Hey everyone, welcome to homeschool and welcome back to the chapter gravitation the most interesting and the most requested chapter isn't it. So if you look at my previous video where I have explained what exactly is the gravitational pull or gravitational force isn't it. So all the fundamental aspects of gravitational force we have discussed and also we have discussed the universal law of gravitation. So that is the most fundamental aspect of the chapter.
And many students were asking me, ma'am, please explain in a deeper way how moon can rotate around the earth. So I said, if this is a earth, right? And the moon always rotates around the earth, right? And I also told you the reason that keeps moon revolving around the earth is a type of gravitational force called centripetal force, centripetal force.
Okay, so some of you have asked me ma'am, please kindly explain the deeper aspects of centripetal force. So why does the moon does not fall on earth so when earth is attracting moon towards itself it should fall towards the earth right but it never falls on earth instead it revolves around earth elliptically in a circular way almost in a circular pattern right so this particular aspect i am going to tell in this video and before you see a further video everybody first and foremost like the video if you are getting at least one percent benefit from this video then you should definitely subscribe to my channel benefit from the video please do like the video and share the video with your friends okay so let's see what is the reason behind the moon revolving in a circular way see here let me take this as earth and imagine here is moon right okay i told you this moon is pulled towards the earth that means it should come towards the earth it should come in this direction right if it is here so what happens is at every moment it will lose the chance of falling towards earth okay at every moment i repeat once again at every moment the moon misses okay let me write it here at every moment you know moon moon misses misses a chance misses a chance to fall on earth ma'am how does this happen right see see it should actually fall on earth in this direction but what happens is somehow it get missed that's what we are lucky enough because it is getting its chance to fall on earth we people are very much lucky we are safe on earth right otherwise at every second you know what if it falls on earth then earth doesn't exist because the moon collides the earth once and it's over in the universe right so there would not be any life on earth so at every moment the moon misses a chance to fall on earth that is what the wonder of the universe here okay so instead of you know the earth will pull the moon towards it but somehow it misses a chance it goes and it comes at this point again here the earth pulls but it misses a chance and it goes like this it comes to this point again at this point the earth will try to pull towards itself it misses a chance and goes there it deviates okay it comes to this point the earth again pulls it towards it but no it misses a chance so that way you know at every point it misses a chance to fall on earth okay so though the earth is pulling it towards its so that's how it its path of traveling is around you know in a circular way around the earth you know this this particular force between earth and moon is what we mean by centripetal force okay see if you tie you a particular for example this chop is i'll tie it with a thread and i'll i'll i'll rotate it okay so how it gets rotated it rotates in a circular manner right so that that strength of a you know thread will hold hold the chalk piece and it allows it to move in a circular manner. So that's what that kind of a is what we mean by centripetal force.
Okay. So it's why, what is the main reason behind the moon rotating around the earth without falling it on earth? At every moment, the earth will try to pull it towards it, but it will miss its chance and goes the other way. Okay. So that particular thing is making it to rotate in a circular manner around the earth.
So this is the explanation for that particular aspect. Okay, so now let us discuss the next aspect of the chapter that is free fall, which is very very important. to understand listen it carefully and it is going to be very interesting and before that if you have not liked the video please like the video because if you like it if you share it it can reach to maximum number of students when maximum number of students watches the real content even we get motivated to do more and more right so every person needs motivation so just motivate me By doing lot of likes and shares.
Okay. So let's quickly understand what exactly we mean by this free fall. See here. Free fall.
Let me write the sentence what exactly we mean by free fall. And later I will give the explanation. See. When an object.
Okay. Imagine any object which is on an on earth. Okay.
Above the earth. When an object. okay, falls, falls towards earth, towards earth only due to, only due to gravitational force, gravitational force alone, so this particular word is a key point here, only when an object falls down due to gravitational force alone, then the object, it in the sense object, it is said to have free fall. said to have free fall okay see for example I have this chalk piece okay see I'll leave this chalk piece it goes down okay so why because the earth is pulling it so this fall of a chalk piece okay this fall which is happening if it happens only due to gravitational force then such a fall of an object is called as free fall let's understand this in a much better way suppose if this is the center of earth okay so this this entire thing is hurt so on earth you have this big building so on this big building there is a person there is a person okay so holding a stone and he is throwing that stone okay stone and and he is also holding a paper okay so he is holding a piece of paper and he is also holding a a stone both of them are falling onto the ground okay so this falling objects freely only due to earth gravity is called as free fall then you can ask me a question ma'am then every every object which is falling on earth is called as free fall only ma'am uh then why specifically we tell uh it's due to gravitational force alone right so there is a difference guys see for example actually Actually speaking, see I have this paper. Okay, so I have this paper and this chalk piece.
So when I leave both of them, chalk piece falls first. Okay, so this is a stone. So this actually falls first. Whereas paper falls later.
Falls later. So can you think of what is the reason? So actually this free fall is there, no? So this free fall.
fall doesn't depend on the mass of object it is not like stone is heavier so you know it is going first onto the ground it is not that concept you know what when it falls onto the ground you know in the atmosphere you have air okay since the paper is lighter in weight the air will push the paper back so there is air so this is a paper when it falls falls down you know the air pushes it up whereas if it is a stone what happens you know it dominates that air resistance so that air pushing up is there no so air pushing up okay against the gravitational pull the air will push it up that is called as air resistance so that is actually called as air resistance okay so whenever the objects are lighter in weight they will expand experience air resistance. If the objects are heavier, they will not experience much air resistance. That is the reason stone falls quickly onto the earth. whereas paper falls little late okay so but you know here both the objects if if you you know neglect this air resistance that way of falling onto the earth due to own and only gravitational force is called as free fall okay but this particular free fall is getting disturbed by air resistance okay but in a glass chamber suppose you remove the air in the atmosphere so you take a big glass jar you take a big glass jar for suppose okay so you throw a stone and you also throw a paper both of them fall with same speed you know okay because both of them are experiencing only gravitational pull okay so in between there is no something called air resistance okay or air push isn't it so free fall this free fall actually do not depend on the mass of the object you know so two objects if you take when you freely put it down both of them will reach the ground at the same time okay so when the objects are only attracted by gravitational pull if they do not have any air resistance or nothing then both of them irrespective of the mass irrespective of the size or whatever both of them fall the earth they reach the earth with the same speed you know they reach at the same time okay so this free falling of an object only under the influence of gravitational force is called as free fall okay so now little let's discuss more detailed aspects of this free fall here see so now uh let me take the same situation so this is our earth a person throwing a stone and it is reaching the earth i mean center of the earth is pulling that stone towards it okay see uh as the stone reaches the earth as it nears the earth you know its speed will increase you know what as the stone falls onto the earth what is that how is the stone falling onto the earth it is due to gravitational force right so it is due to gravitational force that is f Let me call this gravitational force as F.
So whenever force is there, you know, that object will obviously experience so-called acceleration. Acceleration. Isn't it? See here, the stone is falling from here to earth.
As it nears the earth, you know what actually happens? Velocity changes. Its velocity changes.
And velocity increases as it approaches the ground. Okay. So here. Here the initial velocity is 0 but the final velocity gradually it increases as it reaches the earth that you remember.
So velocity changes. Rate of change of velocity is called acceleration. Okay so that means object here object experiences object actually experiences acceleration. So why is an object is experiencing acceleration?
Because of this gravitational force. isn't it? So if this gravitational force was not there, object will not experience that acceleration, okay? And this particular acceleration remains constant for every object that is falling onto the earth, okay? So that particular acceleration which is experienced by the object due to gravitational pull is called as acceleration due to gravity.
gravity acceleration due to gravity very very important and this acceleration due to gravity is indicated with the letter g okay so this acceleration due to gravity that is g is equal to 9.8 meter per second square okay so this is the value of acceleration due to gravity that means at every second the acceleration increases of how much nine 9.8 meter per second. And again, from this point to this point, acceleration increases for about 9.8 meter per second. From this point to this point, if it reaches, acceleration increases for about 9.8 meter per second. So like this, when an object is falling onto the earth, the acceleration experienced by this object is how much?
This much. And this is what we mean by acceleration due to gravity. So now let me give you the formula. uh to calculate the g value i'm showing you how this value has come okay so Let me derive a formula for calculation of G here. So we all know acceleration is always due to force.
So here the acceleration of an object is due to gravitational force. So we know the second law of motion that is F is equal to ma. m is mass of an object, a is acceleration. So here let me change this formula as F is equal to mg. So here a instead of a.
I will consider g. g is what? For a freely falling body the acceleration due to gravity is g.
Okay and in the previous class we have learned the formula for gravitational force that is f is equal to capital G capital M small m by d square whereas this is gravitational constant and this m is mass of a bigger object mass of smaller object or I can say this m let me consider here as mass of mass of earth okay and this m is mass of an object mass of an object which is freely falling onto the earth okay so now I'll substitute f here f is equal to mg you know so instead of this f let me write it as mg mg is equal to capital g capital m small m divided by d square and this m and this m gets cancelled if I bring it here it goes to a denominator this this and this gets cancelled. Okay. So now G is equal to capital G that is gravitational constant and capital M. Capital M is what? Mass of earth.
Mass of earth. Okay. Divided by D square. D square is what? D is what?
Distance between the object and earth here. Okay. So suppose if you take this is earth.
So whenever an object is there on the surface of earth or above the earth, it's a particle. you know the distance from the object and the center of earth is nothing but the radius no so even it is at equator it is r even the object is on pole it is r only okay so now instead of d i will take r r square okay so here r is what radius radius radius of earth radius of earth even if it is is a big building on earth okay so ma'am you can ask me ma'am then the distance from the center to this building is not equal to radius no building is little height you can tell but any object is just like a pinpoint on earth right so as compared to the size of the earth object's size can be negligible so how whatever the big building it is you know it is just a pinpoint on earth so that's why we neglect we directly consider the radius only as the distance between the earth and object here okay so this is the formula okay so through which you can calculate the g so when i put the value for gravitational constant it's a constant 6.7 into 10 power minus 11 and when you substitute the value for mass of earth when you substitute the value for radius you know you will actually get this value that is 9.8 meter per second square. Okay.
So anyway, that's not important. All these values are constant. We can put it up. They won't change. Okay.
So G value, this is what you get, which is also constant. Do not change for any object. Okay.
So from anywhere on the earth, you make it fall onto the ground. You know, it will accelerate with the same value. Its acceleration remains constant every time.
Okay. So this is what we mean by acceleration due to gravity. important value to be remembered. And actually speaking, you know what?
The radius at equator is more. At equator, the radius. Let me write the point here. So, just remember this. At equator, you know, radius is very high.
When radius is very high, g's value is lesser. Okay? At poles, at poles, radius is less.
so G's value is little higher okay so at poles if you go the value of G will be little higher than this value clear but anyway here in this chapter during calculations we consider this value only even if the object is at equator or if the object is at poles doesn't matter for us we consider this so sometimes for the calculations We can take this value as approximately 10 meter per second square also. So in many of the problems you know 10 meter per second square they will take it. Okay so this is all about the free. fall and acceleration due to gravity fine so concept wise it is clear so we understood what is free fall and how this acceleration due to gravity has come and how this 9.8 meter per per second square value has come everything is fine okay so what is important here is applying certain formulas okay so they'll ask you some questions you know what let me give you the formulas about the motion of an objects motion of objects under the influence of you under the influence of gravitational pull, gravitational pull, so every object on earth, you know, when it falls or if it goes above, the motion depends on the gravitational pull, I mean, there the objects will always experience the acceleration of around g is equal to 9.8 meter per second square, okay, so In the previous chapter, we have studied three equations of motion, right? So let me write all those equations now.
These are the three equations, right? So v is equal to u plus at. Here v is final velocity, u is initial velocity, a is acceleration, t is second and s is distance, isn't it?
So these formulas we have already used and we have done n number of problems out of these formulas. Same formulas you can use it in this chapter also. Whenever an object is moving with g you know these formulas can be used so here all the formulas i'll again rewrite by including g instead of a okay so here the formula becomes v is equal to u plus gt so this formula becomes yes sometimes this yes can also be regarded as height of object height of object from earth okay so s is equal to ut plus half half gt square and this formula I can rewrite as v square is equal to u square plus 2 ag.
So here instead of a okay so I have used g for an object which fall onto a ground or the objects which go up from the ground. So whenever you have to do with this kind of motion that is object falling down and object going up. So this motion this about free fall when you are doing a problem regarding motion then these formulas you have to use and here the sign of g is very important okay so whenever remember this particular trick can help you out for solving a problem whenever an object goes goes down you down to earth, to earth, then G value has to be positive. I mean, G's value is 9.8 meter per second square. Okay.
Whenever an object goes up, goes against the gravity, goes up from earth, goes up from earth, then G's value, you should take it as negative. That means G's value, you have to be positive. to consider as minus 9.8 meter per second square okay so here the same formulas you can use to solve the problems of this chapter i mean for what kind of motion you will use these formulas what is the difference between this and this only here a was there here g acceleration due to gravity we are using so any object that is falling due to gravity falling down or going up for such object motion okay motion related aspects when you have to calculate then then these formulas have to be used okay so remember when to consider g value positive and when to consider g value negative so whenever object from up if it is falling down then it is positive from earth if it is going up against the gravity if it is going up then the value should be negative this thing you have to keep in mind okay so here instead of yes no sometimes in some of the books you will have h also so here in see we don't talk about the distance it traveled here the distance traveled in the sense height from how much distance it went from earth to up or from there if it is falling how much height it is from the ground so this is how we deal so instead of s we take height here okay so problems relating to this formula and problems relating to universal law of gravity we will discuss in the next video so hope the concept has become clear like the video and share the videos with your friends and meet you all in the next video thank you