 Can you guys give your attendance? Who all are present? I'll start the class in next 2-3 minutes. Can you guys give your attendance in the chat box please? Okay, so I'll wait for 2-3 more minutes so that more people can join and then I'll start the class. Okay, so let me start. So today's class I'm going to cover two topics. First one is properties of matter second one is mechanical properties of few fluids. So first topic that I'll be covering from next half an hour 45 minutes would be properties of matter. This is a very important topic if you look at the syllabus of autonomous board. So this particular chapter is not very big but there are few concepts and there are concepts which are from where the problems may not come but they will give you 2 marker or 3 marker questions or maybe a 5 marker question also. There is a possibility I'll discuss that possibility while taking the class. And what happens is the questions mostly would be theoretical in nature from this chapter except from the formula of Young's modulus. So I'll take a bit of Young's modulus and I'll explain in properties of matter. So what I'm going to cover in properties of matter is I'll define different kind of solids. So you'll have crystals and mf solids. Then I'll take elasticity and Hook's law Young's modulus and then I'll define stress and strain curve and which will have a broader discussion on how you get yield points and what is yield strength, plastic deformation and all those things. So in the first part I shall be covering that. In the second half of this class I shall be taking mechanical properties of fluids. So there I'll be discussing about fluid mechanics. So thrust and pressure how pressure is developed. Then Pascal's law, application of Pascal's law then Archmedy's principle and after Archmedy's principle law, flotation, then viscosity and surface tension. All these things I shall be taking in details in the later part of the class. So let me start with properties of matter first. So we all know that in solids what happens is molecules and atoms are not very much mobile. I mean their mobility is constrained and their position is more or less fixed with respect to each other. And that is not the case in liquids and gases. So if you look at the compound and three kinds of compounds the first one is solid, the second one is liquid and the third one is gas here primarily we are going to talk about solids and that's why I have divided solids into two parts. So first part is crystals and second part is amorphous. Now just by classification these things doesn't become clear. So we need to look at crystals and amorphous solids in details. And for that what I have done is that I have taken a few properties of crystal and amorphous solids. So first thing that I want to tell you over here is that it becomes very very important from the exam perspective that you know the difference between crystal and amorphous solid. And whenever a difference is asked in the exam the best way to write the answer over here would be that you write in the column format. So you make two columns. One side you write crystals and the second side you write amorphous. So in this one I have taken crystals. Now what do you mean by crystal solids? So crystal solids are where you have atoms arranged in regular geometrical pattern. So whichever side you go suppose this is your solid and whichever side you go you will find fixed pattern of atoms and whichever geometry they are following that geometrical pattern will also be the same. And here as we have geometrical patterns so you will have smaller unit of geometrical patterns. So you will see if it is bounded in a circular manner which I am making on the board right now what happens is that you find these circles. Now these circles or these simplest arrangement of atoms is known as unit cells and these unit cells repeat itself through the volume of this solid and with the repetition of this unit cell the structure of the complete solid is formed. So that is what I have written here in the second line that the unit cell repetition is long range order. Now what happens is these bonds between as the structure is very much determined and it is bonding between the two unit cells is very cohesive in nature what happens that these covalent bonds are equally strong everywhere. So what I am trying to say is that from whichever part of the solid you take bonding between two unit cells you will find that the strength of the bond is same across the solid and due to this property what happens is that this particular this kind of solids will have fixed melting point. Now what happens is due to the arrangement they are categorized into I mean any particular solid is categorized into 3-4 different types depending on their elastic properties so what happens what do I mean by I will discuss elasticity in the next slide so till now I am saying that depending on the elasticity solids are defined into 3-4 different categories one of them is anisotropic and what I mean by anisotropic is that elasticity will not be same in all directions so what happens when we have solids suppose I am taking solid A, solid B and solid C and what I am trying to check is that I am trying to check elasticity of solid A in all the directions so I pull it up in this direction I pull it diagonally I pull it up vertically I pull it up at 30 degrees from horizontal and I try to check elasticity in all the directions so whichever solid does not have elasticity same in all the directions that kind of solid is known as anisotropic solid so you should write it very clearly it is very important most of the people don't know what is anisotropic means because in books it is only written anisotropic and hardly it is explained anywhere so you should write the meaning of anisotropic means elasticity of the solid is not same in all the directions so I am writing here anisotropic means elasticity of solid is not same in all the directions so this is the meaning of anisotropic now let me move to another topic another type of solid which is amorphous solids so what is difference between anisotropic crystalline solids and amorphous solids so amorphous solids you will find that atoms exhibit they will not exhibit regular patterns so in crystals we had regular patterns we had unit cells those unit cells were repeated for long orders and due to repetition of the long unit cells for long order the structure of the solid was created here atoms will not exhibit any long order of any particular unit cells so absence of unit cells is one of the property so that can be written as atoms exhibit only short range order so if this is the solid the pattern of arrangement of atoms would not be same along all the dimensions due to that what will happen that when you will pick two unit cells or when you will pick two molecules or different molecules from here the level of or the strength of the bond here would be different and due to that what happens is the melting point of amorphous solids are not same so melting point it varies over a range of temperature and that is why what happens is you will not find any fixed melting point so why there is no fixed melting point here in crystal solids or crystalline solids if somebody is asking you that question that may be a two marker question you should say that the strength of the bonds across two unit cells is not same in amorphous solids and which is same in the crystalline solids that is why in crystalline solids we find that we have a fixed melting point while in amorphous solids we have a melting point which varies over a range of temperature now as I explained you anisotropic solids let me explain you isotropic solids which are your amorphous solids so what do I mean by anisotropic solids is sorry isotropic solids is elastic property is same in all the directions so what I did was in case of anisotropic I was pulling it from diagonally 30 degree angle horizontally vertically and I found in anisotropic solids that the elasticity was not same here the elasticity would be same in isotropic so these are the differences between crystalline solids and amorphous solids now let me move to another topic which is elasticity so let me explain to you what is elasticity and you will find that elasticity is property of a body to regain its original dimension when the deforming force is removed so what happens in this case is suppose I have a solid over here and I am pulling it from here so what happens is so you take a rubber for that matter or your eraser and you start pulling it from both the sides using your hand and what you will see is that up till certain force there would be no deformity in the eraser so what will happen is if you remove the force if you start if you stop stretching it the eraser will return to its original dimension so that is what elasticity is if I try to deform any particular solid and it can sustain that amount of stress up to certain level and if I remove that stress it comes back to its original dimension that property of a body is known as elastic body so not all bodies are elastic in nature like you take a wire and wire is elastic you take a biscuit and try to break it what will happen? you apply a little bit of force and as soon as it is broken either it will be broken or it will be its original form so not everything is elastic in nature now we need to understand elasticity completely we need to understand two things stress and strain so what happens stress always limit due to its composition or due to its structure there would be external forces acting on it so that is called that is a type of stress inside the body another type of stress can be you apply a force over here so what happens is if you apply the force now there would be initiation of deformity inside this solid so that is called development of external I mean development of stress now what is stress? stress is defined as force per unit area so whatever force is applied per unit area that is known as stress now what is strain so it's very difficult to identify difference between stress and strain here so I am telling you stress I will define once more stress is a force that can cause change in physical body so it's basically tension which is produced in a body to deform it now it can be internal it can be external it can be both internal and external in nature now what happens is because the stress is there in the body due to overcome or to compensate that stress strain is developed in the body so strain is resultant of excessive stress and to overcome it or to try to negate it strain is developed but if you keep on increasing the stress then strain will not be able to overcome stress and deformity will start so strain is defined as change in dimension divided by original dimension so I have written it over here change in dimension divided by original dimensions so I have told you the difference between stress and strain stress can be there when strain is not there because of its internal structure, composition because of how it has been made so because of the composition or the shape size of the solid there can be internal stress you can provide external stress by applying some force onto it due to this stress what happens when it goes beyond a certain limit strain will be developed to overcome or to negate that stress so it means that stress can be developed stress can be there inside a solid without any strain what is strain? strain is a deforming capability so what happens when stress goes beyond a particular limit strain will be able to overcome the stress and deformity of the solid will start now strain is defined by change in dimension divided by original dimension so these are the two formulas that you need to remember from this slide which are strain which is change in dimension divided by original dimension and stress is equal to force divided by area so please have a look at these formulas very properly before you go to your examination room because there can be a question there can be a question which can be asked best on stress and strain or difference between stress and strain so one marker or two marker numerical can also be there you can be given change in dimension like I will discuss it now so you can be given that a solid has an area of or volume of 4 into 5 into 3 and it changes to 4.2, 5.1 and 3.5 after dimension find out what is the strain so you need to find out change so change is not this this is the new dimension so you find out volume 2 here suppose this is volume 1 so change is volume 2 minus volume 1 divided by original dimension is volume 1 so this is how you have to calculate the strain ok so now what I will do is I will move to another topic and for that what I am doing is I am taking so now I will define you what is Hooke's law so Hooke's law says that within the elastic limit strain produced in a body is directly proportional to stress so I told you that whenever there is a body and we start applying stress after a certain limit the strain will produce so what will happen is that stress in so this is stress and this is strain so up till certain limit if the stress increases strain increases in the direct proportion it means that strain is equal to or proportional to directly proportional to stress applied on the body so that is what Hooke's law says now apart from this how will you find out elasticity of a particular solid to find out elasticity of a particular solid there is a coefficient which is used which is called Young's modulus so what do I mean by Young's modulus so Young's modulus tell me Young's modulus is equal to linear stress divided by linear strain what do I mean by linear stress and strain so suppose this is a wire and I start pulling it from both the sides so what will happen first the wire will try to sustain that particular force which I have applied or stress which I have applied after a certain limit there would be initiation of deforming in the wire so what is the capability suppose I have wire w1 and w2 not both and they are made of different materials not both the wires will be able to sustain same amount of stress so to compare the elasticity or elastic nature what is elasticity the maximum stress which can be handled by a particular wire so that if I remove that force or stress it comes to its original position more would be the elasticity so if I have a wire which can sustain a stress of 100 Newton per meter square and come to its original shape and then I have a different wire which can sustain 200 Newton per meter square stress and then also it can come to its original shape and size so the second one will have more elasticity as compared to the first one so Young's modulus tells me how much linear stress and linear means change in linear dimensions so look at here linear stress is mg divided by pi r square force per unit area is generally considered to be cylinders in cylindrical form so this dimension or this area called surface area would always be pi r square so mg divided by pi r square and what would be linear strength so suppose if change in length is x and original length is l find out is mg divided by pi r square multiplied by l into x so this is your Young's modulus so Young's modulus is given or Young's modulus is calculated to find out how much stress can be sustained by a particular solid or a particular wire so by this method you can find out Young's modulus now let me go to next slide and here I come with the stress and strain curve and this is very important from your exam perspective if something is most important from exam perspective in this particular topic is stress and strain curve and it would be anywhere from 4 to 5 markers so you cannot compromise on writing this stress and strain curve or whenever you are to write I will tell you a method, let me first explain it I am explaining it in such a way that you have to write your answers in the similar manner so what happens is if you look at the graph, the graph is divided into different sections so first section is from O to A then you have A to B then you have B to C and then C to D, D to E and then you have here permanent set so you have to write this answer in this order only so that you explain the linear line from O to A then what happens between A to B then B to C then C to D directly from C to E what happens you have to explain exactly in the same manner don't start explaining E and then you go to O and then again you go to C if you do that, marks would be deducted so the first thing that I need to explain is O to A and what I do is look at here, what I do is I do by Hooke's law, up to the elastic limit what happens is the strain will increase proportionally to the stress so you see here I get a straight line over here this is a straight line which I am getting here so O to A is a straight line so what straight line is telling me that stress or strain is directly proportional to stress so you need to say that it follows O to A the critical word is Hooke's law so when you are defining it you say that O to A is an area where Hooke's law is obeyed and stress is proportional to stress so first you define this you say that strain is proportional to stress and point A is a point after which Hooke's law will not be obeyed and that is why point A is known as proportional or elastic limit so you define point A here only in the first explanation only that point A is called proportional or elastic limit and then you write a line which says that in this region and you write in bracket here O A in this region the solid is or the material is whatever you want to write or you can write the wire is completely elastic so three things you have to write for the first region first one you have to say that A follows Hooke's law second thing that you need to write that here the strain is proportional to stress then third thing that you need to say that A is proportional point or elastic point beyond which Hooke's law will not be followed and then you need to conclude by saying that the wire is completely elastic in this range after this what happens is I define A to B so A to B once I move beyond elastic point what happens is that up till a point B though strain will not be proportional to now strain is not proportional to stress but there is a point B till which the solid will be able to uphold its original dimensions if I remove the force so point B is that point till which the solid will be able to sustain its original dimensions if the force is removed and it will come back so what happens first thing I need to write over here is that between O to B if load is removed original dimensions are re-stored this is the first thing that we need to write and then you write that the path of you this is very important and people miss it the path B O A is path of re-estoration and then what we do is then you write that as point B is the last point and after which the re-estoration or coming back to original dimension will not be possible path B is known as yield point one thing I did mistake previously I told path A is elastic point path A is only proportional point point B is your yield point or elastic point after this elasticity will be damaged there would be elasticity after point B so after point B as the elasticity will not be re-stored point B is known as elastic or yield point and you should know that the maximum force or the stress applied at point B or stress corresponding to point B would be known as yield strength so these are the points I will again once again repeat first we need to say that from A to B is that region that if load is removed then the or O to B is region that if load is removed the wire comes to its original dimension then you need to say that the path of re-estoration would be then I need to define point B as yield point or elastic point and fourth I need to say that stress corresponding to point B is known as yield strength so if you are writing these four things you will get full marks for point B now let me go to B to C so what happens is now B to C anyway elasticity is gone but C is a point which tells me that if I remove stress or load applied here then original form will never come but it will not break it will go to some other dimension so what happens here is if the stress applied is removed at B path BAO will be followed so path BAO this path BAO will be followed but if you don't remove stress here if stress is applied beyond point B so point C is a point where what happens is if I remove force over here the original dimensions are not possible but it returns to certain other dimension which does not break which is important so you should write that it should not break down but the original dimension is not possible and it returns to this point so what happens is difference between this zero origin and the point where it returns the strain level is known as permanent set then what happens that once you have defined this you need to go to final explanation C and you say that in this region in the wire different constrictions constrictions means localization of molecules which are called necks and wastes that would be formed and ultimately at this point the wire will break so the point or the stress level at which the point at which the wire is breaking down that is known as fracture point that is known as fracture point now what happens is in fracture point the amount of stress corresponding to fracture point tensile strength so the amount of stress which needs to be applied to break the solid is known as fracture point and that stress amount is known as tensile strength few books also call it ultimate strength so you can use any word you need to write one more thing which is very important which is from C to E this particular region deformation starts happening which is non elastic which cannot I mean this deformation cannot be stopped hence this region is called plastic flow so this region is called plastic flow or instead of flow you can use word deformation also so as permanent deformation is taking place during this particular region of stress and strain curve this region is known as plastic deformation or plastic flow so this is how you have to explain stress and strain curve it has to be divided into four parts the first part will define what is region O A so first part will define region O A you need to write that Hooke's law is followed so I am summarizing it you need to write Hooke's law stress proportional to strain strain proportional to stress then you need to write A is proportional limit point A I called it elastic limit this is not elastic limit B is elastic limit and fourth is wire is perfectly elastic so you should write that in this region perfect elasticity is followed then second region is A to B so first you need to write that if load removed so you start with load removal and say that original dimensions possible then you talk about the retracing path so you say that B A O is path of re-estoration and then you say that that point B is as this is the maximum elastic limit this point B is elastic limit or yield point and then you need to say that stress corresponding to point B is known as yield strength then you need to define point B to C and you say that till points B to C elasticity is completely gone so what elasticity gone so what happens is between B to C if force or load removed doesn't go back to original dimension so the difference here basically you need to define permanent set and then you need to go to C to E so you say that write constant and next and which these three words and then you write that E is your fracture point and the stress corresponding to this is tensile strength and this complete region is known as plastic flow or plastic deformation if you write this much and draw this diagram properly there is nothing in this diagram you just have to draw with a scale a straight line so what if I have to draw this diagram what I do is I take a scale draw X and Y axis this part needs to be eliminated and then I draw this straight line then I make something like this and then I say that this is A and this is B and this is C and then I take it like this and something like this so I say that this is my fracture point so if you explain this much full marks would be allocated now let me go to another topic so with this as I told in the beginning of the session that first 40-45 minutes I will be talking about properties of matter now in your syllabus and this class I am focusing basically only on the board syllabus and the portions only required for writing your board exam so if you know this much of properties of matter you can easily write any question which is coming in your board examination now how to write the answers that also I have discussed having said that please practice it wherever you get an opportunity so when you practice questions what will happen is you will have an idea where you are doing mistake and what you are missing so I have already given you a few hints like stress and strain for a metallic wire if you have to draw this is how you draw it you remember the percentages that this is less than 1% and up to 30% of strain it goes and breaks down so that's how you have to write these questions having taught this now I move to the different topic of today's class which is mechanical properties of fluid so to do that what is required is let me go back so I am starting fluids now what happens is I discussed solid in the first 40-45 minutes of the class now it's time to discuss fluid now what is a fluid so fluid is a substance that can flow this is the basic property I mean a substance which flows is known as fluid and it assumes that the shape of I mean whichever vessel you put into it will take the shape of that vessel as simple as that so now we know that type of compounds we are discussing and we discussed about solids and crystalline and amorphous solids previously now fluids are of two types both liquid and gas both are considered to be fluids and though they are fluids but there is certain difference between liquid and gas so I will list out the basic differences the first one is liquid is incompressible and has a different volume so if I take a jar open jar rectangular jar like this and suppose the liquid is filled up to this level and if I start pressing it the liquid will not go down if I press it more the liquid will start flowing from corners so what I am saying is liquid is incompressible which gives it a certain volume but gas is compressible so you know CNG full form is compressed natural gas so there the gas is compressed while it is transferred from one place to another place why we compress it so that the volume of the gas can be reduced so when gas is up to this limit I start compressing it so it comes only up to this limit why this is possible because the intermolecular distance or interatomic distance between two atoms in gases are more so they can be compressed which is not the case when we consider about liquids now if I talk about fluids fluid is studied at two levels the first level is fluid statistics which is study of fluid at rest and when we go to study at fluid at rest we study about different things first one is hydrostatic pressure then we have Pascal's law then we have Archmage principles, flotation, surface tension and then we discuss about fluid dynamics which is as the name suggests which is study of fluid in motion so we discuss about continuation of continuity and viscosity so whatever I have written it here in this particular slide I am going to take all those topics in the coming slides so what happens is let me go to the next slide so let me define thirst for you so what happens when you have a bigger kind of a thing and you fill it with liquid what liquid will do it will interact with the wall of this particular beaker and due to the interaction of liquid with the wall of the beaker what it will do is it will apply certain amount of force on it and force will always be perpendicular to surface what it will do application of force and direction of force would be perpendicular to wall of sorry perpendicular to to the surface here so thirst is defined as total force exerted by liquid on any surface in contact with it so thirst is nothing but force and why it is applied because if a fluid comes in contact with any particular surface due to the contact it will start applying force the direction of the force would be perpendicular to the surface and the amount of force applied would be known as thirst now let me define pressure now what is pressure so because of this force or the force applied per unit area of the surface so pressure on a point of a surface is thirst acting normally per unit area around that point what I am trying to say to make it very very simple for you pressure is equal to thirst or force applied per unit area on any particular surface so the unit of pressure is Newton per meter square which is also called as so rather than writing Newton per meter square like Newton per meter square but Newton per meter square or unit of pressure has been also renamed as Pascal and you should know that pressure is an pressure is a scalar quantity so what is one Pascal if somebody is asking you to define one Pascal so you should say that one unit or one Newton of force acting on surface acting on surface of area of one meter square so this is what one Pascal is now let me do some derivations for you so the first derivation which I am going to do is to find out pressure created by a liquid column so for that what I am doing is that I am taking a one second let me draw it properly so I am taking a cuboid and what I am trying to do is that I am saying that this cuboid is filled with liquid so this cuboid is filled with liquid so what will happen at this pressure sorry at this surface so due to the weight of the liquid some force would be applied on it so weight of the liquid is equal to mass of liquid multiplied by z and what is mass is mass volume into density so if density where rho is I am writing here V is volume of volume of the vessel for that matter and rho is density of liquid now volume can be written as because I want to apply the height of this liquid column volume can be written as area into height so mass is equal mass can be written as area into height into rho and the weight will become area into height into rho into z and that is the force exerted this is the force exerted on on this particular surface now what is the area I have already assumed to be weight defined by so I have written here weight of the liquid column defined by area A and what is A area is A h rho hg divided by A so I am cancelling this A pressure comes out to be rho hg so pressure applied by any liquid column which has has a height h and the density of the liquid is rho the pressure applied would be rho hg so this is what the formula is now let me go to atmospheric pressure so what is atmospheric pressure so we all know that around us there is an air column so what do I mean by air column there is an earth is surrounded by volume of gas up to a certain height though density of the gas is not equal along the height but we know that certain volume of the gas is surrounding our earth surface so as this is fluid gas is a fluid due to its height so what will happen we can find out the mass and all those things so this gaseous layer will apply certain pressure on earth surface so the force exerted by air column of air on unit area of earth surface so we all know that due to its mass and layer around earth surface a force would be exerted by this layer of air on earth surface and force applied per unit area of earth surface would be known as atmospheric pressure P0 or PA whatever you want to write so this is what atmospheric pressure is how it is created it is created due to the layer of different gases around our earth surface now this is one of the most important topics pressure so first one this is Pascal's law and what Pascal's law tells me that the pressure exerted by, exerted anywhere in confined liquid is transmitted equally and undiminished in all directions throughout the liquid so what happens is if I apply a pressure here or certain force per unit area what is pressure force per unit area I will start pushing this fluid which is here with my hand or a piston or something like that so the force applied per unit area would be pressure and the pressure which is applied by the piston suppose I am using a piston over here rectangular piston I am taking over here and applying pressure due to it the pressure created by this piston would be circulated or transmitted equally in all directions throughout this complete liquid so this is what the Pascal's law is that you take a liquid apply a pressure over here this pressure gets transmitted everywhere equally in all the dimensions and this pressure is not diminished so one thing is that if I apply 20 Pascal of pressure here so this pressure will remain undiminished in all the directions throughout this complete liquid example if you look at the syllabus of class 10th board what happens is Pascal's law apart from its definition has been taken as I mean more of the application side so its application has been taken in real world and what we see in the books is that hydraulic lift and hydraulic brakes has been defined in the book so I have taken both the examples here this is the example of hydraulic lift so what happens in case of hydraulic lift is that there are 2 cylinders so this is cylinder 1, C1 and this is cylinder 2, C2 and one thing that you need to mention very properly this line multiplication of force so you see that hydraulic lift is an application of the first line should be application when you are defining that draw this diagram beautifully like this and then you should write that this is application of Pascal's law then you should write that its use is used for lifting heavy weights and third point which you should mention very properly that it is based on it is based on multiplication of force so it is a force multiplier and how does it happens so look at here these are 2 cylinders and in those 2 cylinders what is filled some liquid or some fluid has been filled over here in this particular cylinder what happens on both end of cylinders it means C1 and C2 I have pistons here pistons have certain characteristics so in construction of hydraulic lift you should mention that there are 2 cylinders C1 and C2 then between these 2 cylinders of fluid has been filled in the end of the 2 cylinders there are 2 pistons suppose P1 and P2 what happens is P1 and P2 these pistons are water tight so that no water leaks into it and they are frictionless they are also frictionless so these things you should mention in the construction now what happens now things become simpler once you write this now you have to explain how this works so it is working I will write here it is working so this is the principle on which the hydraulic lift operates then you write construction of it and then you define working so what happens here you apply a small amount of force and the area is small over here so the pressure applied P over here is F1 divided by A1 and here area is A2 so I am initially only saying that A2 is greater than A1 now what happens this pressure is same as per Pascal's law the same pressure will get transmitted from one place to the other place so here also what is the pressure here also the pressure is P a force would be applied in the upward direction what would be that force? force F2 would be pressure multiplied by area A2 why because here pressure would be force applied divided by area A2 so I am writing force F2 is pressure divided by area A1 now how much it is pressure is equal to F1 divided by A1 into A2 so you should write that force 2 should be equal to F1 by A1 into A2 now as A2 is greater than A1 F2 will be greater than F1 so depending on the cross sectional area or depending on the rectangular area of A1 and A2 this force is more than force F I mean force generated is more than force applied so if I keep this ratio of A2 and A1 A2 by A1 very very big by applying only very small amount of force very huge amount of force can be generated by the usage of hydraulic lift so what we need to write in hydraulic lift in hydraulic lift first we need to write principle in principle I have told you to write 2-3 things I will just repeat it for you so that you write principle here so you write Pascal's law and then you write its uses that for heavy lifting heavy load and then you write one of the most important things that it is force multiplier you write it in the beginning only so that the examiner is very much aware that the person knows the answer the second part is construction this is not given in the books like this so construction you should write cylinder C1 and C2 then you should write that between this there is a fluid then you will say piston P1 and P2 they are water tight and they are frictionless after this you should just see that by piston 1 you are applying force F1 so pressure created would be F1 by A1 and here also pressure would be P so here force generated would be P into A2 which is F1 A2 by A1 you know that A2 is greater than A1 so F2 would be better than F1 this is what you should write that will give such you full marks now let me move to another uses of Pascal's law another application of Pascal's law which is hydraulic brakes so first of all look at the construction of the hydraulic brake so what is there in the construction in construction as the figure is showing over here a hydraulic brake consist of a tube so this is your tube T here so this is your tube T here this is your tube and it contains brakes so this complete arrangement is your tube here is the foot pedal where you apply the brake now what happens one end of the tube is connected to master cylinder so this is your tube this is your this is also the tube where fluid is there so the tube I am talking about is here this is the tube and one end of the tube is so construction first thing I will write as that tube two ends first end is connected to foot pedal and the second is in is connected to master cylinder and what happens is now you should write that this master cylinder is connected to fluid tube or fluid pipe so here you have special fluid special fluid pipe now this fluid pipe as shown in the figure is is connected to wheel cylinder so this particular portion is known as wheel cylinder now what happens in this wheel cylinder two pistons so you see here at the brake here there would be two pistons p1 and p2 and these are the two brake shoes so what I have explained it now I have told you that there is a tube tube one end of the tube is connected to the foot pedal the second end of the tube is connected to the master cylinder the end of the master cylinder is connected to the special fluid tube or special fluid pipe and one part of this fluid pipe is connected to the wheel cylinder now at the end of the front on the both side of the wheel cylinder we have pistons so piston p1 and p2 is there then on the wheel on this brake arrangement there is brake shoes and then we have springs so after this once you have explained this construction we will go to working before that you should also write principle of working so principle of working is again Pascal's law so once you have explained Pascal's law you should go to construction and in construction what you should do is you should say that one end of the pipe connected to foot pedal and cylinder then fluid pipe is connected to wheel cylinder then we have pistons p1 and p2 then we have brake shoe and spring and then you should go to now working so in working what should be defined as once somebody presses this pedal so what will happen once this pedal is pressed this tube is pressed so what happens the master cylinder is pushed due to the master cylinder is pushed there is some pressure applied on this fluid so whatever pressure is applied here the same pressure would be here due to Pascal's law so this pressure gets transmitted here once the pressure gets transmitted here through this oil piston p1 and p2 would be pushed outward so the pistons here p1 and p2 they will be pushed outward so what will happen once they will be pushed outward this brake shoe will start constricting against each other so what will happen is the brake shoe will get pressed against this internal rim so once this is going out this will start getting pressed against this inner rim so this compression will happen in this particular direction so this is direction of compression I will draw it once again so once this is going out this brake shoe will start getting compressed inside this or towards this internal rim due to this compression what will happen is this spring will get compressed and as this spring will get compressed due to compression in this particular spring the wheel will start rotating because it is getting compressed wheel will start rotating because less force would be applied over here so wheel will start rotating slowly and hence brake would be applied so then you need to go to advantages of hydraulic brakes so what are the advantages of hydraulic brakes the master cylinder transmits equal pressure so hydraulic brakes operate uniformly and hence skidding will not happen so braking will happen uniform braking and hence it will prevent skidding this is the first use advantage second is control of the vehicle so what do I mean by control of vehicle so on the pedals I apply very small amount of force and this small amount of force exerted by me creates larger force here which oppose the movement so this wheel drum this complete wheel drum would be more balanced as I am not pushing it with the brake paddles much it will be balanced and the required stress will also be created over here so which will enable me because the pressure is getting transmitted equally and uniformly it will enable the driver to balance the vehicle so you have to write two things properly that it creates uniform braking because the pressure is transmitted as this creates uniform braking the vehicle is controlled because small amount of force applied on foot pedals will act as a force multiplier on the drums of the wheel and hence the driver will be able to control the vehicle properly now let me go to Archimedes principle so what do I mean by Archimedes principle so when a body is partially or wholly immersed in water it suffers apparent loss of weight which is equal to weight of liquid displaced what is it trying to say is that suppose I put a floating form or something and it is floating over here or certain other object is there or even if it is fully immersed so when the solid will go inside the volume of the solid remember this is very important for numerical volume of the solid will be equal to volume of the water displaced and what do I mean by volume of the solid whatever water is displaced by solid so volume of the solid in water is equal to volume of the water displaced this is true in all the cases now what we need to do is that we need to prove this that how this is possible so suppose I have a particular solid and its volume is V and density is rho so weight applied by W of this solid would be rho's mass into G and mass is volume into density so I am writing it V rho G now one way to explain Archimedes principle is that once this solid goes inside the water so an upthrust is applied on this particular solid ideally what will happen is Newton's third law that it is or it is it is creating some kind of disturbance in the fluid so what happens is whatever if it is at balance level so whatever weight it is applying here the weight would be applied on it and that is called upthrust or it is also called buoyant force direction of the upthrust as it is known by the wording itself in the vertically upward direction now if a solid is immersed here what would be upthrust the upthrust would be weight of the liquid displaced so I told you that solid if it is having volume V and weight the volume of the solid in the water is equal to volume of the water displaced so volume of the water here will remain V suppose the density of the sorry suppose the volume of the liquid is V and density of the liquid is rho so weight or upthrust applied by this liquid would be V rho G so total force acting if I apply or if I make a point diagram of this solid so in lower direction V rho G is acting and in the upward direction V sigma G is acting so what is the net force acting over here which I will call net weight is equal to V rho G minus V sigma G so in the air the weight of the solid was V rho G in the water the weight of the solid is V rho G minus V sigma G so what is the change what is the reduction V sigma G so this is equal to I mean the reduction in the weight weight is equal to upthrust applied so it suffers apparent loss which is equal to weight of the liquid displaced what is the weight of the liquid displaced this much so now Arch Midi's principle we have already proved let us go to relative density now what is relative density relative density is ratio of density of substance density of water so you take density of anything so density of suppose let's take mockery so suppose density of mockery is rho M you divide it by density of water it becomes the relative density of mockery as simple as that so relative density I will discuss later also what happens in case of relative density is I told you only rho divided by rho mockery divided by rho W now in this particular case what happens is relative density of solid can also be taken in terms of weight so how because volume remains the same for both of them and you multiply Z in the numerator and denominator this becomes weight of solid this becomes I write here weight of solid in air divided by weight of or you can write that weight loss of solid in water because this is so V rho Mg divided by V sigma g so I just explained you that V sigma g is the weight loss of the solid in the water so you can write that you can either write that weight of the water displaced or the upthust or upthust is equal to the weight of the liquid removed so weight of weight loss of solid in the water so we just proved that V sigma g is weight loss of solid in the water so you can explain it in any manner you should remember both of these formulas from the exam perspective now let me go to another topic which is law of floatation now what is law of floatation so law of floatation states that a body will float in liquid if weight of liquid displaced by a most part of body is equal to or greater than weight of the body so what do I mean by this is when suppose this is a beaker there is a liquid here let me make it once again so suppose this is a beaker and I have a liquid here now what is the law of floatation telling me that body will float in liquid if weight of the liquid displaced by a most part of the body is equal to or greater than so what it is saying is that it will only float when the upthirst is lesser than the total weight of this body so that this upthirst is either it is equal or more than this so what happens is whatever liquid is displaced by it it should be equal or greater than so what happens is if the density is rho here so v rho g is the weight applied over here now what happens v sigma g is the upthirst force if v sigma g is more than v rho g only then this or only when that will float or when it will get submerged it will get submerged when v rho g is equal to v dash sigma g I am taking different volumes because a few part can be here and that can be outside the liquid so what happens over here is let me just change the color what happens over here is v rho g which is the submerged part or in equilibrium whatever volume of the solid is and the density of the solid is this v rho g should be equal to volume of the liquid displaced multiplied by density of the liquid multiplied by g so in this equilibrium only the floatation of the body will occur if this v rho g is lesser than or v dash rho g is lesser than this v rho g it means that weight of this particular solid is enough for it to go and sink over here so it will not float it will go and drown inside the water so now this g can be cancelled from here we can write that v by v dash is equal to sigma divided by rho so this is what the law of floatation is now let me explain you two different things so what is that that is hydrometer what is an hydrometer so first of all I will tell you the principle on which hydrometer performs so I am always telling that whenever you have to write such answers you need to write the principle this is based on law of floatation what is its uses uses is to find out relative density of a liquid so what happens over here is generally if you will see a hydrometer so construction of the hydrometer if I tell you the construction of the hydrometer is something like this so a pipe would be like this which is called stem and then I will have a bulb over here and bulb will carry certain shots into it so this is a lead bulb and so let me write it this is A this is B and this is C here I have shots so this is the construction so if you have to write this how do you write this the common form of the hydrometer so you should write like this that in this form of the hydrometer it consists of a narrow uniform so this is a pipe which is called which can be written as narrow uniform stem and it has been made in such a way that the markup to which a liquid will sink will correspond to the relative density so why these markups are there on this stem is to show the height or the depth to which the sinking of the liquid will happen and depending on that the relative density of the liquid would be found out here I have a bulb B and at the bottom this is another bulb C which has been weighed with mercury or lead shots so this is the construction if you write only this much for construction what will happen is you will get full marks for construction now what is the principle so you should write that the cylindrical body suppose it has a volume V and height H I mean a cylindrical body of volume V and height H is floating in the liquid and it is submerged up to height H so I am saying that it is only submerged this complete height is H and this has been submerged only up to height H so what happens is this complete volume can be written as area into height H so the mass of this solid can be written as A into H density of the solid rho multiplied by J G should be equal to the volume of the liquid displaced so volume of the liquid displaced area remains the same but as it is only submerged up to height H dash hence volume of the liquid replaced would be A H density of the liquid is rho multiplied by G so this comes out to be A H dash sigma G so A A gets cancelled G G gets cancelled H rho comes out to be equal to H dash sigma so H by H dash is equal to sigma divided by rho this is the principle on which if we find out this particular ratio we will find out we will find out the relative density so what happens is in a variable immersion hydrometer which is there in your course this cylindrical object will be made to float in water and the liquid in which the liquid of which the relative density has to be determined and what I will do is that I will find out the depth of the immersion of this solid cylinder in water I will find out the depth of the solid cylinder in the liquid of which the relative density has to be find out and then I will write this equation that H rho G is equal to S that rho G and I know that sigma by rho is equal to H by H dash so this is for water and this is for your this is for the liquid and this is for the solid so sigma by rho can be found out by how it is getting immersed and how much it is getting immersed in water and how much it is getting immersed in any other liquid so that's how relative density can be found out after this I move to two important topics which is surface tension so what is surface tension so surface tension is property of a liquid so let me give you an example so example is if you look at the liquid drops coming out of any any water tab the liquid looks like stopping for some time and then it comes and drops down on the surface that property that stopping of liquid coming out of the water tab for fraction of seconds and then going down to the surface is a property which is called surface tension so if you look at by definition surface tension is property by virtue of free surface of liquid at rest behaves like elastic stretch membrane tending to contact so as to occupy minimum surface area now this is perhaps the definition book is definition which has been given now how do you understand it in very layman language so try to understand whenever our needle is gently placed on surface of the water in trough so trough has to be created and in that trough if you put a very thin needle gently it will start floating the contradiction is the needle should go down and sink inside the water because the density of the needle is more than density of the water but why the needle is floating inside the in the trough because it behaves like stressed membrane and due to this property they just tend to stop for certain seconds before dropping down or before sinking down to understand the surface tension in a very proper manner we need to understand these two forces first one is cohesive force and second one is adhesive force so what happens is cohesive force is force of attraction between molecules of the same substance so same substances are attached together by certain force and that force would be known as force of that force of attraction will be known as cohesive force now adhesive force is force of attraction between molecules of two different substances like you will see that ink sticks to paper while writing why does it stick to paper because of the adhesive force working between the molecule of the ink and the molecules of the paper or water wets the glass surface and liquid is not able to wet the glass surface why because water the adhesive force of the water and the glass surface is able to overcome the cohesive force of the glass but liquid sorry mercury and glass surface whatever is the adhesive force that is not able to overcome the cohesive force of the inside the glass hence liquid will sorry mercury will not be able to wet the glass surface so this is the example of cohesive force and adhesive force now let me define surface tension after this and how does it happen so look at here surface tension suppose I make a beaker again and here is liquid in which I have created certain trough like this so just to create this and I am putting a needle here so what needle will do because it will behave like a membrane elastic membrane this will not sink this will float for certain time so suppose this is line AB and suppose one more assumption I have to make that along line AB the water molecules are in equilibrium or the water is in equilibrium fine now force acting on this line would be proportional to the length of this line so F is proportional to this is what surface tension tells that force acting on this line would be proportional to length of this line so F is proportional to L or F is equal to sigma L where sigma is known as surface tension so force is surface tension is equal to force applied on a imaginary line per unit length is equal to surface tension so if you take any liquid and take any imaginary line into it per unit force applied on that imaginary line would be known as surface tension and due to that force acting it will tend to stop for certain time and then it will drop so next particular topic and perhaps one last topic is capillary let me explain this to you so the next topic is capillary capillarity so what is capillarity so I will first write example and then perhaps you will understand the example is a bloating paper soaks ink this is one example first example second example is oil rises in long narrow space then third we use towels to dry our skin these three examples I am happening what is happening some kind of liquid is getting transferred from one substance to another substance here ink is getting transferred I mean ink is getting soaked in a bloating paper oil is going inside a narrow space and towel is soaking the water from our body why does this happen this happens due to capillary movement so what is capillary movement it is defined as the phenomenon of rise or fall of a liquid in a capillary tube in comparison to the surrounding so what happens is a very very small very thin very infinitely small thing like I mean as thin as hair and this kind of this kind of tube tube as thin as hair is known as capillary tube so this hair like thin tube is known as capillary tube now what will happen what is the property of this capillary tube so suppose I have a glass capillary tube and when the glass capillary tube is dipped in liquid and both the sides are open and what happens is then there are two conditions if liquid is such that it is able to wet the wall of the tube so suppose this is the tube both sides open I have immersed in liquid if the liquid is able to wet this tube then the liquid will rise above and if the liquid is not able to wet this tube then the liquid will go down this is very important so if wetting is happening then liquid will go up if wetting is not happening then liquid will go down and this particular phenomenon of water going up or down depending on in the capillary tube depending on whether wetting is happening or not is known as capillary this phenomenon is known as capillarity so one very important example of capillarity is how detergents are able to take out grease or any other dirt from our clothes so normal water will not be able to take out dirt or if a grease has been applied on your white shirt it will not be able to take it out why because capillarity movement is not happening the grease is not getting soaked up in the water but once you apply the detergent helps the capillary capillary movement and the grease comes out with the help of detergent in the water and our cloth becomes clean so if capillarity movement has been asked capillarity has been asked in your example you should give these 3-4 examples you should explain that thickness explaining thickness is very very important you should say that the thickness should be here like so that is it now let me move to the last topic of today's class which is viscosity so let me go to viscosity now what is viscosity? the property by virtue of which a liquid opposes a relative motion between its different layers so what happens here I am making different layers of liquid and then I will explain viscosity to you so these are the different layers of liquid example is how do I start viscosity is you take water in a bucket and you stir it if you stir it you will see the water flowing for some time and after some time the flow of water will stop and the water will become standstill now how does it happen? why does the moving water stop moving why does the velocity of water vanished in some time? it means that somebody is reducing the speed of the water velocity of the water as soon as it was stirred it was given certain velocity after some time the velocity became zero it means that some resistance is there in the velocity of the water from where does that resistance of resistance is coming in the velocity of the water so what happens is different layers of water oppose movement of each other so you try to understand the water at the surface would be immobile so here the velocity would be zero and as you will go up the velocity of the water will increase the highest layer of the water which you will outside from here will have maximum velocity why does it happen? it happens because when the two layers this layer and this layer will interact so this particular outer layer does not have a layer above it to restricts its motion but any layer inside it will have more number of layers around it to restrict the motion hence the outer most layer will have the maximum velocity any layer which is inside it will not have that velocity because the resistance to the flow is more now what happens if I talk about two consecutive layer so this lower level of the liquid will try to reduce a tri-flotation of this water level above it it will try to reduce the velocity and what this upper level will try that this lower level also comes along with me so what is it doing? this lower level is applying a force if velocity is in this direction it is applying a force in this direction and this upper level is applying a force in this direction its own velocity during this phenomenon both the layers behave in such a way that they tend to reduce the velocity of each other and the phenomenon of different layers opposing relative motion of each other is known as viscosity so viscosity can be defined as the property by virtue of a liquid opposite relative motion between its different layers is known as viscosity so I have explained viscosity properly to you over here where I have shown what happens between two different consecutive layers why the upper most layer will have maximum velocity because there is not much disturbance over there when you come inside the water there are different layers above and below it which creates hindrance in the movement of that layer hence the velocity keeps on decreasing at the lower level and between two consecutive layers the upper layer will try to take the lower level along with itself while the lower level will try to reduce the velocity of the upper layer in this phenomenon both of them tend to reduce the velocity of each other and hence this viscosity works between the viscosity works what viscosity works in the liquid now the other topic in viscosity is or here is equation of continuity so what do I mean by equation of continuity I will just explain it to you so suppose I have let me make the so what happens I have a pipe of varying cross section you see here it is very wide here it is very narrow so this is a pipe of varied cross section now what happens is I have a non viscous fluid in it so what do I have it non viscous fluid non viscous non compressible fluid inside it this is section A and this is section B now what happens is suppose this can be area of cross section here is A1 and area of cross section here is A2 now suppose velocity of the fluid here is V1 and velocity of the fluid here is V2 what we observe is that area multiplied by velocity remains constant throughout the cross section and that is what equation of continuity is so equation of continuity tells that in a pipe of varied cross section area into area of the cross section multiplied by velocity of the fluid will remain constant so it means that what does it tell me it tells me that A1 by A2 is equal to V2 by V1 it means that A is antiproportional to B so if the area of the cross section would be more it means that velocity of the fluid would be less and if the area of the cross section if I tell you which one is more V1 or V2 see here area of cross section is more and here area of cross section is less so as A1 is greater than A2 so V2 would be greater than V1 so this is greater than 1 because A1 is greater than A2 so this is greater than 1 so V2 would be greater than V1 it means that wherever area of cross section is less there the velocity would be more so this is what equation of continuity is equation of continuity tells me that area of a cross section multiplied by velocity of the fluid in that area of cross, in that cross section remains constant. You make this, you explain this, you will get the full marks. So this is it in today's class. I covered properties of matter and then I covered a portions related to mechanical properties of fluids. Please revise it properly. Most of the time you will see that questions related to these topics would be based on certain principles like Archimedes principle, Young Pascal's law in properties of matter, Young's modulus and the most important topic in properties of matter is stress strain curve. So go through these topics very properly and try to write answers so that it gives you confidence while writing your board examination. Also when you write answers, you take five questions from end of the book or from any mock test and you start writing it, you will find your problem areas and then you'll start working on it. Once you'll start working on it, your marks will automatically improve in the board. So thank you so much for joining the class and wish you all the best. Thank you.