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

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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.

UNIT 1 TUTORIAL 2 PHYSICS IN TECHNOLOGY AND SOCIETY

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We can say that technology and thus the society is always interconnected with physics. The present technology may not be directly connected with the physics but in some or the other way the basic principles used in the other way are directly related to physics. For example let us consider the computer you are using now. It has a chip which is made up of silicon and the study of the properties of this materials comes under the branch of physics called as material physics. Or for the sake of easy understanding let us consider the internet which you are using to study this document. In the earlier days there was not internet but telephone was introduced based on the basic laws of electricity and magnetism. That wired telecommunication gradually changed to wireless and finally we are not only communicating with other but also we are exchanging our data based on the laws of electricity and magnetism. Similarly the automobiles which are running on the roads are based on the laws of motion and energy from combustion of the fossil fuels. In similar way there are many examples which can be stated here but I think they are not very necessary as you know most of them. But I will give some data regarding some physicists from different countries of the world who have their major contributions to the subject of physics. Note that this data is not my original work but I have collected this from the NECERT textbook of INDIAN government of page number 5, 6 from Table 1.1. Picture quality is low as it is just for information.

Unit 1 Tutorial 1 What is Physics?

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Human beings have always felt the nature as a wonder and wanted to know the secret behind it. Gravitational pull, flow of fluids, storms, planets, stars, kinematics etcetera. This curiosity was not only for the wonder but also to interact with the nature for his comfort. This led to many inventions and thus the science was created which in turn created physics.

What is science?

The word science comes from the Latin word “Scientia” which means “to know” or “knowledge”. Science is a method or systematic approach to understand the principles or the wonder behind the nature in as much as detail or depth possible using observations and experiments.

There are many persons who contributed for the science and its growth. Some of them are Newton who suggested the gravity, Albert Einstein who found the famous Mass-Energy equation, Neil’s Bohr who suggested the quantum theory using hydrogen atom and many others whom we will see in the upcoming tutorials.

What is physics?

Physics is a derived from a Greek word which means the “knowledge of the nature”. Thus physics can be defined as the branch which deals which the study of matter and its motions in the space and time along with the related concepts like energy and force. In a simple way it can be said that physics is the branch of science which deals about the matter interacting with the nature.

In physics we try to explain nature with regard to some of the universal laws. For example gravitational theory can be used to explain the famous Newton’s falling of an apple and also the rotation of the moon around the earth. In the similar way we can explain all the concepts of nature with respect to the universal laws stated in the physics which we will see in the further tutorials.

Physics is subdivided further into two branches. They are MacroscopicPhysics and Microscopic Physics. Macroscopic physics deals with the nature and its particles which are visible directly to the human eye, while microscopic physics deals with the nature and its particles which are in microscopic size. It can be said that physics is further divided into many braches while we will cover them in the upcoming tutorials.

Finally to conclude physics is a vast subject and it has a large scope which does not have any end. There is not end for physics and every day there is an invention coming under physics out of many a few are making the human life easier.   

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Why I have started tutorials for JEE Mains and Unit 1 syllabus

When I have started this blog I thought of writing about fluid Mechanics but I have seen that there is a need for starting from basics so that if anyone gets doubt in basics then you guys can search about it and get the results. First I will start with the physics and continue to the other subjects so that this blog of mine will serve you very well. You can find our objectives of the first unit and the topics which will be covered in for the first unit here:

This is the unit 1 of the JEE mains and also the basics in physics. Let us have an approach which is different for learning and also useful for JEE mains.

Unit 1 – Physics and Measurement
Tutorial 1: What is Physics?
Tutorial 2: Technology and Society
Tutorial 3: SI Units
Tutorial 4: Fundamental and derived units
Tutorial 5: Least count
Tutorial 6: Accuracy and precision of measuring instruments
Tutorial 7: Errors in measurement
Tutorial 8: Dimensions of physical quantities
Tutorial 9: Dimensional analysis and its applications

Find the PDF of this unit here:

http://www.docdroid.net/file/view/xfty/unit-1.pdf

1.9 Bulk Modulus and Compressibility

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Bulk modulus:

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It is defined as the ratio of change in pressure to the volumetric strain of the fluid.
It should be noted that the volumetric strain is the ratio of change in volume to its original volume.
 Bulk modulus is represented by B and by some authors as K.

This mathematically bulk modulus can be given as

where dp is the change in pressure.
 dV  is the change in volume.
V is the original volume.

It should be noted that here a negative sign is added to the bulk modulus mathematical relation(formula) because the stain is considered to be compressive strain. If the strain is tensile then the negative should not be considered. 

In SI units its dimensional formula can be given as M¹L⁻¹T⁻².

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Compressibility:

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It is defined as the inverse of the bulk modulus. Thus it can be defined as the ratio of the volumetric strain to the change in pressure. Thus mathematically it can be given as

Compressibility = 1/K or 1/B

In SI units its dimensional formula can be given as M^-1L¹T².

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References:
http://en.wikipedia.org/wiki/Bulk_modulus
http://www.britannica.com/EBchecked/topic/84278/bulk-modulus
http://dictionary.reference.com/browse/bulk+modulus
Img Credits: http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/bulk3.gif

1.8 Types of fluids based on viscosity

There are five types of fluids in fluids mechanics

1. Ideal Fluid
2. Real Fluid
3. Ideal Plastic Fluid
4. Newtonian Fluid
5. Non-Newtonian Fluid

1.Ideal Fluid

A Fluid which has an ideal flow and which is incompressible is called as ideal fluid. Ideal fluids are assumed to have zero viscosity.
It should be noted that in practice there is no ideal fluid. 

2. Real Fluid

A fluid which doesn't have ideal flow and which is compressible is called as real fluid. Real Fluids have viscosity and they face friction while they are flowing. 
All the fluids in real practice are Real Fluids

3. Ideal Plastic Fluid

A fluid in which shear stress is more than the yield value and the shear stress is directly proportional to the shear strain(du/dy) is called as Ideal Plastic Fluid.
 One of the example of the Ideal Plastic Fluid is Bingham Plastic. 

4. Newtonian Fluid

The Fluid which obeys the newtons law of viscosity is called as Newtonian Fluid. It should be remembered that the Newtons law o viscosity can be given as

And thus the fluid which obeys this law is called as Newtonian fluid.

5. Non Newtonian Fluid

A Fluid which does not obey the above equation(Newtons law of viscosity) is called as Non-Newtonian Fluid. Thus Non Newtonian fluids deviate from the above equation.

References:
http://en.wikipedia.org/wiki/Bingham_plastic
http://www.definition-of.com/Ideal+Plastic+fluid 
http://encyclopedia2.thefreedictionary.com/Ideal+Fluid  
http://mechteacher.com/fluid/

1.7 Newtons law of viscosity.

It states that the shear stress of  a fluid element in a fluid layer which is flowing with some velocity is directly proportional to the rate of shear strain. The equation we have already seen in viscosity concept is the one proposed by newton. It is given as

And if the constant of proportionality is introduced then the equation becomes

Where, μ is the constant of proportionality and is called as the coefficient of dynamic viscosity or viscosity.
τ is the shear stress and
du/dy is the rate of shear strain 

Types of fluids based on newtons law

1. Newtonian Fluids
2. Non-Newtonian Fluids

1.Newtonian Fluids

Fluids which behave according to the equation of Newtons law of viscosity are called as Newtonian Fluids. 

2. Non Newtonian Fluids

Fluids which do not satisfy the newtons law of viscosity or the newtons equation on viscosity are called as non-newtonian fluids.

Note:

1. All real fluids are Non Newtonian Fluids.
2. All ideal fluids accept the Newtons law of viscosity and are called as Newtonian fluids.
3. Water, thin motor oil are considered to be partially Newtonain Fluids.

Example Problem:
This is an example problem and remember that the values in the real life will be in the order of exponential. All the values given here are for the sake of beginners.
Consider a fluid flowing in a river. If the shear stress is  equal to 10N/m² distance between the fluid layers is 2m. Fluid is flowing with a velocity of 5m/s. 

1. Find whether the fluid is Newtoinain Fluid or non Newtonian fluid if the coefficient of dynamic viscosity is 40N.s/m².
2. Find the viscosity of the fluid if it were a Newtonian fluid.

Sol: 

1.We know from the equation that   

Therefore we can observe that

 10 ≠ 40x5/2

Therefore the given fluid is not a Newtonian Fluid.

2.If it was a Newtonian Fluid then from the above equation it can be found that 

μ = 4N.s/m².

References:

http://en.wikipedia.org/wiki/Non-Newtonian_fluid

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

http://www.enchantedlearning.com/math/symbols/

 

1.6 Kinematic Viscosity

Kinematic viscosity is defined as the ratio of the dynamic viscosity to the density of the given fluid. It is denoted by the symbol v(nu).

v = Viscosity/Density

v = μ/ρ

Video:
It should be noted that the video here also contains about the what is viscosity. I suggest you to watch about the viscosity, to refresh about the viscosity as kinematic viscosity is dependent on viscosity.
 

It's units in SI and MKS system are given by m²/s. In CGS system its units are given by cm²/s.
It should be noted that cm²/s is also called as stoke and 
stoke = 10^-4 m²/s.

Note:

1. 1Stoke = 100 Centistoke

1.5 Viscosity

Viscosity is the measure of the fluid resistance to flow.

Video:
This video also contains about the kinematic viscosity which we are going to cover in the next post. If you want to watch it you can watch it.


It can be said that the resistance is due to the intermolecular forces between the fluid layers. Thus in the figure the top fluid layer only has force on it by the fluid layer under it. But for the fluid layer under it has forces above it and layer under it.


To understand this properly let us consider an example.

Let us consider a fluid moving in x direction as shown in the figure. 

Let us assume that the lines represents the fluid layers and they are dy distance apart. And also assume that the top layer of the fluid is moving at a velocity of u. Now the viscosity is that the layer 2 pulls back the layer 1 for its movement. Thus the velocity of the second layer will be u-du. Therefore the shear stress on the first layer will be towards the left hand side and on the second layer will be towards the right hand side for this example. And we know that the shear stress is defined as the force acting on the given object per unit area. Therefore shear stress can be given as 

Here the proportionality constant becomes the coefficient of viscosity. and is denoted by μ.

Thus the equation can be represented as 

where,

τ is the shear stress 

μ is the coefficient of dynamic viscosity or viscosity.

and du/dy is the rate of shear strain or velocity gradient.

Thus we can write the equation of viscosity can be given as 

Units of viscosity can be given as

and in CGS system can be given as

Where 1 Newton is equal to 100000 dynes and it should be noted that dyne.s/cm² is also called as poise

in MKS system the units can be given as 

and the relation between the MKS system and the SI system can be given as 

Note:

1. All Real fluids have viscosity.
2. Only in ideal fluids viscosity is assumed to be zero.
3. Viscosity is also called as dynamic viscosity. 
4. The More the viscosity the slower the motion of the liquid.