 Hello friends and welcome to another session on physics. So in the previous session, we talked about contact and non-contact forces, isn't it? Now in this session, we are going to understand and in subsequent sessions, we are going to understand about the reason why these forces exist, whether it is a contact force like tension, friction, normal, whatever we discussed last time, or non-contact forces. So we are going to now see the reason why these forces exist or whatever in sciences we have observed or we have discovered the reasons why these forces exist. And we will be talking about four basic fundamental forces which are responsible for all other forces which you see in your day-to-day life. So let's talk about all of them one by one. Now there are four fundamental forces as I talked about. The first one is the gravitational force. So all of you know Sir Isaac Newton in 17th century, there was a plague breakout and all the universities were closed and he had to go back to his native village where he was pondering on various natural phenomena and he came across this discovery where he figured out that any two objects in the universe attract each other in some relation. So that's what is gravitational force. Then later on we talked or we found out that there is another very fundamental property of any matter which is called charges. So charges lead to force of attraction and repulsion. So there was a French scientist called Coulomb who figured out that any charged particle will either attract or repel depending on the type of charges it carries. So this was discovered in somewhere let's say 18th century and we have another fundamental force called electromagnetic force now. Now similarly later on as we went into discovering into nuclear sciences or we could figure out that there is something called atom with which the every element on this or in this universe is made up of then we delve deeper inside it and we figured out that within atom itself there is something called nucleus where there are protons and neutrons and other subatomic particles. So there we saw that there is some bit of attractive force which keeps all these positively charged protons together and neutral neutrons together and that was discovered later that is there is something called nuclear strong force which exists which is responsible for this stability of nucleus. So that's another fundamental force which somewhere in 19th century and then early 20th century we had a lot of work going on. Then the last one is the weak force you'd have heard of beta decay process or where one particular subatomic particle like proton gets converted into an electron and some other subatomic particles when I say subatomic particles meaning particles which exist or whose size is lesser than the size of the atom. So when this conversion takes place for example you'd heard of nuclear fission reaction right. So in let's say creation of an atomic bomb there is a reaction which takes place at nucleus level that's called a nucleus nuclear fission reaction where one nucleus within the atom splits into two parts or multiple parts to you know and in turn give a lot of energy. So there is where when some subatomic particle gets converted into some other subatomic particle there is another force involved and that's called weak force. So basically so far the research in the in the in the vertical of physics we have four basic fundamental forces gravitational electromagnetic nuclear strong force and weak force. Now what we're going to do is we are going to understand each and every force all these fundamental forces one by one and try to see how these forces lead to other contact forces which we came across in the last session. Okay so let's take up gravitational force now. So let's talk about force of gravity so you can see there is one object with let's say capital M mass there is another object with small m mass and this is how we are showing so capital M and small m so two objects are there with first one having capital mass M capital M and the other object having small m as the mass right and now let's say they are separated at you know they are they are placed at a distance D from their center to center let's say you know there is a big ball kept somewhere and the other ball or round shape stuff kept somewhere else and the center to center distance so what is center this is the center right so this is center here is another center here so center to center distance is D okay so this is important thing to be noted that we are talking about the distance from one center to the other center is D. Now let's say there is some arbitrary shaped object kept like that. Here you will come to know later that there is something called center of mass so every object will have a center of mass and from center of mass to another object let's say another object is lying over there and its center of mass is here so from center mass to center of mass this distance is what is D okay so that's what we are going to take D as now so now the force of gravity as per Newton is you know these two objects will attract each other mind you I am saying attract yeah so we are not going to talk about any situation where the force of gravity can be repulsive also latest discoveries in in the again subject of physics there are indications where there could be repulsive gravitational forces but that right now we are not going to touch upon so for the time being in classical mechanics realm that is all or what we say as Newtonian mechanics where whatever Newton gave there we consider gravitation force to be attractive in nature so you can see here I have so I have shown here FAB now what does this mean FAB means the force of attraction applied on A by B and similarly here you can see force of attraction applied on B by A right and you can see they are along the line joining the two centers is it the line joining the two center this is the line joining the two center so keep this in mind and they are equal and opposite in nature that means magnitude wise they will be equal all of you know forces are vectors so magnitude wise as in the amount wise the two forces are going to be same but direction wise they are exactly opposite that is one important criteria you must understand for understanding force of gravity so what did we discuss we discussed forces are in you know along the center to center line and they are equal and opposite that means if you are there in the room and if your brother or sister in the room are there in the room then you are attracting your brother and your brother is attracting you as well like that and the the force of attraction is same equal amount but opposite in direction okay now so you can see this is mass of body A this is mass of body B and distance between A and B is D and what else so force on A by B that's what I discussed and force on B by A is it it now let's talk about the nature of force of gravity so it's attractive in nature no doubt about it that's what we discussed so discussed so far and then two objects attract each other with same magnitude of force that's what also we discussed that the amount of force is going to be the same if this is 5 Newton let's say for an example so this also has to be 5 Newton there is no way one is attracting the other one with 5 Newton and the other one is attracting the first one with 7 or 8 or even 3 Newton no both of them will be same in magnitude but yes they are exactly opposite in direction now so acts along the line joining the centers of the two objects we discussed that as well then directly proportional to the product of the masses of the two objects this is something where we will delve a little bit deeper so this is where the mathematics part of this particular part of physics starts right so directly proportional to what is directly proportional to the force is directly proportional to the force which is there is directly proportional to and directly proportional sign is like this something like that right so directly proportional to the product of the masses that is product of the masses is capital N and small m. This is the product of the masses and also inversely proportional to the square of the distance between the two objects, square of the distance between the two objects. So, the distance was d. So, d square will be the square of the distance, is it not? So, it is being said that this force is inversely proportional. So, inversely proportional is nothing but directly proportional to the reverse of whatever it is or inverse or sorry, reciprocal of whatever it is. So, let us say inversely proportional to d square will mean it is directly proportional to 1 upon d square. So, we will explain you what is directly proportional and what is inversely proportional for the time being just keep this in mind. So, now let us say these are two objects placed and the arrow denotes that these two objects are attracting each other. Then the third object comes into picture and then you can see the third object is being attracted by both of them, both of the first two objects and in return the third object is also pulling the first two objects. So, they are attracting each other. So, you can see these are interactions which are happening. So, there is one interaction here, there is another interaction here, there is third interaction here, interaction as in these objects are attracting each other pair wise now comes the fourth object obviously this fourth object will interact with the first three and here is the interaction line that is now the fourth object is being attracted individually by the first three and all the first three individually as are now being attracted by the fourth one now comes the fifth one and hence the interaction level keeps on increasing I hope you understood what is interaction so every pair will interact with each other right so there will be there are five pairs so you can see how many you know lines are drawn so you know in mathematics we say five C two there will be ten lines which you can see you which are you know so there are ten pairs of or ten interactions happening so you can count one two three four correct five six seven and then eight and then nine and then one more ten right so these are ten interactions or ten forces of equal magnitude but opposite directions are acting on each other so this is what it means so hence if there are lots of particles or bodies there each pair will attract each other that's what is the learning now so let's now talk about this in little mathematical term so this is what I said FAB will be equal to FBA and let us say this is equal to F so F is the variable which denotes the amount of force with which they are attracting each other and then as I told you F is directly proportional to M into M the product of the two masses F is also proportional to 1 upon D square this is also called inversely proportional inversely proportional proportional proportional what is proportionality we'll talk about that inversely proportional to D square is written as 1 upon directly proportional to 1 upon D square and then finally if we club them together so this is what it will be so F is directly proportional to M cross M or M into M divided by D square okay this is what was given by Sir Isaac Newton this is what was observed by Sir Isaac Newton and today we learn this as law of gravity now so this relation between the masses of two objects distance between them in the force of attraction between them was given by Sir Isaac Newton okay and he was just 25 years of age when he was doing all of this in London or in England okay now so what is direct and inverse proportion so let's talk about it briefly so suppose this is the same setup where the body of mass capital M and small m is there and let's say we are to perform an experiment okay where we can change the mass of the object how can you change the mass of an object basically you replace the object with some other mass okay so let us say we did this experiment so what did we do we kept on changing the you know the masses of the two object right that means we kept on replacing with higher mass object so let us say when M was 1 kg and small m was 1 kg these are in 1 kgs and I purposefully not written the unit because it just a dummy experiment just to explain what direct and inverse proportions mean now if one and one are there then let's say assume that the force was 100 Newton I'm just giving you an example so let's say 100 Newton so what is meant by direct proportion then let's say if I increase the mass or double the mass one of the masses you can see the force also has been doubled so doubling one doubles the effect so doubling one cause doubles the effect that is what is called direct proportion if I increase it to 3 you can see it has become tripled isn't it now I keep it back at 1 and now I am doubling this mass the smaller mass and you can see again the effect is doubled and in this experiment I'm assuming that I'm not changing the distance I'm not touching the distance I'm only changing one variable and which is the mass of the object and as I triple the smaller mass object again you can see the effect is tripled right and when I double the first one and triple the second one the net effect is 6 times that is 2 into 3 times right so hence we can clearly say that f here the force is directly proportional to the product of masses that means if you touch the product of mass in increasing order the force will increase if you decrease the product of masses by replacing with suitable masses you will see the force getting decreased this is what is called directly proportional so for example another example from your day-to-day life for direct proportion would be that as you you know grow in age your height grows up so your height is directly proportional to your age right that's you know till up till a particular age you as you grow your height also increases so height is directly proportional to your age isn't it now let's talk about inversely proportional so what is inversely proportional so you can see now I have kept m and n constant so I let's keep the masses constant and let's try to vary the distance so how can I vary so you can imagine the first one was here and then you can bring the second one closer or you can bring or you can take the second one farther away right so this is what we are doing so first let's say this is d1 and this is d2 without changing the masses that is mass remains the same you just simply keep changing the position of the two objects so mass remains the same only the distance varies so let us say the distance was one meter apart and again the force of friction sorry the force was hundred so you can see the net effect is hundred only right now when you change the distance to or double the distance now the force goes down that is hundred divided by two square so one upon two square times it happens right so it becomes 25 that is what is called inversely proportional so as you are increasing the distance your force is going down can you see that here as you are increasing the masses the force was going up so hence one was direct and now this is indirect or inverse proportion right now as you moved up for distance become tripled and this becomes hundred upon three squared now it's the it could be you know only hundred upon three as well but the Newton discovered that it is not hundred upon three actually if you triple the distance between the two objects what I mean let's say initially was one meter okay this is what we are saying so initially the two objects were set aside or by a distance of one meter and there was a force of attraction of hundred Newton in them okay now let's say you kept the first one at the same location and you tripled the distance of the second one like this so let's say this one is three meters three meters then what happens you will see the net force of attraction the attraction attractive force gravitational force is now hundred upon three square or hundred upon nine Newton so meaning thereby you go farther away your force of attraction drops so you can see the hundred Newton force now is only eleven point one one Newton similarly then I went on to you know in I increase the distance further apart and you can say there is a drastic drop in the force of attraction again and when I took it to five meters it became four so this is what is called inversely proportional that is you are increasing distance and the force is dropping in the direct proportion when you increase the mass the force keeps on increasing so I hope by this experiment description you could understand what is direct proportion and what is inverse proportion so what did Newton discover Newton said that the force of attraction will increase if you keep increasing the masses that means indirectly heavier the masses more will be the attractive force lighter the masses lighter will be or lesser will be the attractive force and on the other side closer the objects more will be your attractive force farther the object lesser will be the attractive force is it not now so this is the final summary of force of gravity and then the directly proportional sign is replaced by an equal equality sign and now this is what is called force or gravity law Newton's law of gravity where force will be equal to a factor g which is called a universal gravitational constant multiplied by the two masses divided by the distance squared correct what is the value of g the value of g was 6 or is 6.67 into 10 to the power minus 11 Newton meter square per kg square so please remember the unit also this is a unit with unit constant and it is universal why it is called universal because its value is not going to change with time or with position location space whether you do the experiment in India or in United States or in moon or in some other galaxy you will always see g to be the same value now Henry Cavendish was the first scientist who actually calculated this value of g some hundred years after Newton's life or when Newton existed on this planet right so hence now we know that any two object if the masses are given and if the distance between that their centers is known then we can calculate the force of attraction by which they attract each other so 6.67 into 10 to the power minus 11 is universal gravitational constant its unit is Newton meter square per kg square it's very easily derivable as well as in why this unit is like this because force has a unit of Newton isn't it and then g if you see if I if I use this particular relationship so g can be written as f into d square divided by capital M into small m simple arithmetic here and you will see this is what it is and clearly force unit is Newton d is meter so meter square is will be the unit of d square divided by unit of mass is kg and this mass is also kg so kg squared isn't it and hence this is the unit of g okay so keep this in mind my dear friend