 So as of now you are there and you can see my screen, which is a white blank screen, okay? and Why we are here for today? So we will be having an episode out of many of the center mark Okay, where for today? We will be discussing and spending our time of a dinner time of an appetizing time So as we are meeting for the first time, I am going to discuss with you the mechanical Okay, sure the mechanics portion of the physics, okay, which you have in ninth grade it includes understanding motion Okay, it includes understanding a lot of motion and it also includes understanding gravitation and all right or not This is at least where we have done in the class for few batches where I met in the last two weeks. Yes, we have also crossed the line of work power and energy Okay, so now I'll be dominantly talking about these three parts because this is common for all I am not going to talk about this work power Fine now, you know that now you know that Okay when we talk about Motion laws of motion and gravitation a major name exists over there of uncle Newton right around Uncle Newton in the very first chapter have discussed with us about the three equations of motion, which are these equals to 80 plus you or you plus 80 will work s is equals to ut Plus half a t square and v square is equals to u square plus 2 a s right So if you remember the classroom teachings either you've been in direct Conversation with me or you've been in direct con conversation with someone else Okay, then then then you know that through this the primary numericals were done and they were widely initially classified under horizontal motion and vertical Yeah, post that we jumped into the application of similar equations and vectors Okay, and we completed projectile motion. Yes or no Yeah, sir, we didn't do we didn't do This with Dira Okay, but it is not there No, sir, no problem. No problem. No problem. No problem. Thank you very much for the information But anyway, what I'm going to cover today is primarily first thing with horizontal and vertical motion Okay, so you are very much aware about the fact. I'll tackle the three chapters in three parts Okay, so this is the sole concept which exists in understanding motion Excluding the definition part right or not, you know what is velocity, you know, what is acceleration? You know, what is displacement? What is distance? How distance and displacement are different from each other and all right or not All these things you are thoroughly aware about Yeah now when we look for horizontal and vertical motion and when we study them what thing we should remember is primarily that This vertical motion Okay is By default Supported by the Chotuji Maharaj, right or not. So Yeah, whereas in horizontal motion until and unless stated Acceleration is zero. Am I clear? So until and unless stated otherwise the acceleration will remain zero in in Horizontal motion in vertical motion. Yes, there is an acceleration due to gravity say for example, I'll ask you a very very simple question that dear friends Say for example an object is tossed vertically up with 20 meter per second An object is tossed vertically up with 20 meter per second simple question simple question I'm a simple question that in what time it will reach the maximum height What will be the maximum height? Yeah Can you please answer me as quick as possible? In what time will it reach the maximum height and what is the maximum height? Yeah, time is two seconds times is two second and 40 is the maximum height by idiom Thomas Okay, but time is two second by whom can you please state your name so that For now time is two seconds is absolutely correct Eden are you sure about the line that the height covered is 40 meters? 20 sorry good Eden now I received it. Okay height is 20 meters See, there are direct ways like you square by 2g which can be applied Okay, if you don't want to remember every single bit of a result then you can go by the simple Relation right why because you know that okay, what has to be calculated is? What has to be calculated so you square by 2g is the formula suppose you don't want to Remember everything then yes, what will you do? You will think okay dear what is asked is H Which is analogous with s? Which can be calculated from these two equations okay, as You know time as of now you can put even over here and get the answer Yeah, if at all you don't know the time then directly This is your answer because you know that finally the velocity is going to be zero and it will be nothing but u square Plus two acceleration while going up is minus g and s is H And this is where this result came out very good easy done now my question to you is That okay, you know that the maximum height covered by this object is 20 meters cool Now my question is for the same part in what time Will it reach half the maximum height which is actually 10 meters? So my question is what time will it reach 10 meters? In what time will it reach 10 meters? Half second is wrong answer Please try again Vibhav one second is also wrong answer The reason is again think about it one second would have been the answer if the motion would have been a uniform motion Is it a uniform motion? You will say a loud in your soul that no as acceleration is a non-zero entity This can not be a uniform motion Clear or not? Sure, so this is not a uniform motion. That's why equal distance won't be covered in equal time Yes, something a route to K shop. Yes. Yes. Yes, it is somewhere around it But please re-correct your equation and then you may get a very good answer Chal then I guess instead of investing time. Let me only solve the thing Okay And chat again Two seconds is not the answer because because dear two seconds is the time which was taken by you to Which was taken by you to I don't know to go to the maximum height of 20 to see how will you do you have to calculate time again the same approach I'm telling you a very common approach. Keep it simple. No need to remember every bit of the formula Simple simple simple you say that sir I have to calculate time time can be calculated either by this equation or by this equation Okay, if I want to calculate by this equation, then I need near the initial velocity, which I know Okay, I need to know acceleration which I know, but I don't know the final velocity someone has Send t is equals to u by g who told you this here Hmm T is equals to u by g. Where is it written? Sir for vertical motion t is equals to u by g Literally mutt love for any see Irrespective of what distance is covered time is always u by g No, no this time what you are talking about is the time taken to cover the Maximum height time taken to reach the maximum Aniket Gupta ji Bull day are you come over here? This time with your writing is the time taken to reach the maximum maximum Maximum maximum maximum maximum maximum. I'm good talking about half the height of the head with us Thus thus thus Okay So Yeah, so now back to agenda what we are talking about is you buy I have to calculate time Okay, so this equation is not There why because I don't know the final velocity at 10 Okay, so so now I'm going to use this equation and yes here u is known to me a is known to me Which is g okay, and s is also known to me 10 meters. So I'll write that dear 10 Will be equal to 20 t plus half Minus 10 and t square just for simplification of calculation because my primary motive is to make you comfortable with the calculation part. I am using Acceleration due to gravity as 10. Okay. Now. Isn't it a quadratic equation in polynomial chapter? Haven't you done solving the quadratic equation? Yes, you will realize the same equation and will write that 0 is equal to So no 5 t square minus 20 t plus 10 Okay, you can take five common. You will write t square minus 40 Plus 2 is equal to 0 now you can solve this equation by several methods one of the Favorite method of mine is the method of Sri Dharacharya Sri Dharacharya as the name indicate Okay, an Indian mathematician told that you are if there is a quadratic equation of the form H square plus Vx plus C Then x will be equal to minus b plus minus under root b square minus 4 ac Upon so when you compare this equation with this format then you get t equal to minus b plus or minus under root b square minus 4 ac upon 8 right, so you'll get 2 plus root 2 or 2 minus root 2 now Why this question is important because this question gives you a very good point to discuss about very very good point to discuss about guys think What am I asking? I am asking you that okay dear when I toss this object up it went to a height of 20 meters and is Okay, sure fine In between this what I am asking is what is the time to reach 10 meters and you said several chats Why share others or don't do us like that. Okay, sure. Don't don't See the racharya is easy if you want you can also factorize it. I don't have any problem Mr. Gupta, it is peaceful for you. Good. See the racharya is lit for quadratic equations She the racharya is the ultimate solution. Okay, so t square minus 4 t plus 2 Okay post she the racharya application gave you two results T equal to 2 plus root 2 and t is equal to 2 minus root 2 and I am explaining you both the results because both are real number Say one example one time would have been negative then we would have easily ignored it, right? Yes or no, we would have easily ignored it saying time cannot be negative But here both are positive 2 plus root 2 and 2 minus root 2 So, how are we going to justify this because both are possible answers So see When the movement started, okay? Zero it reached to a height of 20 and again coming back Here the time taken is two seconds. Yes or no to reach here fine and this is 10 over here and this is 10 over here as well. So understand there to reach over here it took up time of 2 minus root 2 and Starting from here to reach over here. It took a time of 2 plus root 2 easy Short from there. You can also say that. Okay, sir The time taken to reach or cover this distance either while going up or While coming down the same Yes or no, and this is where my next explanation is leading to Got it or not. Yes or no So fine So if you have then I am erasing the screen. Okay sure for Your support what I'm doing is I'm keeping it safe for me so that I can share it as the revision notes Okay. Now back to agenda my question is It's clear to you. Okay. As of now the maximum height reached by that object Was in two second the maximum height is 20 meters The time taken to recover the distance of 10 meters is to 2 minus root 2 while going up and 2 plus root 2 while going this way. Yes or no This is clear. Okay sorted fine. Now the question is Same thing same same thing Okay From a platform from the same aim height. Suppose the object is coming down from here Yes or no, this is again the same height of 20 meters the same object. Okay. Now it's coming down only It's coming down only is coming down only my question number one is what is the displacement covered in the first second? What is the displacement covered in the first second? Simple three more question. I'll switch the topic What is the displacement covered in the first second order 23 chats? Nothing much important instead of Tushar sir's Instruction thank you Tushar And someone answer five meter which is good direct application of the equation s is equals to U T plus half a T square yes or no Short T is one so answer is five meter in the same way if I last what is the total displacement covered in two seconds? Not in second a second my question is in two seconds. So your answer will be certainly same zero plus half a T square Yes or no 20 Which leads to a conclusion that okay dear What is the distance covered in the second second and now you can directly answer sir 15 So can you please very quickly answer me two things What is the displacement covered directly in the third second? Kabir 25 Aniket Gupta 25 very good good 25 Kabir good Keshav 25 good Surya 25 good and yes 25 is the answer. Okay sure And can you please tell me that ratio of these three terms tucked tucked and room One is to three is to five. Can you expect the next one? Can you explain the other ones isn't it easy? Isn't it easy? Easy right One is to three is to seven series of all numbers that mean in consecutive seconds if you want if you are interested you can note down the six in consecutive seconds in consecutive seconds the displacement covered The displacement covered has a ratio of one is to three is to five is to seven and so on So if I'll simply ask you for closing this topic for closing this topic if I'll simply ask you that If an object is dropped from a very significantly high point If an object is dropped from a significantly high point Yeah, so so so so what is the displacement covered in the 11th second For the one who will answer first chocolate And run and you're making many silly mistakes Prana M You're correct Prana M Prana M. I received my first answer Prana M and Prana is going to get the chocolate It will reach to you Prana. Don't worry good those So how he did it many people are responding now great great great good How he did it? He said in this series the 11th odd number Will be 22 so The 21 21. Okay. He multiplied five to it and he got five zero five Okay easy Sure Good for everyone this is the explanation for those who understand fine, so this is a Good information about the vertical motion Okay, now we are moving to work We are skipping projectile as of now Not in this class, but in a company. I'll take up next section We'll only only only talk about projectile motions. Okay, sure this session. I am Moving a bit further and now we are going to talk for next five to ten minutes about average velocity on Not on vertical ground on horizontal. Okay, so Chalo fine now the question is Let's go into the vertical of average velocity average below Okay, so don't visit I can hear Now Velocity Average by its very definition is what? The total displacement covered Upon the total time taken yes or no When it talk about speed the displacement just gets displayed By distance yes or no clear When we were in class We have done some special types of these primarily to Average velocity in case of equal distance covered Average velocity in case of equal durations Okay Say for example To to to Parts of a journey both of equal distance Okay, someone Okay Thank you. Thank you. Thank you. Both of equal Length are covered by speed v1 and v2 or velocity v1 and 2 as we are as of now going only in one dimension Speed and velocity are safe. Okay, so the average velocity will be given by 2 v1 v2 upon v1 plus easy so okay, and Then if there is equal duration that mean what please if you are Undercut like in control of erasing it. Can you please? A journey of total trs is covered in t by 2 rs and t by 2 rs with the speed of velocity v1 and v2 Then the average speed of velocity is directly the average So for my dear friends because we always tell you things of elevation Suppose it becomes 3 so your answer will be 3 v1 v2 v3 upon lcm v1 v2 Plus v2 v3 plus v3 v1 Yes or no, suppose this goes 3 so v1 plus v2 plus v3 by m i clear Sir, I do not understand Aditya Gupta ji very good, uh, which part Which part did you did not understand? Can you please ping me again? Yeah multiplication of five Kabir yes multiplication of five Anike Gupta is stating a formula beautiful Okay, the ratio yes, okay. I'll re help you out For the first one bit of which the fool my dear friend Okay, you are owing my name so For the first one which which one can you please be a bit see you have to just type so it's easy if you Okay, sir, could you explain how you got v1 plus v2 by 2 again? Okay If you want I can derive it you you want the derivation of it. It will take a bit time, but I'll do that. Don't worry Both if you need this and this Okay, as of now you have only asked this so I'll do this only So suppose a journey Total span is t so denominator is t Speed 1 and speed 2 so you don't know as of now. What is the total distance? So you'll say speed is equals to distance upon time. So distance is equals to Speed into time But is this time t t only no the time is half of t and half of t 2 equals spans So you'll say okay total distance is v1 t by 2 plus v2 t by 2 t by 2 common t say t would you mind? Answer is v1 plus v2 by 2 easy. That's similar will be for 3 and all right Chat kind Okay, now for the d by 2 case. Okay. No problem I hope as of now this case is clear v1 plus v2 by 2 now. I'm talking about the d by 2 other case, okay So think Equal displacement or distance. Okay d by 2 d by 2 v1 v2. So see you don't know the total time, but you know the total distance d Total time so speed is equals to distance upon time. So time is equals to distance upon speed Similarly, next time is equals to distance Once we put it over here d by 2 v1 plus d by 2 v2 Take the lcm and it will go up and 2 2 common and get cancelled and dd common and get cancelled and you will get 2 v1 v2 v1 plus v2 Yes or no Okay, one is to three is to five. Yes nafel. You did not understood one is to three is to five. Don't worry. I'll redo it Aniket Don't distract me I can anytime go to youtube This was for aniket m Okay, so back to agenda Guys, if you want to understand the ratio other thing, I'm just giving you a quick view Calculate displacement in first second. You will say five Calculate displacement in second second. So you will say total displacement in two seconds minus total displacement in one second Answer will be 15 Total third if I last total displacement in three second minus total displacement in two seconds answer will be 25 when you take the Ratio five ones five threes and five fives. This is how it comes Okay, don't don't don't Test the patience here. If you are doing it knowingly, don't test the patient, please Okay, sure. Let it be in a happy mood Sure, let's not the dinner be more salty Okay, please If you're doing it knowingly, don't do that again. Okay I'll try because I have to again distract myself Reach over here and do it whereas an Annotation it is a Thank you. Thank you. Thank you. So this is about the average velocity value game Okay, a simple question quick answer simple question and Quick answer, okay a journey of 100 kilometers a journey of 100 kilometers Was covered in three parts Okay, so Fine 50 25 25 For this part the speed was 40 For this part the speed was 60 And again this part the speed is 40 Kilometer per hour by default here as well clear May I please know the average velocity The first one to answer will get a chocolate Where is chat? Yeah, I have to read bachaloks answer Okay, sir aditi k try Answer answer answer the first one to answer will get a chocolate 5 by 7 kilometer per hour. It's not possible the air 48 no keisha 46.6 13 kilometer per hour 2.29 You can also answer in fractions. Don't worry 140 by 3 sounds something 39.4 no no no no no sir it's 46.6 140 by 3 or 46.6 bar, which was actually answered Keshav, I guess answered the first About 43.6. No dear check the calculation Pranav Before Keshav kushag Kushagra answered it first kushagra See guys no unfair thing. I'm just Keshav All right 5 by 7 Keshav no, so Keshav answered it first Keshav buddy. You'll get it. Don't worry Okay, too many indranagar aspirants. Maybe directly or indirectly Okay So now Got it. This was about average velocity. I said I'll talk about it for maximum 10 minutes. We had a conversation of 15 minutes Okay, chalo fine back to agenda Yeah Fine anyone Okay with Linear motion as of now we have not discussed about yet relative motion and projectile motion. Okay So Chalo now we are going into laws of motion. Okay, and this is going to be interesting now Because this is my favorite chapter might be yours too So when you talk about laws of motion Again a great contribution by uncle newton to the world I'm not I'm not I'm not discussing projectile aditi promise. I'm not discussing projectile law. Okay Laws of Newton can be said uncle but it is actually He's being Modest said that it'd be laws of motion given by uncle newton. So What happens is Three laws first law also called law of inertia Tells you that until unless you are pinned by your parents or us you won't study clear second law law of Conservation of momentum can be said but actually law which defines motion the rate of change of linear Momentum and force are directly proportional to each other This law only will in future become f is equals to ma for rigid bodies And a bigger expression when you will be in 11th grade Okay, you will read about a bigger expression for bodies, which will be changing their mass post application of force as of now you will be dealing with only rigid bodies and that's the reason that Yeah, how will mass change better rocket? See in general what happens is if I'll push you your mass would change Else all the gyms will be closed people in order to reduce mass will only be referring the cars They're the car right, but no that's not the case. What is the case that? Rigid bodies as we are Don't change their mass in general post application of force But there are bodies which may change their mass post application of force or by some Thing from themselves or externally applied like a rocket. You know a rocket propels is by Newton's third law every action will have an equivalent opposite reaction But as the fuel burns out, don't you think that its mass is reducing? Yes or no? So Yeah so so so so There are bodies which do change their mass post application of force We are as of now not at all talking about them. We are as of now Not at All talking about it. Okay. Now back to agenda second law and the third law states every action will have an equal and Opposite reaction First acted by two on one will be having equal application Of force from one onto but in opposite direction clear or not When we have a discussion of these three laws Yes, what we discuss about are their applications Yes or no So Examples and all when we talk about the numericals associated with them So I ask a general question what it is That suppose on a floor There are two blocks. This is of 3 kg This is of 1 kg I am applying a force of 20 Newton. I am applying a force of 20 Newton here to pull this up Simple question simple and very simple question What is the tension in the string? Not in this direction I mean I literally mean Within this domain. What is the tension in this spring? 10 10 60 Something but it disproves the law of gravity what? Newton's third law second law what? 60 Newton. How will it be? 60 Newton is not possible Pradavaranar 60 Newton. How is it possible? Reason being I am applying 20 Newton. How can tension be more than the applied force? Aniket Gupta 20 yes 10 and all let's see So guys simple thing That when this is applied the total acceleration possessed by the body is equal to total force applied by total mass which is equal to 5 Yes, that means force utilized by this block I am writing in orange Or I am writing in Another color here. Give me a good color 5 into 1 yes or no mass into acceleration So remaining force goes here 15 Newton The force experienced by this block is only by tension That's why tension is equal to 15 Newton How we achieve this is mathematically Okay termed as free body Diagram I hope all of you are thoroughly aware about this term Can't chat What is tension? Okay, sir even in buoyancy newton's third law of motion comes into play as a solid applies pressure on Yes, correct. What is tension Aditya Gupta? Very good question Anyone else sir? What is tension again Aditya Gupta? Sorry dear. I missed your initial request So first thing what is tension? So Aditya tension is the name of force given to A restoring force actually say for example, I'll simply ask you a question very very simple question. Say for example, this is ceiling From the ceiling if there is a mass hanging down. Yes or no? Clear, then I'll ask you. What is the force acting on this mass? So you will say you guys sir the force acting on this mass is mg Now my dear friend as is a string. This is a mass this force is mg By this intuition tow by This intuition this object should go down by newton's uncle's first law Because the total force acting is unbalanced and is in one direction Yes or no But you see the ball object doesn't go down Hence As the object is not going down Then there is Surely something existing which is canceling this mg down In order to cancel please remove the purple thing in order to cancel in order to cancel In order to cancel in order to cancel this The thing which we are assuming should exist vertically upward opposite to this And exactly in this string you know that there exist a stretch In the opposite direction right or not when you pull a string Toward you it tends to stretch back Within itself right restore its shape that restoring force in a non stretchable string is tension Here or not Have I done my part? Sorry, I did the G. Sorry, but I hope Yes or no One force opposing the other Great balancing it Okay, right. So back to agenda tension So how did we achieve this? Is by the help of is by the help of is by the help of is by the help of is by the help of Body diagram free body diagram Okay Please see all these things because this is something which can't happen By mistake, okay So this is drawn. So don't please please please don't check patients, you know now Back to agenda free body diagram free body diagram is drawn the definition Uh tension Okay, so tension is the force developed in a body in general string on application of a force This force primarily should be stretching force So when we try to stretch a string It tends to restore its shape and this restoring force Is tension Okay, now back to agenda dear tension and free body diagram. So see When we look at a body on which force are being applied. So I am first drawing body number one like that is The block of one cage Okay, if you see it I am applying a force of 20 newtons here Okay, because of tension there is a force Clear and also this body is having an acceleration here in this direction Suppose this acceleration is a and the mass is m Then you will write an equation that mass into acceleration the total force Is a result of supportive force minus opposing force Yes or no supportive force minus opposing force This equation is called free body equation. This diagram is called free body diagram These diagrams help us out In to write it the force balancing equations the second law of motion equations Yeah, this is what we have written is a equation balancing all the force clear So we have covered in the classroom as we are many over here So that's why I have just given a revision over sir. Can I leave the class? I have to charge my phone only three percent. Thank you. Okay, Aditi ke shallow Even we are going to complete it in the next two or three minutes I'll get the g Again the free body diagram. I'll explain. No, don't worry. Yes, napple free day free body diagram What is it? Okay. I'm re explaining it dear So chakra you wanted to say something I didn't receive any of your texts and all If without the string there won't be any tension. No Tension exists in a stretching body They are tending to stretch body. Okay. I am explaining one more time the free body diagram See as of now I have kept this body individually over here And taking into considering all the forces acting on this body I should also draw this But as we are considering motion in this direction I have not drawn g you will say sir actually mg is also acting and from the surface There is a normal reaction also acting So in this case as the object is not moving like this Vertically so you can say okay n is equal to mg normal reaction from the surface Is equal to the acceleration like m into acceleration due to gravity Pranam raise hand. What happened Pranam? Sir, how do you calculate the tension in the 3 kg and 1 kg? Question after finding both forces. That's what I'm telling you dear see Here as there are two bodies only and there are really less number of like only two forces By this okay equation only you can calculate You got this equation Yes or no the acceleration this is moving is the total force on it is m into a And this m into a is equal to supportive force minus opposing force here Now by the formula that acceleration is equal to total force upon total mass of the system You got acceleration is 5 and you are also aware about the line that mass is equals to 1 kg You put it over here 1 kg into 5 so 5 Newton Is equals to 20 minus tension so tension is equals to 15 Newton easy I just did it Hashtag loner k r m for life As of now we have not given any friction not yet Surely when I'll give friction then the things will also roll down Okay Yeah, when I'll give friction then the things will the of friction will An arrow will also participate over here from the friction line Not individually normal equal to zero or mg equal to zero the net influence from normal and mg equal to The total influence caused by normal and mg is zero because both are balancing each other. Okay, yes Can be can it be in the different direction? I didn't get you link from b t o w d r what In different direction the tension the force or what? tension Guys for this body as you are pulling this way the tension in the string will be this way That you always as I told you your tension is a restoring So as you are pulling this object this way the tension in the string will be this way clear So for a simple understanding tension Okay, we'll always oppose the body We'll always in the opposite direction of the body Like this this is the body then tension will go here Okay This is the body tension will go away from it clear Sure So hello now times up Surely I think that what I had planned we have not covered that much I hope you guys have enjoyed it learned something something out of it Surely another one-hour session. We'll have we'll proceed from here only Okay, also feel free to state your request Okay, like if you want to understand you sir as of now instead of going for a back-end chapter of chapter one chapter two and all yeah, feel free to Thank you, sir as of now in our school Gravitation or work power energy or sound is going on. So can we Yeah, can we Have a discussion of those topics and all clear Don't spam the screen again Okay, thank you very much. Thank you very much. Thank you very much. Good day. Thank you, sir Thank you, sir Thank you, sir Thank you, sir