JEE MAINS PHYSICS UNIT 1 TUTORIAL 4 FUNDAMENTAL AND DERIVED UNITS

Tutorial 4 Fundamental and Derived Units

We have discussed about units in the last tutorial. By now we know that units are further divided into fundamental units and derived units.

Fundamental and derived units

Fundamental Units:

Fundamental units are a group or a set of units of the given physical quantities from which other units can be generated. Or otherwise they can defined as that these units can neither be derived from one another nor can be resolved into any other units. They are independent. Fundamental units are also called as base units. There are 7 units of physical quantities which are defined as fundamental units by the international system of units. As I have stated earlier that all my tutorial will be in SI units unless otherwise stated. So the Fundamental units in SI units are as follows: (It should be noted that the definitions in the given table are new definitions according to the international standards. There is no need for remembering all the values in the given table or definitions but I would suggest to remember everything except definitions.)

Name	Symbol & Full Form	Measure	Current Definition	Dimensional Symbol
Length	m(Meter)	Length	The meter is the length of the path travelled by light in vacuum during a time interval of 1 ⁄ 299792458 of a second	L
Kilogram	kg(Kilo Gram)	Mass	The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram	M
Second	s(Second)	Time	The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.	T
Ampere	A(Ampere)	Electric Current	The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per meter of length.	I
Kelvin	K(Kelvin)	Thermodynamic temperature	The kelvin, unit of thermodynamic temperature, is the fraction 1 ⁄ 273.16 of the thermodynamic temperature of the triple point of water.	Θ
Mole	mol(Mole)	Amount of substance	The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is 'mol.	N
Candela	cd(Candela)	Luminous Intensity	The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.	J

Derived units:

The units which are derived from the fundamental units are called as derived units. For example we know that Force is the product of “Mass” and “Acceleration”. We know that that acceleration is equal to the ratio of the distance travelled to the square of the time (Precise definition will be given in the upcoming tutorials. For now just consider this.), so the units of force in SI units can be written as

F = Mass(kg).Acceleration(meter/ second²)

Thus the units of force are the  

It can be seen that the units of force are product of one or more base units. Thus it can be said that force is a derived quantity.

Some examples of other derived units in the real life can be given as, voltage, Resistance, Magnetic induction, Velocity, Acceleration, Volume, Area and many others come under derived quantity.

Some of the derived units which have specific names for their derived unit are, plane angle(radian), solid angle(steradian), frequency(hertz), force(newton), pressure,stress(pascal), energy, work, quantity of electricity(coulomb) and others.

I think there is no need to remember these units except the base units for now because you will get used to these units and automatically remember them while you will complete learning all the tutorials.

Finally it should be remembered that this topic is very important not only in real life but also for your exam as this is the basics for the upcoming tutorials.

References:

http://en.wikipedia.org/wiki/International_System_of_Units

http://en.wikipedia.org/wiki/SI_base_unit

http://en.wikipedia.org/wiki/Units_of_measurement

http://physics.nist.gov/cuu/Units/units.html

You can also download the pdf version of this document from here:

UNIT 1 JEE MAINS PHYSICS SI UNITS

You can download the pdf version of this document and read it.

What is a unit?

Let us say you were to measure the height of the person. The answer wouldn’t be that the person is tall or short but the answer would be that the person is 160 centimeters tall or 200 centimeters tall or some other value depending on the height of the person.

Now we have compared the height of the person to centimeter and have counted how many times the person is to that of the centimeter. But what if the person height is to be given in Feet and Inches? You would simply compare the person’s height with that of Feet and Inches.

So measurement of any physical quantity with respect to the universally accepted reference is called as unit. Let us simplify this definition with the above given example. Here the physical quantity to be measured is the height. The universally accepted reference is the centimeter. Thus the reference centimeter is called as the unit.

We will return the result of the measurement of a physical quantity with a number followed by the unit.

Why should we use units?

In the above example if you say that the person is tall, then in your point of view the height of the person may be more than 160 centimeters but according to my point of view it may be above 150 centimeters. So if you say tall then I would consider 150 centimeters but according to your point of view it is 160 centimeters and there will be a sort of confusion between the two. But if you specify that the height of the person as 160 centimeters exactly then there will not be any confusion between both of us instead of using the word tall.

Units are further divided into Fundamental and Derived Units which we will be covering in the next tutorial.

There are many universally accepted units among different countries. Some of the well known unit systems are:

FPS: In FPS the measurement of length is done with Foot, mass with Pound, Time with Seconds.

CGS: In CGS systems length is measured in Centimeters, Weight in Grams, Time in Seconds.

MKS: In MKS length is measured in meters, mass in kilograms, time in seconds.

The system which is presently used and accepted is the SI unit. Full form of SI unit is Système Internationale. This is accepted universally and are used in industries and other places worldwide. They have adapted SI units as standard because it is easy to use and also it is easy to convert from this unit to others. It is to be remembered that we shall use SI units in all our tutorials.