 Now, I will talk about few concepts which will be used to solve questions which are beyond your school level. The first one is field, gravitation field. So I will start with why we need this particular term or this particular concept. So, we are done with your school requirement, now I am going beyond your schools. So suppose two point masses are there, two point masses are there, m1 and m2 are the masses and distance between them is r. What will be the force on m1 due to m2, how much that will be? It is given by gm1 m2 by r square, simple, right? Now I tell you this, now suppose you have a rod, rod of mass capital M and length L, okay? And you have a mass over here, let us say mass is m, okay? This distance is r, can you directly get the expression for force between these two? Between the rod and mass small m, can you directly get the value of the force? Just like you got the above expression, can you get it directly? Not possible, right? Okay, Shravan wrote something. Now Shravan, have you applied any fundamental while, okay? Those who are answering, have you used any fundamental or you have just guessed it? It is a wild guess, it is just a guess, okay? It is not necessarily correct, okay? So if you consider the rod made of many point masses, let us say one point mass is over here, okay? The other one is there, all right? So we have multiple point masses at different locations. Suppose this is a point mass, which is part of the rod only. I am dividing the rod into different different masses. If this distance is x, okay? And this point mass is mass is dm. The force will be equal to g into m into dm divided by x square. Now I can use this expression. This expression is valid only for point masses, okay? But in order to get the total force, this is small force df. In order to get total force, I need to integrate and find out, okay? Now there are two variables, dm and x. So I need to write one in terms of the other to get the value of total force, all right? Now the problem is that at times there could be rod, there could be some other irregular shape, there could be so many other different kinds of scenario, okay? So we need to define something which can be helpful for us to determine the effect of the distribution of mass. For example, what is the effect due to the rod at this point, okay? So basically what I'm trying to say here that the force depends on both the masses, right? Let's take an example of this only. Suppose you have two masses, m1 and m2, okay? And the force between them is a function of both m1 and m2, okay? But I want to find a function which is only of m1. So basically what I'm trying to say here is that suppose m2 is there, so m2 will experience a force, okay? Why it experiences a force? Because of the presence of m1, okay? Because if you remove m1, f will become 0, fine? Now similarly if you remove m2, force will be 0 because m2 is not there. But even if m2 is not here, there must be something happening over here because of m1, because of which if I place a mass over here, immediately it starts feeling of force in this direction, okay? So there must be something here which depends only on m1, okay? So basically I'm trying to define the effect of m1, okay? The force is also effect of m1 only. But the problem is that the effect of m1 cannot be a function of both m1 and m2, okay? So effect of m1 should be a function of only m1, okay? So I am trying to define a function which only depends on m1, okay? Now I will define a function, let's say, okay, let me scroll. So the force is gm1m2 by r square, right? So force divided by m2 is gm1 by r square, okay? So force per unit mass is a function of only m1, okay? So this particular thing, this particular expression gm1 by r square which only depends on m1 can be referred as field due to m1 at a distance of r, okay, m1 is point mass, okay? So this is gravitational field, all right? So if I define a gravitational field, if I know gravitational field is x at a particular location and if I place mass m, then all you have to do is multiply x with m, I'll get the value of force because field is force per unit mass, okay? So we have just now defined gravitational field because of a point mass. Is this clear to all of you? Any doubts? Please feel free to ask, okay? Don't hesitate. Is this thing clear? See I want to define an expression which I can treat as an effect of mass m1, okay? The effect of mass m1 is also the gravitational force, okay? Which is gm1m2 by r square but that effect depends on m2 as well, okay? I want to define the effect of m1 as only the function of m1, okay, right? So I am using the force expression only, I am using the expression of force only to define a function which depends only on m1. So what I am doing is I am dividing the force by m2, okay? So force is gm1m2 by r square. So if I define the force by m2, I get gm1m2 by r square. Now this expression depends only on m1, okay? Fine? So this expression, we call it as field due to m1 at a distance of r. So force per unit mass is the field because of m1 at a distance of r. Yes, Shushan, you can say that. See this thing will be more clear as you proceed further, okay? It will not be clear, it will not be that everything will be clear right now itself. But I want you to be, at least we appreciate the fact that we need something which depends only on m1, okay? Otherwise, what will happen is that every time suppose there is only, let's say, or you can say that suppose black hole is there, okay? Suppose there is a black hole, okay? I want to find out what will be the effect of this black hole at the neighboring places, fine? So in order to find the effect, you don't put a mass over here and then try to find the force with which black hole will pull it, right? So if you know the mass and radius of this black hole, you can find the gravitational field of the black hole, okay? Which only depends on what the black hole is, what is the size and dimension, what is the mass of that black hole. So there has to be a function which only depends on the mass which is surrounding, okay? Now let me proceed further, it will be more clear, okay? Otherwise we'll just keep on talking about the same thing over and over again. So you'll appreciate quickly why we need something like gravitational field, okay? Let's say you have a rod, okay? You have a rod which has mass m and length l. Mass is distributed uniformly over the length, okay? Now I want to find out the field at this point because of the rod. That point is at a distance of, this is at a distance of let's say d, okay? At this point, what is the field because of this rod, okay? So once you get the field, let's call it as e, the field multiplied by the mass will be the force on the mass because the field is force per unit mass, right? But the field which you have defined gm by r square, this is the field only for the point mass but the rod is not a point mass, okay? So now try to attempt this one. See it will be wrong to say that field is same as acceleration because there can be other forces also. Net force may not be equal to just gravitational force, okay? Let me do this now. So we have the expression for the field due to a point mass, okay? But then in front of us, there is a rod, all right? So what we'll do is that we can divide this entire rod into point masses, different different point masses. So let's say there is this small length dx which can be treated like a point mass and that dx, let us say that is at a distance of x from the point where you are trying to find the field, okay? So this dx can be treated like a point mass, right? Total mass is m. Can you tell me what is the mass of that dx? Dm is what? If total mass is m, the mass of this dx element is what? dx length is what? So mass per unit length which is m by l into dx, this is dm, fine? So the field over here because of dx, because of dx, the field over here will be what? I can directly use this formula because dx is a point mass. So the field, let's call it as de because that is only because of the dx, right? So this is g dm which is this divided by x square, okay? So this can be written as gm by l into dx by x square, all right? Now tell me one thing, is the field scalar or vector? Field is a scalar or a vector? See listen how it is, the mass into field should be force, right? Force is a vector, mass is a scalar. So field has to be a vector, then only scalar times vector is a vector, okay? So the field has to be a vector only, okay? Now tell me what is the direction of the field, which direction the field will be? Direction of field is same as the force would be, okay? Because mass into field is force, so it is along this direction. Now the thing is whichever dx element you take, wherever you go in this rod, all of them will have the same direction the electric field, sorry, the gravitational field. So the total field will be just integral of this, okay? And the limits will be from where to where, limits will be from D, it starts from D, the rod starts from D and it goes from D to D plus l, okay? So the total field E will be equal to minus of gm by l, integral of 1 by x square is minus 1 by x, minus I have taken outside. So this can be written as g times m by l 1 by d minus 1 by d plus l, okay? This is the field, okay? All of you clear it till now? Direction of force, direction of field will be direction of force which a point mass kept over here will experience, it will experience a force in this direction, that is the direction of field. Is this thing clear? How the field due to the rod we have derived, field due to rod is this? So once you know the field, the force at that point, suppose if field is E, if I keep a mass over m over here, the force will be what, force will be m into E only, simply, okay? So it's a good idea to derive the expression for field for different kind of shapes and sizes so that if you know the expression for field at a point for a particular geometry, if you place a mass m over here, the force will be simply mass m into field, okay? The unit for the field will be Newton per kg. Any doubts guys on this, whatever we have done just now in front of your screen, is there any doubt? Ashutosh, there is no logic as such why it should be like this, okay? We will not assume that, yes, we can derive similarly for other objects and that is what I am right now will be asking you to do.