in second.
Do you know?
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The standard one kilogram mass is the weight of
platinum-iridium cylinder kept at 0oC at the International Bureau
of Weights and measures in France. This mass is equal to mass of 1 liter of
water at 4o C.
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Advantages of SI units
1. It is a rational system of units. That is, this system makes use of only one unit for one physical quantity. For example, joule is used as the unit of energy for all types of energies e.g. mechanical, heat, electrical etc. In CGS and MKS systems, mechanical energy is measured in joule, heat energy is measured in calorie and electrical energy is measured in kilowatt-hour.
2. It is a consistent and coherent system of units. In this system, all the derived units can be easily obtained from fundamental units.
3. It is a metric system. That is, multiples and sub-multiples of SI units can be expressed as power of 10. It makes calculation easy and saves time and space.
1. It is a rational system of units. That is, this system makes use of only one unit for one physical quantity. For example, joule is used as the unit of energy for all types of energies e.g. mechanical, heat, electrical etc. In CGS and MKS systems, mechanical energy is measured in joule, heat energy is measured in calorie and electrical energy is measured in kilowatt-hour.
2. It is a consistent and coherent system of units. In this system, all the derived units can be easily obtained from fundamental units.
3. It is a metric system. That is, multiples and sub-multiples of SI units can be expressed as power of 10. It makes calculation easy and saves time and space.
Fundamental Units
The
unit which is independent on other units is called fundamental units.
The table below shows seven fundamental quantities and their SI
units are:
Fundamental
Quantity
|
Fundamental
Units
|
Symbols
|
Length
|
meter
|
m
|
Mass
|
kilogram
|
kg
|
Time
|
second
|
a
|
Temperature
|
kelvin
|
K
|
Electric
current
|
ampere
|
A
|
Luminous
intensity
|
candela
|
cd
|
Amount
of substance
|
mole
|
mol
|
Derived Units
The unit which is expressed in terms of two or more fundamental units is called
a derived unit.
Some derived units and their relation with fundamental units are
given in the following table:
S.No.
|
Derived Quantity
|
Related formulae
|
Symbol of unit name
|
Derived Units
|
Fundamental units
involved
|
|
1
|
Area
|
length ×
breadth(l×b)
|
square meter
|
m2
|
m×m
|
|
2
|
Volume
|
length × breadth ×
height(l×b×h)
|
cubic meter
|
m3
|
m×m×m
|
|
3
|
Velocity
|
displacement/time
(s/t)
|
meter per second
|
ms-1
|
m/s
|
|
4
|
Acceleration
|
change in
velocity/time (v/t)
|
meter per square
second
|
ms-2
|
m/(s×s)
|
|
5
|
Force
|
mass × acceleration
(m×a)
|
newton
|
N
|
(kg×m) / (s×s)
|
|
6
|
Density
|
mass/volume (m/v)
|
kilogram per cubic
meter
|
kg/m3
|
kg/(m×m×m)
|
|
7
|
Pressure
|
force/area (F/A)
|
pascal
|
Nm-2 or
Pa
|
kg/(m×s×s)
|
|
8
|
Momentum
|
mass ×
velocity(m×v)
|
newton meter
|
kg ms-1
|
kg×m/s
|
|
9
|
Work and Energy
|
force ×
displacement(f×s)
|
joule
|
J
|
(kg×m×m)/(s×s)
|
|
10
|
Power
|
work done/time
(W/t)
|
watt
|
W
|
(kg×m×m)/(s×s×s)
|
|
11
|
Frequency
|
velocity/wavelength
(v/λ)
|
hertz
|
Hz
|
cycle/s
|
|
12
|
Potential
Difference
|
work done/charge
(W/q)
|
volt
|
V
|
(kg×m×m)/(s×s×s×A)
|
|
13
|
Ressistance
|
potential
difference/current (V/I)
|
ohm
|
Ω
|
(kg×m×m)/(s×s×s×A×A)
|
Example 1: The unit of power is called a derived unit, why?
Ans: The unit of power is watt.
We know that,
Power = work done/time =W/t = (F*s)/t =
(m*a*s)/t [∵ F= m.a]
Now, substituting the related units,
∴ Watt = (kg*m*m)/(s*s*s)
= kg m2s-3
The unit of power is expressed in the terms of
fundamental unit kg m2s-3. Thus, the unit of power is
called a derived unit.
Differences between fundamental unit and derived
unit
S.No.
|
Fundametal unit
|
S.No.
|
Derived unit
|
1.
|
This id the unit of a fundamental quantity.
|
1.
|
This is the unit of derived quantity.
|
2.
|
This is independent of other units.
|
2.
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This unit is obtained from two or more fundamental units.
|
3.
|
There are only 7 fundamental units. They are meter,
kilogram, second, Kelvin, ampere, candela and mole.
|
3.
|
It is formed in many types using 7 fundamental units. They
are Newton, Pascal, Joule, Watt, Hertz, Ohm etc.
|
Some Reasonable Facts
1. 1. We use SI
units for a scientific purpose all over the world, why?
2. Ans: We use SI
units for a scientific purpose all over the world because the results of
experiments conducted in different countries are comparable.
3.
4. 2. Sometimes,
a special name is given to derived units, why?
Ans: Sometimes, a special name is given to derived
units because to honour a noteworthy physicist. For example, the derived SI
unit of force (kg ms-2) is called Newton in honour of Issac Newton.
